// Numbas version: exam_results_page_options {"name": "Spectroscopy practice", "metadata": {"description": "A set of questions about spectroscopy used for formative assessment purposes. ", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Energy of Photon from Frequency, Wavenumber (Joules per photon)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}, {"name": "Hanno Kossen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2434/"}], "variable_groups": [], "tags": [], "parts": [{"showCorrectAnswer": true, "customName": "", "marks": 0, "type": "gapfill", "unitTests": [], "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "scripts": {}, "gaps": [{"type": "numberentry", "unitTests": [], "correctAnswerStyle": "plain", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "mustBeReducedPC": 0, "useCustomName": false, "minValue": "{Energy_mantissa2}-{Energy_mantissa2}/50", "mustBeReduced": false, "customName": "", "marks": 1, "customMarkingAlgorithm": "", "allowFractions": false, "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "{Energy_mantissa2}+{Energy_mantissa2}/50", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0}, {"type": "numberentry", "unitTests": [], "correctAnswerStyle": "plain", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "mustBeReducedPC": 0, "useCustomName": false, "minValue": "{Energy_log}+{Energy_log}/50", "mustBeReduced": false, "customName": "", "marks": 1, "customMarkingAlgorithm": "", "allowFractions": false, "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "{Energy_log}-{Energy_log}/50", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0}], "variableReplacements": [], "prompt": "

Calculate (to 3 significant figures) the energy, E, of a photon of light of {Solution} {Solution_units} in {definer} in units of Joules;

[[0]] $\\times$ 10^[[1]]

\n\n\n", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "useCustomName": false}], "variablesTest": {"maxRuns": "200", "condition": ""}, "variables": {"Frequency_randomiser_units": {"templateType": "anything", "name": "Frequency_randomiser_units", "group": "Ungrouped variables", "description": "", "definition": "if(Answer_2<1000,Answer_2_units,Answer_1_units)"}, "Frequency_mantissa": {"templateType": "anything", "name": "Frequency_mantissa", "group": "Ungrouped variables", "description": "", "definition": "siground(Frequency/(10^(Frequency_log)),5)"}, "Solution_units": {"templateType": "anything", "name": "Solution_units", "group": "Ungrouped variables", "description": "

\n\n\n", "definition": "if (Solution=Frequency_randomiser,Frequency_randomiser_units,wavenumber_units)"}, "Planck_mantissa": {"templateType": "anything", "name": "Planck_mantissa", "group": "Ungrouped variables", "description": "", "definition": "6.626"}, "Frequency": {"templateType": "anything", "name": "Frequency", "group": "Ungrouped variables", "description": "", "definition": "siground(random(Frequency_MW,Frequency_IR,Frequency_Visible),5)"}, "Frequency_log": {"templateType": "anything", "name": "Frequency_log", "group": "Ungrouped variables", "description": "", "definition": "floor(log(frequency))"}, "Solution": {"templateType": "anything", "name": "Solution", "group": "Ungrouped variables", "description": "", "definition": "random(Frequency_randomiser,wavenumber)"}, "Frequency_Visible": {"templateType": "anything", "name": "Frequency_Visible", "group": "Ungrouped variables", "description": "

\n", "definition": "(4.55*10^(14))+((random(1..1000))*2.95*10^(11))"}, "Frequency_list": {"templateType": "anything", "name": "Frequency_list", "group": "Ungrouped variables", "description": "", "definition": "[Frequency/1000000,Frequency/1000000000,Frequency/1000000000000]"}, "Energy_mantissa2": {"templateType": "anything", "name": "Energy_mantissa2", "group": "Ungrouped variables", "description": "", "definition": "siground(Energy_mantissa/(10^floor(log(Energy_mantissa))),3)"}, "definer": {"templateType": "anything", "name": "definer", "group": "Ungrouped variables", "description": "", "definition": "if (Solution=Frequency_randomiser,\"frequency\",\"wavenumber\")"}, "Frequency_IR": {"templateType": "anything", "name": "Frequency_IR", "group": "Ungrouped variables", "description": "", "definition": "(1.50*10^(12))+((random(1..1000))*2.99*10^(11))"}, "wavenumber": {"templateType": "anything", "name": "wavenumber", "group": "Ungrouped variables", "description": "", "definition": "siground((Frequency/30000000000),5)"}, "Frequency_randomiser": {"templateType": "anything", "name": "Frequency_randomiser", "group": "Ungrouped variables", "description": "", "definition": "if(Answer_2<1000,Answer_2,Answer_1)"}, "Answer_2": {"templateType": "anything", "name": "Answer_2", "group": "Ungrouped variables", "description": "", "definition": "(if (Frequency_list[1]<1,Frequency_list[0],Frequency_list[1]))"}, "Energy_mantissa": {"templateType": "anything", "name": "Energy_mantissa", "group": "Ungrouped variables", "description": "", "definition": "(Planck_mantissa*Frequency_mantissa)"}, "Answer_1_units": {"templateType": "anything", "name": "Answer_1_units", "group": "Ungrouped variables", "description": "", "definition": "(if (Frequency_list[2]<1,Frequency_units_list[1],Frequency_units_list[2]))"}, "Planck_log": {"templateType": "anything", "name": "Planck_log", "group": "Ungrouped variables", "description": "", "definition": "-34"}, "Answer_1": {"templateType": "anything", "name": "Answer_1", "group": "Ungrouped variables", "description": "", "definition": "(if (Frequency_list[2]<1,Frequency_list[1],Frequency_list[2]))"}, "Answer_2_units": {"templateType": "anything", "name": "Answer_2_units", "group": "Ungrouped variables", "description": "", "definition": "(if (Frequency_list[1]<1,Frequency_units_list[0],Frequency_units_list[1]))"}, "Frequency_MW": {"templateType": "anything", "name": "Frequency_MW", "group": "Ungrouped variables", "description": "", "definition": "(3*10^(8))+((random(1..1000))*3.0*10^(8))"}, "Energy_log": {"templateType": "anything", "name": "Energy_log", "group": "Ungrouped variables", "description": "", "definition": "siground(Planck_log+Frequency_log+(floor(log(Energy_mantissa))),3)"}, "wavenumber_units": {"templateType": "anything", "name": "wavenumber_units", "group": "Ungrouped variables", "description": "", "definition": "html(\"\"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\")"}, "Frequency_units_list": {"templateType": "anything", "name": "Frequency_units_list", "group": "Ungrouped variables", "description": "", "definition": "[\"MHz\",\"GHz\",\"THz\"]"}}, "statement": "

\n\n\n", "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Question requires students to interchange units of Hz with MHz, GHz, THz. Question is not very efficient at present- frequencies spanning many orders of magnitude are generated by variables in a clumsy way. Could be improved by having frequency generated by a 10^((random(1000..4000)/1000) variable instead, for example.

"}, "rulesets": {"": []}, "advice": "

If presented with a wavenumber, you will need to start by converting this into a frequency while noting that;

\\[c=\\lambda\\nu\\]

and therefore

\\[\\nu~{\\rm{in~s^{-1}}}=\\frac{c}{\\lambda}=c ~({\\rm in~cm~s^{-1}})~\\times~{\\rm wavenumber~(in~cm)}\\]

\\[2.998 \\times 10^{10}~{\\rm cm~s^{-1}}\\times~\\var{wavenumber}~{\\rm cm^{-1}}=\\var{Frequency_randomiser}~\\var{Frequency_randomiser_units}\\]

Now, we can use;

\\[E=h\\nu\\]

\\[ E~= {h\\nu}={\\var{Planck_mantissa} \\times 10^{\\var{Planck_log}}~{\\rm J~s}~\\times~\\var{Frequency_mantissa}~\\times~10^\\var{Frequency_log}~{\\rm s}^{-1}}=\\var{Energy_mantissa2}~\\times~10^{\\var{Energy_log}}~{\\rm J}\\]

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Given that the wavelength of light, $\\lambda$, is equal to {wavelength_mantissa} $\\times$ 10^{{wavelength_log}} m;

", "advice": "

a) If you are given a quantity in wavenumbers, convert this into a wavelength;

\\[[\\frac{1}{\\lambda}={\\rm wavenumber}]~{\\rm and~therefore}~[\\frac{1}{\\rm wavenumber}={\\lambda}]\\]

If you specify wavelength in cm, you will obtain the wavenumber in cm^-1 ;

\\[\\frac{1}{{\\var{wavelength_mantissa}~\\times~10^{\\var{wavelength_log_cm}}~\\rm cm}}=\\var{wavenumber}~\\rm cm^{-1}\\]

b) Calculate the energy of a single photon using;

\\[E=h\\nu=6.626~\\times~10^{-34}~{\\rm~J~s}~\\times~\\var{Frequency_mantissa}~\\times~10^{\\var{Frequency_log}}~{\\rm~s^{-1}}=\\var{Energy_mantissa}\\times~10^\\var{Energy_log}~{\\rm~J}\\]

c) Then, multiply by the Avogadro number, and divide by 1000 J kJ^-1 to convert this into an energy in kJ mol^-1;

\\[\\frac{\\var{Energy_mantissa}\\times~10^\\var{Energy_log}~{\\rm~J}~\\times~6.022~\\times~10^{23}~{\\rm~mol^{-1}}}{1000~\\rm J~kJ^{-1}}=\\var{Energy_molar}~{\\rm kJ~mol^{-1}}\\]

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randomi

", "templateType": "anything", "can_override": false}, "wavelength_log": {"name": "wavelength_log", "group": "Ungrouped variables", "definition": "floor(log(wavelength))", "description": "", "templateType": "anything", "can_override": false}, "frequency": {"name": "frequency", "group": "Ungrouped variables", "definition": "10^(8+(frequency_randomiser/1000))", "description": "", "templateType": "anything", "can_override": false}, "wavelength": {"name": "wavelength", "group": "Ungrouped variables", "definition": "siground((3*10^8)/frequency,3)", "description": "", "templateType": "anything", "can_override": false}, "quantity_label": {"name": "quantity_label", "group": "Ungrouped variables", "definition": "[\"wavenumber\",\"frequency\"][randomiser_units]", "description": "", "templateType": "anything", "can_override": false}, "wavelength_log_cm": {"name": "wavelength_log_cm", "group": "Ungrouped variables", "definition": "wavelength_log+2", "description": "", "templateType": "anything", "can_override": false}, "Energy": {"name": "Energy", "group": "Ungrouped variables", "definition": "siground((Energy_molar*1000)/(6.022*10^(10)),3)", "description": "", "templateType": "anything", "can_override": false}, "Energy_molar": {"name": "Energy_molar", "group": "Ungrouped variables", "definition": "siground(frequency*(((6.626*10^-34)*(6.022456*10^23))/1000),3)", "description": "", "templateType": "anything", "can_override": false}, "wavenumber": {"name": "wavenumber", "group": "Ungrouped variables", "definition": "siground((1/(wavelength*100)),4)", "description": "", "templateType": "anything", "can_override": false}, "frequency_mantissa": {"name": "frequency_mantissa", "group": "Ungrouped variables", "definition": "siground((frequency/(10^(frequency_log))),4)", "description": "", "templateType": "anything", "can_override": false}, "": {"name": "", "group": "Ungrouped variables", "definition": "", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["frequency_randomiser", "frequency", "frequency_mantissa", "frequency_log", "wavelength", "wavelength_mantissa", "wavelength_log", "wavenumber", "Energy_molar", "randomiser_units", "units_list", "units_output", "quantity_label", "Energy", "Energy_log", "Energy_mantissa", "wavelength_log_cm", ""], "variable_groups": [], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}, "molecule_name": {"parameters": [["atoms", "list"]], "type": "number", "language": "jme", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}, "isotope_name": {"parameters": [["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

what is the wavenumber in units of cm^-1?

", "minValue": "{wavenumber}-{wavenumber/50}", "maxValue": "{wavenumber}+{wavenumber/50}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The energy, E, of a single photon is;

[[0]] $\\times$ 10^[[1]] J

The energy, E, of one mole of photons is [[0]] kJ mol^-1.

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Given that the wavelength, $\\lambda$, of light is {wavelength_um} $\\mu$m;

", "advice": "

a) Note that;

\\[c=\\lambda\\nu\\]

so (after converting the wavelength so that it is expressed in m);

\\[\\frac{c}{\\lambda}=\\nu=\\frac{3.0~\\times~10^{8}~{\\rm~m~s^{-1}}}{\\var{wavelength_mantissa}~\\times~10^{\\var{wavelength_log}}~{\\rm~m}}=\\var{Frequency_mantissa}~\\times~10^{\\var{Frequency_log}}~{\\rm Hz}\\]

b) Calculate the energy of a single photon using;

\\[E=h\\nu=6.626~\\times~10^{-34}~{\\rm~J~s}~\\times~\\var{Frequency_mantissa}~\\times~10^{\\var{Frequency_log}}~{\\rm~s^{-1}}=\\var{Energy_mantissa}\\times~10^\\var{Energy_log}~{\\rm~J}\\]

c) Then, multiply by the Avogadro number, and divide by 1000 J kJ^-1 (ie the number of Joules in 1 kiloJoule) to convert this into an energy in kJ mol^-1;

\\[\\frac{\\var{Energy_mantissa}\\times~10^\\var{Energy_log}~{\\rm~J}~\\times~6.022~\\times~10^{23}~{\\rm~mol^{-1}}}{1000~\\rm J~kJ^{-1}}=\\var{Energy_molar}~{\\rm kJ~mol^{-1}}\\]

", "rulesets": {"": []}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"wavelength": {"name": "wavelength", "group": "Ungrouped variables", "definition": "(3*10^8)/frequency", "description": "", "templateType": "anything", "can_override": false}, "frequency_mantissa": {"name": "frequency_mantissa", "group": "Ungrouped variables", "definition": "siground((frequency/(10^(frequency_log))),4)", "description": "", "templateType": "anything", "can_override": false}, "units_list": {"name": "units_list", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"{wavenumber}\"+\" \"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+\"{frequency_mantissa}\"+\" \"+\"× \"+\"10\"+\"^{\"+\"{frequency_log}\"+\"}\"+\" \"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything", "can_override": false}, "frequency_randomiser": {"name": "frequency_randomiser", "group": "Ungrouped variables", "definition": "random(2000..8000)", "description": "", "templateType": "anything", "can_override": false}, "units_output": {"name": "units_output", "group": "Ungrouped variables", "definition": "units_list[randomiser_units]", "description": "", "templateType": "anything", "can_override": false}, "frequency": {"name": "frequency", "group": "Ungrouped variables", "definition": "10^((8+(frequency_randomiser/1000)))", "description": "", "templateType": "anything", "can_override": false}, "frequency_log": {"name": "frequency_log", "group": "Ungrouped variables", "definition": "floor(log(frequency))", "description": "", "templateType": "anything", "can_override": false}, "Energy_log": {"name": "Energy_log", "group": "Ungrouped variables", "definition": "floor(log(Energy))-10", "description": "", "templateType": "anything", "can_override": false}, "wavelength_log": {"name": "wavelength_log", "group": "Ungrouped variables", "definition": "floor(log(wavelength))", "description": "", "templateType": "anything", "can_override": false}, "wavelength_um": {"name": "wavelength_um", "group": "Ungrouped variables", "definition": "siground(wavelength*10^6,3)", "description": "", "templateType": "anything", "can_override": false}, "quantity_label": {"name": "quantity_label", "group": "Ungrouped variables", "definition": "[\"wavenumber\",\"frequency\"][randomiser_units]", "description": "", "templateType": "anything", "can_override": false}, "wavelength_mantissa": {"name": "wavelength_mantissa", "group": "Ungrouped variables", "definition": "siground((wavelength/(10^(wavelength_log))),4)", "description": "", "templateType": "anything", "can_override": false}, "Energy_mantissa": {"name": "Energy_mantissa", "group": "Ungrouped variables", "definition": "Energy/10^({Energy_log}+10)", "description": "", "templateType": "anything", "can_override": false}, "Energy": {"name": "Energy", "group": "Ungrouped variables", "definition": "siground((Energy_molar*1000)/(6.022*10^(13)),3)", "description": "", "templateType": "anything", "can_override": false}, "wavenumber": {"name": "wavenumber", "group": "Ungrouped variables", "definition": "siground((1/(wavelength*100)),4)", "description": "", "templateType": "anything", "can_override": false}, "randomiser_units": {"name": "randomiser_units", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "

randomi

", "templateType": "anything", "can_override": false}, "wavelength_log_nm": {"name": "wavelength_log_nm", "group": "Ungrouped variables", "definition": "wavelength_log+9", "description": "", "templateType": "anything", "can_override": false}, "Energy_molar": {"name": "Energy_molar", "group": "Ungrouped variables", "definition": "siground(frequency*(((6.626*10^-34)*(6.022456*10^23))/1000),3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["frequency_randomiser", "frequency", "frequency_mantissa", "frequency_log", "wavelength", "wavelength_mantissa", "wavelength_log", "wavenumber", "randomiser_units", "units_list", "units_output", "quantity_label", "Energy", "Energy_log", "Energy_mantissa", "wavelength_log_nm", "wavelength_um", "Energy_molar"], "variable_groups": [], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}, "isotope_name": {"parameters": [["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}, "molecule_name": {"parameters": [["atoms", "list"]], "type": "number", "language": "jme", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": false, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

the frequency, $\\nu$, is [[0]] $\\times$ 10^[[1]] Hz;

What is the energy, E, of a single photon?

[[0]] $\\times$ 10^[[1]] J

The energy, E, of one mole of photons is [[0]] kJ mol^-1.

Light has wavenumber of {wavenumber} {wavenumber_units}.

", "advice": "

You can convert wavenumber into wavelength after re-arranging;

\\[\\rm wavenumber=\\frac{1}{\\lambda}\\]

to give

\\[\\lambda=\\frac{1}{\\rm wavenumber}\\]

while noting that using a wavenumber in cm^-1 in the equation above will give a wavelength in units of cm. A wavelength which is known in cm must be divided by 100 to give a wavelength in units of metres.

\\[\\frac{1}{\\var{wavenumber}}=\\var{wavelength_mantissa}~\\times~10^\\var{wavelength_cm_log}~{\\rm cm}\\]

\\[\\frac{\\var{wavelength_mantissa}~\\times~10^\\var{wavelength_cm_log}{\\rm cm}}{100}=~\\var{wavelength_mantissa}~\\times~10^\\var{wavelength_log}~{\\rm m}\\]

You can convert wavenumber into frequency noting that;

\\[c=\\lambda\\nu\\]

and therefore

\\[\\nu~{\\rm{in~s^{-1}}}=\\frac{c}{\\lambda}=c ~({\\rm in~cm~s^{-1}})~\\times~{\\rm wavenumber~(in~cm)}\\]

\\[2.998 \\times 10^{10}~{\\rm cm~s^{-1}}\\times~\\var{wavenumber}~{\\rm cm^{-1}}=\\var{Frequency_randomiser}~\\var{Frequency_randomiser_units}\\]

Now, we could use;

\\[E=h\\nu\\]

...to obtain a result in units of Joules per photon (J photon^-1) where the energy (E) will be expressed in Joules (J) per photon provided that $\\nu$ is expressed in Hz and h is in J s. Note that s^-1 and Hz are equivalent units. But to obtain an energy in kJ mol^-1, we additionally need to multiply by Avogadro's number (the number of photons in one mole of photons) and then divide by 1000 (to convert Joules into kJ). So, we can use;

\\[ E~({\\rm kJ~mol^{-1}}) = \\frac{h\\nu~\\times~N_{A}}{1000}=\\frac{6.626 \\times 10^{-34}~{\\rm J~s}~\\times~\\var{Frequency_mantissa}~\\times~10^\\var{Frequency_log}~{\\rm Hz}~\\times~6.022~\\times~10^{23}~{\\rm molecules~mol^{-1}}}{1000~{\\rm J~kJ^{-1}}}=\\var{Energy}~{\\rm kJ~mol^{-1}}\\]

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"Solution", "group": "Ungrouped variables", "definition": "random(Frequency_randomiser,wavenumber)", "description": "", "templateType": "anything", "can_override": false}, "Frequency": {"name": "Frequency", "group": "Ungrouped variables", "definition": "siground(random(Frequency_MW,Frequency_IR,Frequency_Visible),5)", "description": "", "templateType": "anything", "can_override": false}, "Frequency_list": {"name": "Frequency_list", "group": "Ungrouped variables", "definition": "[Frequency/1000000,Frequency/1000000000,Frequency/1000000000000]", "description": "", "templateType": "anything", "can_override": false}, "Answer_1": {"name": "Answer_1", "group": "Ungrouped variables", "definition": "(if (Frequency_list[2]<1,Frequency_list[1],Frequency_list[2]))", "description": "", "templateType": "anything", "can_override": false}, "definer": {"name": "definer", "group": "Ungrouped variables", "definition": "if (Solution=Frequency_randomiser,\"frequency\",\"wavenumber\")", "description": "", "templateType": "anything", "can_override": false}, "Frequency_mantissa": {"name": "Frequency_mantissa", "group": "Ungrouped variables", "definition": "Frequency/(10^(Frequency_log))", "description": "", "templateType": "anything", "can_override": false}, "Planck": {"name": "Planck", "group": "Ungrouped variables", "definition": "((6.626*10^-34)*(6.022456*10^23))/1000", "description": "", "templateType": "anything", "can_override": false}, "Frequency_randomiser": {"name": "Frequency_randomiser", "group": "Ungrouped variables", "definition": "if(Answer_2<1000,Answer_2,Answer_1)", "description": "", "templateType": "anything", "can_override": false}, "Energy": {"name": "Energy", "group": "Ungrouped variables", "definition": "siground(Planck*Frequency,3)", "description": "", "templateType": "anything", "can_override": false}, "Frequency_log": {"name": "Frequency_log", "group": "Ungrouped variables", "definition": "floor(log(frequency))", "description": "", "templateType": "anything", "can_override": false}, "Answer_2": {"name": "Answer_2", "group": "Ungrouped variables", "definition": "(if (Frequency_list[1]<1,Frequency_list[0],Frequency_list[1]))", "description": "", "templateType": "anything", "can_override": false}, "wavenumber_units": {"name": "wavenumber_units", "group": "Ungrouped variables", "definition": "html(\"\"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\")", "description": "", "templateType": "anything", "can_override": false}, "Frequency_randomiser_units": {"name": "Frequency_randomiser_units", "group": "Ungrouped variables", "definition": "if(Answer_2<1000,Answer_2_units,Answer_1_units)", "description": "", "templateType": "anything", "can_override": false}, "wavenumber": {"name": "wavenumber", "group": "Ungrouped variables", "definition": "siground((Frequency/30000000000),5)", "description": "", "templateType": "anything", "can_override": false}, "Answer_2_units": {"name": "Answer_2_units", "group": "Ungrouped variables", "definition": "(if (Frequency_list[1]<1,Frequency_units_list[0],Frequency_units_list[1]))", "description": "", "templateType": "anything", "can_override": false}, "Frequency_Visible": {"name": "Frequency_Visible", "group": "Ungrouped variables", "definition": "(4.55*10^(14))+((random(1..1000))*2.95*10^(11))", "description": "", "templateType": "anything", "can_override": false}, "Answer_1_units": {"name": "Answer_1_units", "group": "Ungrouped variables", "definition": "(if (Frequency_list[2]<1,Frequency_units_list[1],Frequency_units_list[2]))", "description": "", "templateType": "anything", "can_override": false}, "wavelength": {"name": "wavelength", "group": "Ungrouped variables", "definition": "siground((300000000/Frequency),3)\n", "description": "", "templateType": "anything", "can_override": false}, "wavelength_mantissa": {"name": "wavelength_mantissa", "group": "Ungrouped variables", "definition": "Wavelength/(10^(Wavelength_log))", "description": "", "templateType": "anything", "can_override": false}, "wavelength_log": {"name": "wavelength_log", "group": "Ungrouped variables", "definition": "floor(log(wavelength))", "description": "", "templateType": "anything", "can_override": false}, "wavelength_cm_log": {"name": "wavelength_cm_log", "group": "Ungrouped variables", "definition": "floor(log((wavelength*100)))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["Frequency_Visible", "Frequency_IR", "Frequency_MW", "Frequency", "Energy", "Planck", "Frequency_list", "Frequency_units_list", "Answer_1", "Answer_1_units", "Answer_2", "Answer_2_units", "Frequency_randomiser", "Frequency_randomiser_units", "wavenumber_units", "wavenumber", "Solution", "Solution_units", "definer", "Frequency_log", "Frequency_mantissa", "wavelength", "wavelength_mantissa", "wavelength_log", "wavelength_cm_log"], "variable_groups": [], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}, "isotope_name": {"parameters": [["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}, "molecule_name": {"parameters": [["atoms", "list"]], "type": "number", "language": "jme", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the wavelength, $\\lambda$, in units of metres.

[[0]] $\\times$ 10^[[1]]

Calculate the frequency, $\\nu$, in units of Hz;

[[0]] $\\times$ 10^[[1]]

Calculate the energy, E, in units of kJ mol^-1:

", "minValue": "{Energy}-{Energy}/50", "maxValue": "{Energy}+{Energy}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Energy per Mole of Photons from Frequency, Wavenumber (mixed units)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}], "tags": [], "metadata": {"description": "Question requires students to interchange units of Hz with MHz, GHz, THz. Question is not very efficient at present- frequencies spanning many orders of magnitude are generated by variables in a clumsy way. Could be improved by having frequency generated by a 10^((random(1000..4000)/1000) variable instead, for example.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "

If you are given a quantity in wavenumbers, convert this to units of frequency (Hz which are equivalent to s^-1)

\\[\\rm wavenumber~(in~cm^{-1})~\\times~3.0~\\times~10^{10}~cm~s^{-1}~=~Frequency~(Hz)\\]

\\[\\var{wavenumber}~{\\rm~cm^{-1}}~\\times~3.0~\\times~10^{10}{\\rm~cm~s^{-1}}=\\var{Freq_mantissa}~\\times~10^{\\var{Freq_log}}~{\\rm Hz}\\]

Now, remember that;

\\[E=h\\nu\\]

so;

\\[E=h\\nu=6.602~\\times~10^{-34}~\\times~\\var{Freq_mantissa}~\\times~10^{\\var{Freq_log}}=~\\var{Energy_molec_mantissa}~\\times~10^{\\var{Energy_molec_log}}~{\\rm J}\\]

Multiply by the Avogadro number to convert to J mol^-1, then divide by 1000 to convert to kJ mol^-1;

\\[\\frac{6.022~\\times~10^{23}~{\\rm~mol^{-1}}~\\times\\var{Energy_molec_mantissa}~\\times~10^{\\var{Energy_molec_log}}}{1000~{\\rm~J~kJ^{-1}}}=\\var{Energy}~{\\rm~kJ~mol^{-1}}\\]

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[["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the energy, E, of light of {Solution} {Solution_units} in {definer} in units of kJ mol^-1:

", "minValue": "{Energy}-{Energy}/50", "maxValue": "{Energy}+{Energy}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Beer Lambert Law for Abs [Random]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}, {"name": "Hanno Kossen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2434/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

$A={\\rm log(\\frac{{\\it {I}}_0}{{\\it {I}}_t})}=\\varepsilon ~c~l$

The molar absorption coefficient, $\\epsilon$ of a solute at 540 nm is {epsilon} mol^-1 dm³ cm^-1 . When light of that wavelength passes through a {l} mm cell containing a solution of the solute, the transmitted light intensity, I_t, is {it} % of I₀.

\n\n\n", "advice": "

\\[A={\\rm log(\\frac{{\\it{I}}_0}{{\\it {I}}_t})}=\\varepsilon ~c~l\\]

Where

\\[I_t=\\var{it}\\% \\]

\\[~\\]

Substitute into \\[A={\\rm log(\\frac{{\\it I}_o}{{\\it I}_t})}=\\varepsilon~c~l\\]

\\[I_{\\rm 0} ~\\rm is~ \\therefore ~100~\\% ~relative ~to~ the~ observed ~ray\\]

\\[A={\\rm log(\\frac{\\var{io}}{\\var{it}})}=\\var{a}\\ \\]

", "rulesets": {}, "variables": {"io": {"name": "io", "group": "Ungrouped variables", "definition": "100", "description": "

\n\n\n", "templateType": "anything"}, "it": {"name": "it", "group": "Ungrouped variables", "definition": "decimal((random(300..650))/10)", "description": "

\n\n\n", "templateType": "anything"}, "l_cm": {"name": "l_cm", "group": "Ungrouped variables", "definition": "l/10", "description": "

\n\n\n", "templateType": "anything"}, "conc": {"name": "conc", "group": "Ungrouped variables", "definition": "siground(a/((l/10)*epsilon),3)", "description": "

\n\n\n", "templateType": "anything"}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "decimal(random(45..85)/10)", "description": "

\n\n\n", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "siground(log(io/it),3)", "description": "

\n\n

\n\n\n\n", "templateType": "anything"}, "epsilon": {"name": "epsilon", "group": "Ungrouped variables", "definition": "random(200..340)", "description": "

\n\n\n\n\n\n\n\n\n", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["it", "io", "A", "conc", "epsilon", "l", "l_cm"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the absorbance, A, of the solution?

\n", "minValue": "{A}-{A}/50", "maxValue": "{A}+{A}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Beer Lambert Law for epsilon [Random]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}, {"name": "Hanno Kossen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2434/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}], "tags": ["2012", "b4", "B4", "FEEDBACK", "feedback", "L3", "l3", "Latex", "LATEX", "LaTeX", "lATEX", "latex", "random", "Random", "RANDOM"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

$A={\\rm log(\\frac{{\\it {I}}_0}{{\\it {I}}_t})}=\\varepsilon ~c~l$

When light passes through a {l} mm cell containing a concentration, c, of solute of {conc_coeff} $\\times$ 10^{conc_log} mol dm^-3, the transmitted light intensity, I_t, is {it} % of I₀. Calculate the molar absorption coefficient, $\\epsilon$, of the solute at the wavelength at which the experiment is performed in units of mol^-1 dm³ cm^-1.

\n\n\n", "advice": "

\\[A={\\rm log(\\frac{{\\it{I}}_0}{{\\it {I}}_t})}=\\varepsilon ~c~l\\]

Where

\\[I_t=\\var{it}\\% \\]

\\[~\\]

Substitute into \\[A={\\rm log(\\frac{{\\it I}_o}{{\\it I}_t})}=\\varepsilon~c~l\\]

\\[I_{\\rm 0} ~\\rm is~ \\therefore ~100~\\% ~relative ~to~ the~ observed ~ray\\]

\\[A={\\rm log(\\frac{\\var{io}}{\\var{it}})}=\\var{a}\\ \\]

Remember to convert the value of pathlength from mm to cm

\\[\\var{l}~\\rm mm=\\var{l_cm}~cm\\]

Rearrange for $\\epsilon$

\\[\\epsilon=\\frac{A}{c~ \\times~ l}=\\frac{\\var{A}}{\\var{conc}~\\rm mol~ dm^{-3}~\\times \\var{l_cm}~cm}=\\var{epsilon}~\\rm mol^{-1} ~dm^{3}~cm^{-1}\\]

", "rulesets": {}, "variables": {"conc_log": {"name": "conc_log", "group": "Ungrouped variables", "definition": "floor(log(conc))\n", "description": "

conc

", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "siground(log(io/it),3)", "description": "", "templateType": "anything"}, "epsilon": {"name": "epsilon", "group": "Ungrouped variables", "definition": "random(200..340)", "description": "", "templateType": "anything"}, "io": {"name": "io", "group": "Ungrouped variables", "definition": "100", "description": "", "templateType": "anything"}, "conc": {"name": "conc", "group": "Ungrouped variables", "definition": "siground(a/((l/10)*epsilon),3)", "description": "", "templateType": "anything"}, "conc_coeff": {"name": "conc_coeff", "group": "Ungrouped variables", "definition": "conc/(10^(conc_log))", "description": "", "templateType": "anything"}, "it": {"name": "it", "group": "Ungrouped variables", "definition": "decimal(random(300..650)/10)", "description": "", "templateType": "anything"}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "decimal(random(45..85)/10)", "description": "", "templateType": "anything"}, "l_cm": {"name": "l_cm", "group": "Ungrouped variables", "definition": "l/10", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["it", "io", "A", "conc", "epsilon", "l", "l_cm", "conc_log", "conc_coeff"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the value of epsilon, $\\epsilon$, in units of mol^-1 dm³ cm^-1?

\n\n\n", "minValue": "{epsilon}-{epsilon}/50", "maxValue": "{epsilon}+{epsilon}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Beer Lambert Law for conc [Random]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

$A={\\rm log(\\frac{{\\it {I}}_0}{{\\it {I}}_t})}=\\varepsilon ~c~l$

The molar absorption coefficient, $\\epsilon$, of a solute at 540 nm is {epsilon} mol^-1 dm³ cm^-1 . When light of that wavelength passes through a {l} mm cell containing a solution of the solute, the transmitted light intensity, I_t, is {it} % of I₀.

", "advice": "

\\[A={\\rm log(\\frac{{\\it{I}}_0}{{\\it {I}}_t})}=\\varepsilon ~c~l\\]

Where

\\[I_t=\\var{it}\\% \\]

\\[~\\]

Substitute into \\[A={\\rm log(\\frac{{\\it I}_o}{{\\it I}_t})}=\\varepsilon~c~l\\]

\\[I_{\\rm 0} ~\\rm is~ \\therefore ~100~\\% ~relative ~to~ the~ observed ~ray\\]

\\[A={\\rm log(\\frac{\\var{io}}{\\var{it}})}=\\var{a}\\ \\]

Remember to convert the value of pathlength from mm to cm

\\[\\var{l}~\\rm mm=\\var{l_cm}~cm\\]

Rearrange for $c$

\\[c=\\frac{A}{\\epsilon \\times l}=\\frac{\\var{A}}{\\var{epsilon}~\\rm mol^{-1}~ dm^3 ~cm^{-1} \\times \\var{l_cm}~cm}=\\var{conc}~\\rm mol ~dm^{-3}\\]

", "rulesets": {}, "variables": {"it": {"name": "it", "group": "Ungrouped variables", "definition": "decimal(random(300..650)/10)", "description": "", "templateType": "anything"}, "l_cm": {"name": "l_cm", "group": "Ungrouped variables", "definition": "l/10", "description": "", "templateType": "anything"}, "conc": {"name": "conc", "group": "Ungrouped variables", "definition": "siground(a/((l/10)*epsilon),3)", "description": "", "templateType": "anything"}, "io": {"name": "io", "group": "Ungrouped variables", "definition": "100", "description": "", "templateType": "anything"}, "epsilon": {"name": "epsilon", "group": "Ungrouped variables", "definition": "random(200..340)", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "siground(log(io/it),3)", "description": "", "templateType": "anything"}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "decimal(random(45..85)/10)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["it", "io", "A", "conc", "epsilon", "l", "l_cm"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the concentration, c, in units of mol dm^-3?

", "minValue": "{conc}-{conc}/50", "maxValue": "{conc}+{conc}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Energy- PIAB", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}, {"name": "Hanno Kossen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2434/"}], "tags": [], "metadata": {"description": "Question requires students to themselves calculate how many electrons are in the conjugated system for the molecules included in this question. As is standard for applications of the \"particle in a box\" model, the embedded assumption is that one electron is donated to the pi-system by each carbon within the conjugated chain. Students instructed to assume that there are 22 conjugated electrons in Beta-carotene. ", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

\n\n\n", "advice": "

a) Each carbon atom contributes one electron to the conjugated system. Electrons are paired within molecular orbitals. Therefore, after adding the {ne} electrons of {Molecule} to molecular orbitals (filling the lowest energy orbitals first), we discover that the HOMO is {n}.

We need to remember that 1 $\\unicode{x212B}$ in length is equal to 1 $\\times$ 10^-10 m.

Next, we can note that;

\\[E(n)=\\frac{n^2h^2}{8m_e^2L^2}=\\frac{\\var{n}^2\\times (\\var{h_mantissa}\\times~10^{\\var{h_log}}{\\rm~J~s})^2}{8~\\times\\var{me_mantissa}~\\times~10^{\\var{me_log}}~{\\rm kg}~\\times~(\\var{Length}~\\times~10^{-10})^2~{\\rm m^2}}\\]

It's a good idea to rearrange this to collect powers of ten;

\\[\\frac{\\var{n}^2~\\times~(\\var{h_mantissa}\\times~10^{\\var{h_log}}{\\rm~J~s})^2}{8~\\times~\\var{me_mantissa}\\times~10^{\\var{me_log}}~{\\rm kg}~\\times~(\\var{Length}\\times ~10^{-10})^2~{\\rm m^2}}\\]

\\[=\\frac{\\var{n}^2\\times\\var{h_mantissa}^2}{8\\times\\var{me_mantissa}\\times\\var{Length}^2}\\times\\frac{(10^{\\var{h_log}})^2}{10^{\\var{me_log}}\\times(10^{-10})^2}~{\\rm~~~ J}\\]

\\[=\\var{E_homo_mantissa}\\times10^\\var{E_homo_log}~{\\rm~J}\\]

b) Electrons are paired within molecular orbitals. After adding the {ne} electrons of {Molecule} to molecular orbitals (filling the lowest energy orbitals first), we discover that the LUMO is {LUMO}.

We need to remember that 1 $\\unicode{x212B}$ in length is equal to 1 $\\times$ 10^-10 m.

Next, we can note that;

\\[E(n)=\\frac{(n+1)^2h^2}{8m_e^2L^2}=\\frac{\\var{LUMO}^2~\\times~(\\var{h_mantissa}~\\times~10^{\\var{h_log}}{\\rm~J~s})^2}{8~\\times~\\var{me_mantissa}~\\times~ 10^{\\var{me_log}}~{\\rm kg}~\\times~(\\var{Length}~\\times~10^{-10})^2~{\\rm m^2}}\\]

It's a good idea to rearrange this to collect powers of ten;

\\[\\frac{\\var{LUMO}^2~\\times~(\\var{h_mantissa}~\\times~10^{\\var{h_log}}{\\rm~J~s})^2}{8~\\times~\\var{me_mantissa}~\\times~10^{\\var{me_log}}~{\\rm kg}~\\times~ (\\var{Length}~\\times~10^{-10})^2~{\\rm m}}\\]

\\[=\\frac{\\var{LUMO}^2\\times\\var{h_mantissa}^2}{8~\\times~\\var{me_mantissa}~\\times~\\var{Length}^2}~\\times~\\frac{(10^{\\var{h_log}})^2}{10^{\\var{me_log}}~\\times~(10^{-10})^2}~{\\rm~~~ J}\\]

\\[=\\var{E_lumo_mantissa}\\times10^\\var{E_lumo_log}~{\\rm~J}\\]

c) Perhaps the most direct way to the answer to this question is simply to subtract the answer to (a) from that of (b);

\\[\\var{E_lumo_mantissa}\\times10^\\var{E_lumo_log}~{\\rm~J}-\\var{E_homo_mantissa}\\times10^\\var{E_homo_log}~{\\rm~J}=\\var{Delta_E_mantissa}~\\times~10^{\\var{Delta_E_log}}~{\\rm~J}\\]

but it is worth knowing that there is a more general route to a solution that avoids the need to calculate the energies of the HOMO and LUMO;

\\[E(n+1)-E(n)=\\frac{(n+1)^2h^2}{8m_e^2L^2}-\\frac{n^2h^2}{8m_e^2L^2}\\]

\\[=(\\frac{(n^2+2n+1)h^2}{8m_eL^2})-(\\frac{n^2h^2}{8m_eL^2})\\]

\\[=\\frac{(2n+1)h^2}{8m_eL^2}\\] so

\\[\\frac{(2~\\times~\\var{n}+1)~\\times~\\var{h_mantissa}^2}{8~\\times~\\var{me_mantissa}~\\times~\\var{Length}^2}~\\times~\\frac{(10^{\\var{h_log}})^2}{10^{\\var{me_log}}~\\times~(10^{-10})^2}~{\\rm~~~ J}\\]

\\[=\\var{Delta_E_mantissa}~\\times~10^{\\var{Delta_E_log}}~{\\rm~J}\\]

d) We need to take the energy associated with the transition and divide it by the Planck constant;

\\[E=h\\nu\\]

\\[\\nu=\\frac{E}{h}=\\frac{\\var{Delta_E_mantissa}~\\times~10^{\\var{Delta_E_log}}~{\\rm J}}{\\var{h_mantissa}~\\times~10^{\\var{h_log}}{\\rm~J~s}}\\]

\\[={\\var{Frequency_mantissa}\\times10^{\\var{Frequency_log}}~{\\rm~Hz}}\\]

e) To obtain the wavelength from the frequency, we need to remember that;

\\[c=\\lambda\\nu\\]

\\[\\frac{c}{\\nu}=\\lambda=\\frac{3.0~\\times~10^8~{\\rm m~s^{-1}}}{\\var{Frequency_mantissa}~\\times~10^{\\var{Frequency_log}}{\\rm~s^{-1}}}=\\var{Wavelength_m_mantissa}~\\times~10^\\var{Wavelength_m_log}{\\rm~m}\\]

and noting that 1 $\\times~10^9$ nm = 1 m, we can note that;

\\[\\var{Wavelength_m_mantissa}~\\times~10^\\var{Wavelength_m_log}{\\rm~m}=\\var{Wavelength}{\\rm~nm}\\]

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Delta_E_log": {"name": "Delta_E_log", "group": "Ungrouped variables", "definition": "floor(log(Delta_E))", "description": "", "templateType": "anything", "can_override": false}, "LUMO": {"name": "LUMO", "group": "Ungrouped variables", "definition": "n+1", "description": "", "templateType": "anything", "can_override": false}, "Frequency": {"name": "Frequency", "group": "Ungrouped variables", "definition": "Delta_E/h", "description": "", "templateType": "anything", "can_override": false}, "Wavelength_m": {"name": "Wavelength_m", "group": "Ungrouped variables", "definition": "wavelength*10^-9", "description": "", "templateType": "anything", "can_override": false}, "me": {"name": "me", "group": "Ungrouped variables", "definition": "9.1093856*10^-31", "description": "", "templateType": "anything", "can_override": false}, "Molecule": {"name": "Molecule", "group": "Ungrouped variables", "definition": "Data[0]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "Data[2]", "description": "", "templateType": "anything", "can_override": false}, "E_lumo_mantissa": {"name": "E_lumo_mantissa", "group": "Ungrouped variables", "definition": "siground((E_lumo)/10^(E_lumo_log),3)", "description": "", "templateType": "anything", "can_override": false}, "E_homo": {"name": "E_homo", "group": "Ungrouped variables", "definition": "((n^2)*(h^2))/(8*me*(10^-20)*Length^2)", "description": "", "templateType": "anything", "can_override": false}, "me_mantissa": {"name": "me_mantissa", "group": "Ungrouped variables", "definition": "siground((me/(10^(me_log))),4)\n", "description": "", "templateType": "anything", "can_override": false}, "Wavelength": {"name": "Wavelength", "group": "Ungrouped variables", "definition": "siground(((2.99792458*10^8)/Frequency)*10^9,3)", "description": "", "templateType": "anything", "can_override": false}, "Parameters": {"name": "Parameters", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\\"Molecule\\\":\\\"1,3-butadiene\\\",\\\"Length\\\":5.6,\\\"HOMO\\\":2},\\n{\\\"Molecule\\\":\\\"1,3,5-hexatriene\\\",\\\"Length\\\":8.4,\\\"HOMO\\\":3},\\n{\\\"Molecule\\\":\\\"1,3,5,7-octatetraene\\\",\\\"Length\\\":9.7,\\\"HOMO\\\":4},\\n{\\\"Molecule\\\":\\\"Beta-carotene\\\",\\\"Length\\\":18.3,\\\"HOMO\\\":11}\\n]\"))", "description": "", "templateType": "json", "can_override": false}, "E_homo_mantissa": {"name": "E_homo_mantissa", "group": "Ungrouped variables", "definition": "siground((E_homo)/10^(E_homo_log),3)", "description": "", "templateType": "anything", "can_override": false}, "E_lumo_log": {"name": "E_lumo_log", "group": "Ungrouped variables", "definition": "floor(log(E_lumo))", "description": "", "templateType": "anything", "can_override": false}, "Data": {"name": "Data", "group": "Ungrouped variables", "definition": "[\n get((Parameters[randomiser]),\"Molecule\",0),\n get((Parameters[randomiser]),\"Length\",0),\n get((Parameters[randomiser]),\"HOMO\",0)\n]", "description": "

((get((Parameters[randomiser]),\"Molecule\",0)),4),
((get((Parameters[randomiser]),\"Length\",0)),4)

", "templateType": "anything", "can_override": false}, "E_homo_log": {"name": "E_homo_log", "group": "Ungrouped variables", "definition": "floor(log(E_homo))", "description": "", "templateType": "anything", "can_override": false}, "E_lumo": {"name": "E_lumo", "group": "Ungrouped variables", "definition": "(((n+1)^2)*(h^2))/(8*me*(10^-20)*Length^2)", "description": "

(((n+1)^2)*(h^2))/(8*me*(10^-20)*Length^2)

", "templateType": "anything", "can_override": false}, "Length": {"name": "Length", "group": "Ungrouped variables", "definition": "Data[1]", "description": "", "templateType": "anything", "can_override": false}, "Wavelength_m_log": {"name": "Wavelength_m_log", "group": "Ungrouped variables", "definition": "floor(log(wavelength_m))", "description": "", "templateType": "anything", "can_override": false}, "h_log": {"name": "h_log", "group": "Ungrouped variables", "definition": "floor(log(h))", "description": "", "templateType": "anything", "can_override": false}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}, "h_mantissa": {"name": "h_mantissa", "group": "Ungrouped variables", "definition": "siground((h/(10^(h_log))),4)", "description": "", "templateType": "anything", "can_override": false}, "Frequency_log": {"name": "Frequency_log", "group": "Ungrouped variables", "definition": "floor(log(Frequency))", "description": "", "templateType": "anything", "can_override": false}, "Delta_E": {"name": "Delta_E", "group": "Ungrouped variables", "definition": "E_lumo-E_homo", "description": "", "templateType": "anything", "can_override": false}, "wavelength_m_mantissa": {"name": "wavelength_m_mantissa", "group": "Ungrouped variables", "definition": "wavelength_m/(10^(wavelength_m_log))", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "6.62607004*10^(-34)", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "((6.626^2))/(8*9.31*Length^2)", "description": "", "templateType": "anything", "can_override": false}, "Delta_E_mantissa": {"name": "Delta_E_mantissa", "group": "Ungrouped variables", "definition": "siground((Delta_E)/10^(Delta_E_log),3)", "description": "", "templateType": "anything", "can_override": false}, "me_log": {"name": "me_log", "group": "Ungrouped variables", "definition": "floor(log(me))", "description": "", "templateType": "anything", "can_override": false}, "Frequency_Mantissa": {"name": "Frequency_Mantissa", "group": "Ungrouped variables", "definition": "siground(Frequency/(10^Frequency_log),3)", "description": "", "templateType": "anything", "can_override": false}, "ne": {"name": "ne", "group": "Ungrouped variables", "definition": "n*2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "Parameters", "Data", "randomiser", "Molecule", "Length", "me", "me_mantissa", "me_log", "h", "h_mantissa", "h_log", "E_homo", "E_homo_log", "E_homo_mantissa", "E_lumo", "E_lumo_log", "E_lumo_mantissa", "Delta_E", "Delta_E_log", "Delta_E_mantissa", "Frequency", "Frequency_Mantissa", "Frequency_log", "Wavelength", "ne", "LUMO", "Wavelength_m", "Wavelength_m_log", "wavelength_m_mantissa", "test"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the energy, E (in J), of the HOMO of {Molecule}* if it is assumed that the \"particle-in-a-box model\" can be applied and the length of the box, l, is {Length} $\\unicode{x212B}$?

[[0]] $\\times$ 10^[[1]]

*If you are asked a question about beta-carotene, assume that there are 22 electrons in its conjugated system.

\n\n\n", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "E_homo_mantissa-(E_homo_mantissa/50)", "maxValue": "E_homo_mantissa+(E_homo_mantissa/50)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "E_homo_log+(E_homo_log/50)", "maxValue": "E_homo_log-(E_homo_log/50)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the energy, E (in J), of the LUMO of {Molecule} if it is assumed that the \"particle-in-a-box model\" can be applied and the length of the box, l, is {Length} $\\unicode{x212B}$?

[[0]] $\\times$ 10^[[1]]

*If you are asked a question about beta-carotene, assume that there are 22 electrons in its conjugated system.

What is the difference in energy, $\\Delta$E (in J) between the HOMO and the LUMO of {Molecule}?

[[0]] $\\times$ 10^[[1]]

*If you are asked a question about beta-carotene, assume that there are 22 electrons in its conjugated system.

What is the frequency, $\\nu$ (in Hz), of the electronic transition of {Molecule} that has the longest wavelength?

[[0]] $\\times$ 10^[[1]]

What is the wavelength, $\\lambda$ (in nm), of the electronic transition of {Molecule} that has the longest wavelength?

", "minValue": "wavelength-wavelength/50", "maxValue": "wavelength+wavelength/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Nick's copy of Moment of inertia from rotational constant", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_DTrtxfw.png", "/srv/numbas/media/question-resources/image_DTrtxfw.png"], ["question-resources/image_gxf2p8m.png", "/srv/numbas/media/question-resources/image_gxf2p8m.png"], ["question-resources/image_YiGalQz.png", "/srv/numbas/media/question-resources/image_YiGalQz.png"], ["question-resources/image_izx86lb.png", "/srv/numbas/media/question-resources/image_izx86lb.png"], ["question-resources/image_EFznxB4.png", "/srv/numbas/media/question-resources/image_EFznxB4.png"], ["question-resources/image_QRX8AOx.png", "/srv/numbas/media/question-resources/image_QRX8AOx.png"], ["question-resources/image_SkqSr5d.png", "/srv/numbas/media/question-resources/image_SkqSr5d.png"], ["question-resources/image_RvwZ0jx.png", "/srv/numbas/media/question-resources/image_RvwZ0jx.png"], ["question-resources/image_jI1pj1c.png", "/srv/numbas/media/question-resources/image_jI1pj1c.png"], ["question-resources/image_m7iIRpR.png", "/srv/numbas/media/question-resources/image_m7iIRpR.png"], ["question-resources/image_e6HMPkZ.png", "/srv/numbas/media/question-resources/image_e6HMPkZ.png"], ["question-resources/image_Hbraekd.png", "/srv/numbas/media/question-resources/image_Hbraekd.png"], ["question-resources/image_fPp87EN.png", "/srv/numbas/media/question-resources/image_fPp87EN.png"], ["question-resources/image_lrBQiRH.png", "/srv/numbas/media/question-resources/image_lrBQiRH.png"], ["question-resources/image_Eyq56eh.png", "/srv/numbas/media/question-resources/image_Eyq56eh.png"], ["question-resources/image_FjdLy57.png", "/srv/numbas/media/question-resources/image_FjdLy57.png"], ["question-resources/image_fFsskYr.png", "/srv/numbas/media/question-resources/image_fFsskYr.png"], ["question-resources/image_7yxkxrh.png", "/srv/numbas/media/question-resources/image_7yxkxrh.png"], ["question-resources/image_TKd4KFA.png", "/srv/numbas/media/question-resources/image_TKd4KFA.png"], ["question-resources/image_qhno0zh.png", "/srv/numbas/media/question-resources/image_qhno0zh.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}], "tags": [], "metadata": {"description": "The reduced masses are pre-calculated for this question and included in a list. It would be more elegant to program Numbas to permute atoms together to generate diatomic molecules while constraining the permutations to those which are chemically/physically reasonable, so as to allow calculation of each reduced mass directly from the atomic masses- but organising this with high computational efficiency might be a significant programing task (add to \"to do\" list). ", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Given that the rotational constant, B, of {HTML} is {B_html_output};

", "advice": "

If presented with a wavenumber, you will need to start by converting this into a frequency while noting that;

\\[c=\\lambda\\nu\\]

and therefore

\\[\\nu~{\\rm{in~s^{-1}}}=\\frac{c}{\\lambda}=c ~({\\rm in~cm~s^{-1}})~\\times~{\\rm wavenumber~(in~cm)}\\]

\\[2.998 \\times 10^{10}~{\\rm cm~s^{-1}}\\times~\\var{wavenumber}~{\\rm cm^{-1}}=\\var{B_value2_mantissa}~\\times~10^{\\var{B_value2_log}}~{\\rm Hz}\\]

(a) First, calculate the moment of inertia, I

\\[I=\\frac{h}{8\\pi^{2}B}\\]

\\[I=\\frac{h}{8\\pi^{2}B}=\\frac{6.626~\\times~10^{-34}{\\rm~J~s}}{8\\pi^{2}~\\times\\var{B_value2_mantissa}\\times 10^{\\var{B_value2_log}}~{\\rm s^{-1}}}=\\var{mantissa_inertia_x}\\times ~10^{\\var {log_inertia_x}}~{\\rm kg~m^{2}}\\]

(b) To calculate the reduced mass in g mol^-1, where m₁ is the mass of the first atom and m₂ is the mass of the second atom, each expressed in units of g mol^-1;

\\[\\frac{m_{1}~\\times~m_{2}}{m{_1}+m_{2}}=\\var{reduced_mass}~\\rm g~mol^{-1}\\]

(c) To calculate the reduced mass in kg molecule^-1, divide the reduced mass in g mol^-1 by (the Avogadro number multiplied by 1000)

\\[\\frac{\\var{reduced_mass}~\\rm {g~mol^{-1}}}{1000~{\\rm g~kg^{-1}}~\\times~6.022~\\times~10^{23}~{\\rm molecules~mol^{-1}}}=\\var{mantissa_reduced_mass_kg}\\times 10^{\\var{log_reduced_mass_kg}}\\rm ~kg~ molecule^{-1}\\]

(d) To determine the bond length from the moment of inertia and reduced mass;

\\[I=\\mu~r^{2}~~~~~~~~~~{\\rm so}~~~~~~~~~ r=\\sqrt{\\frac{I}{\\mu}}\\]

\\[r=\\sqrt{\\frac{I}{\\mu}}=\\sqrt{\\frac{\\var{mantissa_inertia_x}\\times ~10^{\\var {log_inertia_x}}}{\\var{mantissa_reduced_mass_kg}\\times 10^{\\var{log_reduced_mass_kg}}}}=\\var{bond_length_angstroms}\\times10^{-10}~{\\rm m}=\\var{bond_length_angstroms}~{\\unicode{x212B}}\\]

", "rulesets": {"": []}, "variables": {"mantissa_reduced_mass_kg": {"name": "mantissa_reduced_mass_kg", "group": "Ungrouped variables", "definition": "reduced_mass_kg/(10^(floor(log(reduced_mass_kg))))", "description": "", "templateType": "anything"}, "Inertia_x": {"name": "Inertia_x", "group": "Ungrouped variables", "definition": "siground((6.626*10^(13))/(8*(3.14^2)*(B_list[1])),4)", "description": "", "templateType": "anything"}, "reduced_mass_kg": {"name": "reduced_mass_kg", "group": "Ungrouped variables", "definition": "siground((reduced_mass/6.022),3)", "description": "", "templateType": "anything"}, "rot_constants": {"name": "rot_constants", "group": "Chemical element masses", "definition": "json_decode(safe(\"[\\n{\\\"Formula\\\":\\\"H35Cl\\\",\\\"reduced mass\\\":0.979592539,\\\"nu\\\":2990.946,\\\"B\\\":1.059341600000000e+001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647010\\\",\\\"SQUIB\\\":\\\"1979HUB/HER\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"H81Br\\\",\\\"reduced mass\\\":0.995426835,\\\"nu\\\":2648.975,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":8.464880000000001e+000,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10035106\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"HI\\\",\\\"reduced mass\\\":0.999884347,\\\"nu\\\":2309.01,\\\"B\\\":6.426365000000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"6.426365000000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10034852\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na35Cl\\\",\\\"reduced mass\\\":13.87068615,\\\"nu\\\":366,\\\"B\\\":2.180630000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647145\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na79Br\\\",\\\"reduced mass\\\":17.80343514,\\\"nu\\\":302,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":1.512533000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.512533000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647156\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"LiF\\\",\\\"reduced mass\\\":5.123810029,\\\"Comment\\\":\\\"7Li\\\",\\\"nu\\\":910.34,\\\"B\\\":1.345257590000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.345257590000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7789244\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Li35Cl\\\",\\\"reduced mass\\\":5.843574224,\\\"nu\\\":643.31,\\\"B\\\":7.065225000000001e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7447418\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63CuF\\\",\\\"reduced mass\\\":14.59283587,\\\"Comment\\\":\\\"Y01\\\",\\\"nu\\\":622.6,\\\"B\\\":3.794029400000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"3.794029400000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"13478416\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linera\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63Cu35Cl\\\",\\\"reduced mass\\\":22.47814771,\\\"Comment\\\":\\\"63Cu 35Cl\\\",\\\"nu\\\":415.29,\\\"B\\\":1.782489000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.782489000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7758896\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"}\\n]\"))", "description": "

Rotational constants data from;

<https://catalog.data.gov/dataset/nist-computational-chemistry-comparison-and-benchmark-database-srd-101>

augmented with reduced masses calculated from IUPAC Green Book.

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randomi

The moment of inertia, I, is [[0]] $\\times$ 10^[[1]]kg m².

What is the reduced mass, $\\mu$, in units of g mol^-1?

", "minValue": "{reduced_mass}-{reduced_mass}/50", "maxValue": "{reduced_mass}+{reduced_mass}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

The reduced mass, $\\mu$, is [[0]] $\\times$ 10^[[1]] kg molecule^-1.

The bond length, r, is [[0]] $\\times$ 10^[[1]] m.

For {molecule}, calculate the number of rotational modes:

[[0]]

", "marks": 0}, {"showCorrectAnswer": true, "customName": "", "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "sortAnswers": false, "type": "gapfill", "useCustomName": false, "gaps": [{"showCorrectAnswer": true, "customName": "", "maxValue": "{GET_VIB}", "variableReplacements": [], "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "{GET_VIB}", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "mustBeReduced": false, "useCustomName": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "marks": 1}], "variableReplacementStrategy": "originalfirst", "prompt": "

For {molecule}, calculate the number of vibrational modes:

[[0]]

", "marks": 0}, {"displayColumns": 0, "type": "1_n_2", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "displayType": "radiogroup", "minMarks": 0, "variableReplacementStrategy": "originalfirst", "prompt": "

Is {molecule} microwave active?

", "showCorrectAnswer": true, "customName": "", "variableReplacements": [], "maxMarks": 0, "distractors": ["", ""], "shuffleChoices": false, "matrix": ["if({get_mic=true,1,0)", "if({get_mic=false,1,0)"], "scripts": {}, "useCustomName": false, "showCellAnswerState": true, "choices": ["Yes", "No"], "marks": 0}, {"showCorrectAnswer": true, "customName": "", "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "sortAnswers": false, "type": "gapfill", "useCustomName": false, "gaps": [{"showCorrectAnswer": true, "customName": "", "maxValue": "{get_ir}", "variableReplacements": [], "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "{get_ir}", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "mustBeReduced": false, "useCustomName": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "marks": 1}], "variableReplacementStrategy": "originalfirst", "prompt": "

For {molecule}, calculate the number of infrared active modes:

[[0]]

", "marks": 0}], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "functions": {}, "preamble": {"css": "", "js": ""}, "variable_groups": [], "tags": ["cc", "CC", "l5", "L5", "random", "RANDOM", "Random"], "variables": {"DATA": {"templateType": "json", "name": "DATA", "definition": "json_decode(safe(\"[\\n {\\n \\\"name\\\": \\\"nitrogen\\\",\\n \\\"formula\\\": \\\"N_2\\\",\\n \\\"freedom\\\": 1,\\n \\\"ir\\\": 0,\\n \\\"rotational\\\": 2,\\n \\\"vibrational\\\": 1,\\n \\\"microwave\\\": false,\\n \\\"ir active\\\": false\\n },\\n {\\n \\\"name\\\": \\\"hydrogen chloride\\\",\\n \\\"formula\\\": \\\"HCl\\\",\\n \\\"freedom\\\": 1,\\n \\\"ir\\\": 1,\\n \\\"rotational\\\": 2,\\n \\\"vibrational\\\": 1,\\n \\\"microwave\\\": true,\\n \\\"ir active\\\": true\\n },\\n {\\n \\\"name\\\": \\\"carbon dioxide\\\",\\n \\\"formula\\\": \\\"CO_2\\\",\\n \\\"freedom\\\": 4,\\n \\\"ir\\\": 3,\\n \\\"rotational\\\": 2,\\n \\\"vibrational\\\": 4,\\n \\\"microwave\\\": false,\\n \\\"ir active\\\": true\\n },\\n {\\n \\\"name\\\": \\\"nitrous oxide\\\",\\n \\\"formula\\\": \\\"N_2O\\\",\\n \\\"freedom\\\": 4,\\n \\\"ir\\\": 4,\\n \\\"rotational\\\": 2,\\n \\\"vibrational\\\": 4,\\n \\\"microwave\\\": true,\\n \\\"ir active\\\": true\\n },\\n {\\n \\\"name\\\": \\\"water\\\",\\n \\\"formula\\\": \\\"H_2O\\\",\\n \\\"freedom\\\": 3,\\n \\\"ir\\\": 3,\\n \\\"rotational\\\": 3,\\n \\\"vibrational\\\": 3,\\n \\\"microwave\\\": true,\\n \\\"ir active\\\": true\\n },\\n {\\n \\\"name\\\": \\\"hydrogen sulfide\\\",\\n \\\"formula\\\": \\\"H_2S\\\",\\n \\\"freedom\\\": 3,\\n \\\"ir\\\": 3,\\n \\\"rotational\\\": 3,\\n \\\"vibrational\\\": 3,\\n \\\"microwave\\\": true,\\n \\\"ir active\\\": true\\n },\\n {\\n \\\"name\\\": \\\"carbon monoxide\\\",\\n \\\"formula\\\": \\\"CO\\\",\\n \\\"freedom\\\": 1,\\n \\\"ir\\\": 1,\\n \\\"rotational\\\": 2,\\n \\\"vibrational\\\": 1,\\n \\\"microwave\\\": true,\\n \\\"ir active\\\": true\\n }\\n]\"))", "group": "Ungrouped variables", "description": ""}, "select": {"templateType": "anything", "name": "select", "definition": "random(0..6)", "group": "Ungrouped variables", "description": "

select

"}, "get_freedom": {"templateType": "anything", "name": "get_freedom", "definition": "(get((data[select]),\"freedom\",0))", "group": "Ungrouped variables", "description": ""}, "ir_active": {"templateType": "anything", "name": "ir_active", "definition": "(get((data[select]),\"ir active\",0))", "group": "Ungrouped variables", "description": ""}, "molecule": {"templateType": "anything", "name": "molecule", "definition": "(get((data[select]),\"name\",0))", "group": "Ungrouped variables", "description": ""}, "get_mic": {"templateType": "anything", "name": "get_mic", "definition": "(get((data[select]),\"microwave\",0))", "group": "Ungrouped variables", "description": ""}, "get_ir": {"templateType": "anything", "name": "get_ir", "definition": "(get((data[select]),\"ir\",0))", "group": "Ungrouped variables", "description": ""}, "get_vib": {"templateType": "anything", "name": "get_vib", "definition": "(get((data[select]),\"vibrational\",0))", "group": "Ungrouped variables", "description": ""}, "get_rot": {"templateType": "anything", "name": "get_rot", "definition": "(get((data[select]),\"rotational\",0))", "group": "Ungrouped variables", "description": ""}}, "advice": "

a) It is always straightforward to calculate the number of rotational modes for a molecule. If the molecule is linear (and note that all diatomic molecules are linear) then it has 2 rotational modes. If the molecule is non-linear then it has three rotational modes.

\\[\\rm {For}~{\\var {molecule}}~{\\rm the~number~of~rotational~modes~is~equal~to~} {\\var {get_rot}}\\]

b) The overall motion of a molecule can be described using 3N coordinates (where N is the number of atoms in the molecule). This number arises because each individual atom has three degrees of freedom (ie, three coordinates) of translational motion. Simply stated, each individual atom moves in three dimensional space (x,y,z). A detailed analysis (which we won't do here) would confirm that; (i) three of the coordinates that describe the movement of the overall molecule turn out to be translations (the molecule moves in 3 dimensional space, along x,y and z coordinates) and two or three (depending on whether or not a molecule is linear, see part (a) above for explanation) of the coordinates that describe the movement of the overall molecule turn out to be rotations. When we subtract the number of translational coordinates and the number of rotational coordinates from 3N for a particular molecule, we calculate the number of vibrational coordinates that a molecule has. Note that normal modes can also be referred to as \"coordinates\" or \"degrees of freedom\". For all practical purposes, these three terms are interchangeable. Expressing the information above in a succinct, mathematical form, we can say that;

For a linear molecule\\[{\\rm Number~of~vibrational~modes}=3N-5\\]

For a non-linear molecule\\[{\\rm Number~of~vibrational~modes}=3N-6\\]

These descriptions yield very simple results, though they are only easy to visualise for small, highly symmetrical molecules. Diatomic molecules have only one vibrational mode (the symmetric stretch). Linear triatomic molecules have four vibrational modes (a degenerate bending motion (\"degenerate\" means that the molecule bends in two planes, each of which counts as a different mode), a symmetric stretch and an asymmetric stretch) while non-linear triatomics have three vibrational modes (the two stretches and a single, non-degenerate bend). These can be visualised using the animation at this University of Liverpool web site (select from the panel on the left hand side and \"click to see vibration list\" to animate the modes);

<http://www.chemtube3d.com/vibrationsH2O.htm>

So;

\\[\\rm {For}~{\\var {molecule}}~{\\rm the~number~of~vibrational~modes~is~equal~to~} {\\var {get_vib}}\\]

(c) If a molecule has a permanent electric dipole moment, then it absorbs microwave radiation and a microwave spectrum can be measured for it. If it doesn't have an electric dipole moment, the opposite is true.

So;

\\[\\rm {It~is}~{\\var {get_mic}}~that~{\\var {molecule}}~is~microwave~active.\\]

(d)

In order to answer this part, you must decide which of the vibrations of the molecule cause the electric dipole moment of the molecule to oscillate in phase with the vibration.

For a diatomic molecule, this is easy. If it is homonuclear, then the single vibrational mode is infrared active. If it is heteronuclear, then the single vibrational mode is not infrared active.

Larger molecules require more detailed examination. While referring to this link;

<http://www.chemtube3d.com/vibrationsH2O.htm>

select the CO₂ molecule in the left hand panel. Then click \"CLICK HERE to show frequency list\". The degenerate ${\\Pi}_{\\rm u}$ vibrations (there are two different ${\\Pi}_{\\rm u}$ modes) and the ${\\Sigma}_{\\rm u}$ vibration each cause the electric dipole moment of the molecule to oscillate in phase with the vibration. The ${\\Sigma}_{\\rm g}$ vibration does not cause the electric dipole moment to oscillate in phase with the vibration. CO₂ therefore has three infrared-active vibrational modes and one vibrational mode (the ${\\Sigma}_{\\rm g}$ mode) that is not infrared active.

If performing the analysis for a linear molecule that does not have a centre of inversion (such as OCS), the molecule will have two ${\\Pi}_{\\rm u}$ modes (ie bending) and two ${\\Sigma}_{\\rm u}$ modes (stretching) such that all 4 modes will be IR active. Performing the analysis for a non-linear molecule such as H₂O will reveal 1 bending motion, 1 symmetric stretch and 1 antisymmetric stretch which will all be infrared-active.

\\[\\rm {The~number~of~infrared~active~modes~of}~{\\var {molecule}}~is~therefore~{\\var {get_ir}}.\\]

Point groups, character tables and symmetry analysis greatly simplify the analysis for molecules with more than 3 atoms. The ${\\Pi}$ and ${\\Sigma}$ symbols in the feedback above are symmetry labels. You will not learn about these in CHY1201 but it will be a topic of future studies. If you wish a more sophisticated explanation of symmetry point groups and character tables now, this is a good source;

<https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Vibrational_Spectroscopy/Vibrational_Modes/Normal_Modes>

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Given that the {html_definer} of the vibrational stretch of {HTML} is {nu_html_outpu}, calculate the force constant, k, in N m^-1;

", "advice": "

a) If necessary, convert wavenumber to Hz

\\[{\\rm wavenumber}\\times {c}={\\nu}\\]

\\[\\nu=\\var{wavenumber}~\\rm cm^{-1}\\times 3\\times 10^{10}~cm~s^{-1}=\\var{nuval2man}\\times 10^{\\var{nu_value2_log}}~Hz\\]

Calculate $\\mu$

\\[\\mu=\\frac{m_1\\times m_2}{m_1+m_2}=\\var{reduced_mass}~\\rm g~mol^{-1}\\]

Convert from g mol^-1 to kg mol^-1....

\\[\\frac{\\var{reduced_mass}{~\\rm g~mol^{-1}}}{1000}=\\var{reduced_mass}\\times 10^{-3}~\\rm kg~mol^{-1}\\]

...then divide by Avogadro's number to obtain a value in kg molecule^-1;

\\[\\frac{\\var{reduced_mass}\\times 10^{-3}~\\rm kg~mol^{-1}}{6.022\\times 10^{23}~{\\rm molecules~mol^{-1}}}=\\var{reduced_mass_mantissa}\\times10^{\\var{reduced_mass_log}}~\\rm kg~molecule^{-1}\\]

Rearrange for $k$

\\[\\nu=\\frac{1}{2\\pi}\\sqrt{\\frac{k}{\\mu}}\\]

\\[(2\\pi v)^2\\mu=k\\]

then substitute values in for each of the variables;

\\[k =(2\\pi \\times \\var{nuval2man}\\times 10^{\\var{nu_value2_log}})^2\\times\\var{reduced_mass_mantissa}\\times10^{\\var{reduced_mass_log}}{\\rm ~kg~molecule^{-1}} =\\var{force_constant}~\\rm N~m^{-1}\\]

(b) Note that;

\\[{\\rm Zero~point~energy}=\\frac{1}{2}h\\nu\\]

so;

\\[{\\rm Zero~point~energy}=\\frac{1}{2}\\times 6.626 \\times 10^{-34}~{\\rm J~s} \\times \\var{nuval2man}\\times 10^{\\var{nu_value2_log}}~{\\rm Hz}\\]

\\[=\\var{ZPE_mantissa}\\times 10^{\\var{ZPE_log}}~{\\rm J}\\]

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randomi

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random(0..9)

", "templateType": "anything"}, "ZPE": {"name": "ZPE", "group": "Ungrouped variables", "definition": "0.5*nu_list[1]*6.626*10^(-34)", "description": "", "templateType": "anything"}, "nu_list": {"name": "nu_list", "group": "Ungrouped variables", "definition": "[\n ( \n (siground((get((rot_constants[randomiser]),\"nu\",0)),4)),\n (siground((get((rot_constants[randomiser]),\"nu\",0)*3*10^(10)),4))\n )\n]", "description": "", "templateType": "anything"}, "nu_value2_log": {"name": "nu_value2_log", "group": "Ungrouped variables", "definition": "floor(log(nu_list[1]))", "description": "", "templateType": "anything"}, "reduced_mass": {"name": "reduced_mass", "group": "Ungrouped variables", "definition": "siground(get((rot_constants[randomiser]),\"reduced mass\",0),4)", "description": "", "templateType": "anything"}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "Molecule_identifiers[randomiser]", "description": "

0 = CO
1 = H35Cl

2= H81Br
3= HI
4= Na35Cl

5= Na79Br
6= LiF
7= Li35Cl
8= 63CuF
9= 63Cu35Cl

", "templateType": "anything"}, "rot_constants": {"name": "rot_constants", "group": "Chemical element masses", "definition": "json_decode(safe(\"[\\n{\\\"Formula\\\":\\\"CO\\\",\\\"reduced mass\\\":6.856208638,\\\"nu\\\":2169.81358,\\\"B\\\":1.931280870000000e+000,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"630080\\\",\\\"SQUIB\\\":\\\"1979HUB/HER\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"H35Cl\\\",\\\"reduced mass\\\":0.979592539,\\\"nu\\\":2990.946,\\\"B\\\":1.059341600000000e+001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647010\\\",\\\"SQUIB\\\":\\\"1979HUB/HER\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"H81Br\\\",\\\"reduced mass\\\":0.995426835,\\\"nu\\\":2648.975,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":8.464880000000001e+000,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10035106\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"HI\\\",\\\"reduced mass\\\":0.999884347,\\\"nu\\\":2309.01,\\\"B\\\":6.426365000000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"6.426365000000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10034852\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na35Cl\\\",\\\"reduced mass\\\":13.87068615,\\\"nu\\\":366,\\\"B\\\":2.180630000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647145\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na79Br\\\",\\\"reduced mass\\\":17.80343514,\\\"nu\\\":302,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":1.512533000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.512533000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647156\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"LiF\\\",\\\"reduced mass\\\":5.123810029,\\\"Comment\\\":\\\"7Li\\\",\\\"nu\\\":910.34,\\\"B\\\":1.345257590000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.345257590000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7789244\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Li35Cl\\\",\\\"reduced mass\\\":5.843574224,\\\"nu\\\":643.31,\\\"B\\\":7.065225000000001e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7447418\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63CuF\\\",\\\"reduced mass\\\":14.59283587,\\\"Comment\\\":\\\"Y01\\\",\\\"nu\\\":622.6,\\\"B\\\":3.794029400000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"3.794029400000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"13478416\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linera\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63Cu35Cl\\\",\\\"reduced mass\\\":22.47814771,\\\"Comment\\\":\\\"63Cu 35Cl\\\",\\\"nu\\\":415.29,\\\"B\\\":1.782489000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.782489000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7758896\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"}\\n]\"))", "description": "

Rotational constants data from;

<https://catalog.data.gov/dataset/nist-computational-chemistry-comparison-and-benchmark-database-srd-101>

augmented with reduced masses calculated from IUPAC Green Book.

", "templateType": "json"}, "reduced_mass_mantissa": {"name": "reduced_mass_mantissa", "group": "Ungrouped variables", "definition": "siground((reduced_mass_kg)/(10^(reduced_mass_log+26)),3)", "description": "", "templateType": "anything"}, "Molecule_identifiers": {"name": "Molecule_identifiers", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"C\"+\"O\"+\"\"),\n html(\"\"+\"H\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"H\"+\"^\"+\"81\"+\"\"+\"Br\"+\"\"),\n html(\"\"+\"H\"+\"I\"+\"\"),\n html(\"\"+\"Na\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"Na\"+\"^\"+\"79\"+\"\"+\"Br\"+\"\"),\n html(\"\"+\"Li\"+\"F\"+\"\"),\n html(\"\"+\"Li\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"^\"+\"63\"+\"\"+\"Cu\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"63\"+\"\"+\"Cu\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\")\n )\n]", "description": "", "templateType": "anything"}, "nu_html": {"name": "nu_html", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+{nu_value}+\" \"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+{nuval2man}+\" \"+\"× \"+\"10\"+\"^{\"+\"{nu_value2_log}\"+\"}\"+\" \"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything"}, "nu_value": {"name": "nu_value", "group": "Ungrouped variables", "definition": "nu_list[randomiser_units]", "description": "", "templateType": "anything"}, "ZPE_log": {"name": "ZPE_log", "group": "Ungrouped variables", "definition": "floor(log(ZPE))", "description": "", "templateType": "anything"}, "nuval2man": {"name": "nuval2man", "group": "Ungrouped variables", "definition": "nu_list[1]/(10^(nu_value2_log))", "description": "", "templateType": "anything"}, "ZPE_mantissa": {"name": "ZPE_mantissa", "group": "Ungrouped variables", "definition": "siground(ZPE/(10^(ZPE_log)),3)", "description": "", "templateType": "anything"}, "wavenumber": {"name": "wavenumber", "group": "Ungrouped variables", "definition": "nu_list[0]", "description": "", "templateType": "anything"}, "nu_html_outpu": {"name": "nu_html_outpu", "group": "Ungrouped variables", "definition": "nu_html[randomiser_units]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["randomiser", "Molecule_identifiers", "HTML", "randomiser_units", "nu_list", "nu_value", "nuval2man", "nu_value2_log", "nu_html", "nu_html_outpu", "html_definer", "force_constant", "wavenumber", "reduced_mass", "reduced_mass_log", "reduced_mass_mantissa", "reduced_mass_kg", "ZPE", "ZPE_log", "ZPE_mantissa"], "variable_groups": [{"name": "Chemical element masses", "variables": ["rot_constants"]}], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}, "molecule_name": {"parameters": [["atoms", "list"]], "type": "number", "language": "jme", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}, "isotope_name": {"parameters": [["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{force_constant}-{force_constant}/50", "maxValue": "{force_constant}+{force_constant}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the zero-point vibrational energy in units of Joules;

[[0]] $\\times$ 10^[[1]]

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Given that the rotational constant, B, of {HTML} is {B_html_rotconst_output};

", "advice": "

a) If presented with a wavenumber, you will need to start by converting this into a frequency while noting that;

\\[c=\\lambda\\nu\\]

and;

\\[{\\rm wavenumber}=\\frac{1}{\\lambda}\\]

therefore

\\[\\frac{\\nu}{c}=\\frac{1}{\\lambda}={\\rm wavenumber}\\] and \\[{\\rm wavenumber}~\\times~c~=\\nu\\]

\\[{\\var{wavenumber}~{\\rm cm^{-1}}}~\\times~3~\\times~10^{10}{~\\rm cm~s^{-1}}={\\var{B_value2_mantissa}~\\times~10^{\\var{B_value2_log}}~{\\rm Hz}}=B\\]

Revise how the interval between transitions in an observed spectrum (see figure), which is sometimes referred as the \"line spacing\", connects with the transitions between energy levels in a molecule. Examine how the photon energy (the value on the x axis) associates with transitions between rotational levels.

There is a simple relationship between photon energy and the J involved with transitions (where the J used in the equation is that of the lower state involved in the transition);

\\[\\nu=2B(J+1)\\]

The energy of a photon is proportional to the frequency of light (remember, E=h$\\nu$). The above relationship therefore holds whether you know B in units of Hz (frequency), or units of J (energy). However, you must be consistent throughout the calculation. For example, if you specify B in units of Hz, you will get a result for $\\nu$ in Hz. If you specify B in Joules, the result of your calculation will be an energy in Joules instead. The question specificies B in units of Hz so we will proceed as follows;

\\[\\nu=2B(J+1)\\] so

\\[\\nu=2B(J+1)=2~\\times~\\var{B_value2_mantissa}\\times 10^{\\var{B_value2_log}}\\times(\\var{random_trans}+1)~{\\rm Hz}={\\var{freq_trans_mantissa}}\\times10^{{\\var{freq_trans_log}}}~{\\rm Hz}\\]

(b) To calculate the moment of inertia, I;

\\[I=\\frac{h}{8\\pi^{2}B}\\]

\\[I=\\frac{h}{8\\pi^{2}B}=\\frac{6.626~\\times~10^{-34}{\\rm~J~s}}{8\\pi^{2}~\\times\\var{B_value2_mantissa}\\times 10^{\\var{B_value2_log}}~{\\rm Hz}}=\\var{mantissa_inertia_x}\\times ~10^{\\var {log_inertia_x}}~{\\rm kg~m^{2}}\\]

(c) To calculate the reduced mass in g mol^-1, where m₁ is the mass of the first atom and m₂ is the mass of the second atom, each expressed in units of g mol^-1;

\\[\\frac{m_{1}~\\times~m_{2}}{m{_1}+m_{2}}=\\var{reduced_mass}~\\rm g~mol^{-1}\\]

(d) To calculate the reduced mass in kg molecule^-1, divide the reduced mass in g mol^-1 by (the Avogadro number multiplied by 1000)

(e) To determine the bond length from the moment of inertia and reduced mass;

\\[I=\\mu~r^{2}~~~~~~~~~~{\\rm so}~~~~~~~~~ r=\\sqrt{\\frac{I}{\\mu}}\\]

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", "templateType": "anything"}, "line_spacing_html": {"name": "line_spacing_html", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"{2*B_list[0]}\"+\" \"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+\"{line_spacing_mantissa}\"+\" \"+\"× \"+\"10\"+\"^{\"+\"{line_spacing_log}\"+\"}\"+\" \"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything"}, "freq_trans_log": {"name": "freq_trans_log", "group": "Ungrouped variables", "definition": "floor(log(freq_trans_select))", "description": "

fre1q

", "templateType": "anything"}, "units_output": {"name": "units_output", "group": "Ungrouped variables", "definition": "units_html[randomiser_units]", "description": "", "templateType": "anything"}, "freq_trans": {"name": "freq_trans", "group": "Ungrouped variables", "definition": "[\n 2*(B_value2_mantissa*10^{B_value2_log})*(1),\n 2*(B_value2_mantissa*10^{B_value2_log})*(2),\n 2*(B_value2_mantissa*10^{B_value2_log})*(3)\n ]", "description": "", "templateType": "anything"}, "line_spacing_log": {"name": "line_spacing_log", "group": "Ungrouped variables", "definition": "floor(log(line_spacing[1]))", "description": "", "templateType": "anything"}, "log_reduced_mass_kg": {"name": "log_reduced_mass_kg", "group": "Ungrouped variables", "definition": "floor(log(reduced_mass_kg))+(-26)", "description": "", "templateType": "anything"}, "line_spacing": {"name": "line_spacing", "group": "Ungrouped variables", "definition": "[2*B_list[0],2*B_list[1]]", "description": "", "templateType": "anything"}, "B_value2_log": {"name": "B_value2_log", "group": "Ungrouped variables", "definition": "floor(log(B_list[1]))", "description": "", "templateType": "anything"}, "randomiser_units": {"name": "randomiser_units", "group": "Ungrouped variables", "definition": "random(0..1)", "description": "

randomi

", "templateType": "anything"}, "log_angstroms": {"name": "log_angstroms", "group": "Ungrouped variables", "definition": "-10", "description": "", "templateType": "anything"}, "reduced_mass": {"name": "reduced_mass", "group": "Ungrouped variables", "definition": "siground(get((rot_constants[randomiser]),\"reduced mass\",0),4)", "description": "", "templateType": "anything"}, "B_html_rotconst_output": {"name": "B_html_rotconst_output", "group": "Ungrouped variables", "definition": "B_html_rotconst[randomiser_units]", "description": "", "templateType": "anything"}, "mantissa_inertia_x": {"name": "mantissa_inertia_x", "group": "Ungrouped variables", "definition": "precround(Inertia_x/(10^floor(log(Inertia_x))),3)", "description": "", "templateType": "anything"}, "mantissa_reduced_mass_kg": {"name": "mantissa_reduced_mass_kg", "group": "Ungrouped variables", "definition": "reduced_mass_kg/(10^(floor(log(reduced_mass_kg))))", "description": "", "templateType": "anything"}, "units_html": {"name": "units_html", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything"}, "freq_trans_mantissa": {"name": "freq_trans_mantissa", "group": "Ungrouped variables", "definition": "freq_trans_select/(10^{freq_trans_log})", "description": "", "templateType": "anything"}, "line_spacing_output": {"name": "line_spacing_output", "group": "Ungrouped variables", "definition": "line_spacing_html[randomiser_units]", "description": "", "templateType": "anything"}, "wavenumber": {"name": "wavenumber", "group": "Ungrouped variables", "definition": "B_list[0]", "description": "", "templateType": "anything"}, "B_list": {"name": "B_list", "group": "Ungrouped variables", "definition": "[\n (siground((get((rot_constants[randomiser]),\"B\",0)),4)),\n (siground((get((rot_constants[randomiser]),\"B\",0))*3*10^10,4))\n]", "description": "", "templateType": "anything"}, "log_inertia_x": {"name": "log_inertia_x", "group": "Ungrouped variables", "definition": "floor(log(Inertia_x))+(-47)", "description": "", "templateType": "anything"}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "Molecule_identifiers[randomiser]", "description": "", "templateType": "anything"}, "B_html_rotconst": {"name": "B_html_rotconst", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"{B_list[randomiser_units]}\"+\" \"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+{B_value2_mantissa}+\" \"+\"× \"+\"10\"+\"^{\"+{B_value2_log}+\"}\"+\" \"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything"}, "bond_length_angstroms": {"name": "bond_length_angstroms", "group": "Ungrouped variables", "definition": "siground(((mantissa_inertia_x*10^(log_inertia_x)*10^(20)*1000)/((get((rot_constants[randomiser]),\"reduced mass\",0))/(6.022*10^(23))))^(0.5),4)", "description": "", "templateType": "anything"}, "B_value": {"name": "B_value", "group": "Ungrouped variables", "definition": "B_list[randomiser_units]", "description": "", "templateType": "anything"}, "freq_trans_select": {"name": "freq_trans_select", "group": "Ungrouped variables", "definition": "freq_trans[random_trans]", "description": "", "templateType": "anything"}, "rot_constants": {"name": "rot_constants", "group": "Chemical element masses", "definition": "json_decode(safe(\"[\\n{\\\"Formula\\\":\\\"H35Cl\\\",\\\"reduced mass\\\":0.979592539,\\\"nu\\\":2990.946,\\\"B\\\":1.059341600000000e+001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647010\\\",\\\"SQUIB\\\":\\\"1979HUB/HER\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"H81Br\\\",\\\"reduced mass\\\":0.995426835,\\\"nu\\\":2648.975,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":8.464880000000001e+000,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10035106\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"HI\\\",\\\"reduced mass\\\":0.999884347,\\\"nu\\\":2309.01,\\\"B\\\":6.426365000000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"6.426365000000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10034852\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na35Cl\\\",\\\"reduced mass\\\":13.87068615,\\\"nu\\\":366,\\\"B\\\":2.180630000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647145\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na79Br\\\",\\\"reduced mass\\\":17.80343514,\\\"nu\\\":302,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":1.512533000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.512533000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647156\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"LiF\\\",\\\"reduced mass\\\":5.123810029,\\\"Comment\\\":\\\"7Li\\\",\\\"nu\\\":910.34,\\\"B\\\":1.345257590000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.345257590000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7789244\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Li35Cl\\\",\\\"reduced mass\\\":5.843574224,\\\"nu\\\":643.31,\\\"B\\\":7.065225000000001e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7447418\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63CuF\\\",\\\"reduced mass\\\":14.59283587,\\\"Comment\\\":\\\"Y01\\\",\\\"nu\\\":622.6,\\\"B\\\":3.794029400000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"3.794029400000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"13478416\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linera\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63Cu35Cl\\\",\\\"reduced mass\\\":22.47814771,\\\"Comment\\\":\\\"63Cu 35Cl\\\",\\\"nu\\\":415.29,\\\"B\\\":1.782489000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.782489000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7758896\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"}\\n]\"))", "description": "

Rotational constants data from;

<https://catalog.data.gov/dataset/nist-computational-chemistry-comparison-and-benchmark-database-srd-101>

augmented with reduced masses calculated from IUPAC Green Book.

", "templateType": "json"}, "B_value2_mantissa": {"name": "B_value2_mantissa", "group": "Ungrouped variables", "definition": "B_list[1]/(10^(B_value2_log))", "description": "", "templateType": "anything"}, "Molecule_identifiers": {"name": "Molecule_identifiers", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"H\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"H\"+\"^\"+\"81\"+\"\"+\"Br\"+\"\"),\n html(\"\"+\"H\"+\"I\"+\"\"),\n html(\"\"+\"Na\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"Na\"+\"^\"+\"79\"+\"\"+\"Br\"+\"\"),\n html(\"\"+\"Li\"+\"F\"+\"\"),\n html(\"\"+\"Li\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"^\"+\"63\"+\"\"+\"Cu\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"63\"+\"\"+\"Cu\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\")\n )\n]", "description": "", "templateType": "anything"}, "line_spacing_mantissa": {"name": "line_spacing_mantissa", "group": "Ungrouped variables", "definition": "siground((line_spacing[1]/(10^(line_spacing_log))),3)", "description": "", "templateType": "anything"}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..8)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["randomiser", "Molecule_identifiers", "HTML", "randomiser_units", "B_list", "wavenumber", "B_value", "B_value2_mantissa", "B_html_rotconst_output", "B_html_rotconst", "B_value2_log", "units_html", "units_output", "Inertia_x", "mantissa_inertia_x", "log_inertia_x", "bond_length_angstroms", "log_angstroms", "reduced_mass", "reduced_mass_kg", "mantissa_reduced_mass_kg", "log_reduced_mass_kg", "line_spacing", "line_spacing_mantissa", "line_spacing_log", "line_spacing_html", "line_spacing_output", "trans_def", "trans", "random_trans", "freq_trans", "freq_trans_select", "freq_trans_log", "freq_trans_mantissa"], "variable_groups": [{"name": "Chemical element masses", "variables": ["rot_constants"]}], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}, "isotope_name": {"parameters": [["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}, "molecule_name": {"parameters": [["atoms", "list"]], "type": "number", "language": "jme", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": false, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

what is the frequency, $\\nu$, in units of Hz, of the {trans} transition in the microwave spectrum of this molecule?

[[0]] $\\times$ 10^[[1]]

The moment of inertia, I, is [[0]] $\\times$ 10^[[1]]kg m².

What is the reduced mass, $\\mu$, in units of g mol^-1?

", "minValue": "{reduced_mass}-{reduced_mass}/50", "maxValue": "{reduced_mass}+{reduced_mass}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The reduced mass, $\\mu$, is [[0]] $\\times$ 10^[[1]] kg molecule^-1.

The bond length, r, is [[0]] $\\times$ 10^[[1]] m.

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{bond_length_angstroms}-{bond_length_angstroms}/50", "maxValue": "{bond_length_angstroms}+{bond_length_angstroms}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{log_angstroms}+{log_angstroms}/50", "maxValue": "{log_angstroms}-{log_angstroms}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Nick's copy of Moment of inertia from rotational constant_3", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_DTrtxfw.png", "/srv/numbas/media/question-resources/image_DTrtxfw.png"], ["question-resources/image_gxf2p8m.png", "/srv/numbas/media/question-resources/image_gxf2p8m.png"], ["question-resources/image_YiGalQz.png", "/srv/numbas/media/question-resources/image_YiGalQz.png"], ["question-resources/image_izx86lb.png", "/srv/numbas/media/question-resources/image_izx86lb.png"], ["question-resources/image_EFznxB4.png", "/srv/numbas/media/question-resources/image_EFznxB4.png"], ["question-resources/image_QRX8AOx.png", "/srv/numbas/media/question-resources/image_QRX8AOx.png"], ["question-resources/image_SkqSr5d.png", "/srv/numbas/media/question-resources/image_SkqSr5d.png"], ["question-resources/image_RvwZ0jx.png", "/srv/numbas/media/question-resources/image_RvwZ0jx.png"], ["question-resources/image_jI1pj1c.png", "/srv/numbas/media/question-resources/image_jI1pj1c.png"], ["question-resources/image_m7iIRpR.png", "/srv/numbas/media/question-resources/image_m7iIRpR.png"], ["question-resources/image_e6HMPkZ.png", "/srv/numbas/media/question-resources/image_e6HMPkZ.png"], ["question-resources/image_Hbraekd.png", "/srv/numbas/media/question-resources/image_Hbraekd.png"], ["question-resources/image_fPp87EN.png", "/srv/numbas/media/question-resources/image_fPp87EN.png"], ["question-resources/image_lrBQiRH.png", "/srv/numbas/media/question-resources/image_lrBQiRH.png"], ["question-resources/image_Eyq56eh.png", "/srv/numbas/media/question-resources/image_Eyq56eh.png"], ["question-resources/image_FjdLy57.png", "/srv/numbas/media/question-resources/image_FjdLy57.png"], ["question-resources/image_fFsskYr.png", "/srv/numbas/media/question-resources/image_fFsskYr.png"], ["question-resources/image_7yxkxrh.png", "/srv/numbas/media/question-resources/image_7yxkxrh.png"], ["question-resources/image_TKd4KFA.png", "/srv/numbas/media/question-resources/image_TKd4KFA.png"], ["question-resources/image_qhno0zh.png", "/srv/numbas/media/question-resources/image_qhno0zh.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}], "tags": [], "metadata": {"description": "The reduced masses are pre-calculated for this question and included in a list. It would be more elegant to program Numbas to permute atoms together to generate diatomic molecules while constraining the permutations to those which are chemically/physically reasonable, so as to allow calculation of each reduced mass directly from the atomic masses- but organising this with high computational efficiency might be a significant programing task (add to \"to do\" list). ", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Given that the bond length, r, of {HTML} is {B_html_output};

", "advice": "

(a) To calculate the reduced mass in g mol^-1, where m₁ is the mass of the first atom and m₂ is the mass of the second atom, each expressed in units of g mol^-1;

\\[\\frac{m_{1}~\\times~m_{2}}{m{_1}+m_{2}}=\\var{reduced_mass}~\\rm g~mol^{-1}\\]

(b) To calculate the reduced mass in kg molecule^-1, divide the reduced mass in g mol^-1 by (the Avogadro number multiplied by 1000)

\\[I={\\mu}r^{2}\\]

\\[I=\\var{mantissa_reduced_mass_kg}~\\times~10^{\\var{log_reduced_mass_kg}}~{\\rm kg}~\\times~(\\var{bond_length_angstroms}~\\times~10^{{\\var{log_angstroms}}}~{\\rm m})^{2}\\]

\\[=\\var{mantissa_inertia_x}\\times 10^{\\var{log_inertia_x}}~{\\rm~kg~m^{2}}\\]

(d)

(a) Finally, calculate the rotational constant, B

\\[B=\\frac{h}{8\\pi^{2}I}\\]

\\[B=\\frac{h}{8\\pi^{2}I}=\\frac{6.626~\\times~10^{-34}{\\rm~J~s}}{8\\pi^{2}~\\times\\var{mantissa_inertia_x}\\times 10^{\\var{log_inertia_x}}{\\rm kg~m^2}}={\\var{B_value2_mantissa}\\times ~10^{\\var {B_value2_log}}~{\\rm Hz}}\\]

", "rulesets": {"": []}, "variables": {"log_inertia_x": {"name": "log_inertia_x", "group": "Ungrouped variables", "definition": "floor(log(Inertia_x))+(-47)", "description": "", "templateType": "anything"}, "randomiser_units": {"name": "randomiser_units", "group": "Ungrouped variables", "definition": "0", "description": "

randomi

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Rotational constants data from;

<https://catalog.data.gov/dataset/nist-computational-chemistry-comparison-and-benchmark-database-srd-101>

augmented with reduced masses calculated from IUPAC Green Book.

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What is the reduced mass, $\\mu$, in units of g mol^-1?

The reduced mass, $\\mu$, can also be expressed as [[0]] $\\times$ 10^[[1]] kg molecule^-1.

The moment of inertia, I, is [[0]] $\\times$ 10^[[1]] kg m².

The rotational constant, B, is [[0]] $\\times$ 10^[[1]]Hz.

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{B_value2_mantissa}-{B_value2_mantissa}/50", "maxValue": "{B_value2_mantissa}+{B_value2_mantissa}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{B_value2_log}-{B_value2_log}/50", "maxValue": "{B_value2_log}+{B_value2_log}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}]}, {"name": "Moment of inertia from rotational constant_2", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_DTrtxfw.png", "/srv/numbas/media/question-resources/image_DTrtxfw.png"], ["question-resources/image_gxf2p8m.png", "/srv/numbas/media/question-resources/image_gxf2p8m.png"], ["question-resources/image_YiGalQz.png", "/srv/numbas/media/question-resources/image_YiGalQz.png"], ["question-resources/image_izx86lb.png", "/srv/numbas/media/question-resources/image_izx86lb.png"], ["question-resources/image_EFznxB4.png", "/srv/numbas/media/question-resources/image_EFznxB4.png"], ["question-resources/image_QRX8AOx.png", "/srv/numbas/media/question-resources/image_QRX8AOx.png"], ["question-resources/image_SkqSr5d.png", "/srv/numbas/media/question-resources/image_SkqSr5d.png"], ["question-resources/image_RvwZ0jx.png", "/srv/numbas/media/question-resources/image_RvwZ0jx.png"], ["question-resources/image_jI1pj1c.png", "/srv/numbas/media/question-resources/image_jI1pj1c.png"], ["question-resources/image_m7iIRpR.png", "/srv/numbas/media/question-resources/image_m7iIRpR.png"], ["question-resources/image_e6HMPkZ.png", "/srv/numbas/media/question-resources/image_e6HMPkZ.png"], ["question-resources/image_Hbraekd.png", "/srv/numbas/media/question-resources/image_Hbraekd.png"], ["question-resources/image_fPp87EN.png", "/srv/numbas/media/question-resources/image_fPp87EN.png"], ["question-resources/image_lrBQiRH.png", "/srv/numbas/media/question-resources/image_lrBQiRH.png"], ["question-resources/image_Eyq56eh.png", "/srv/numbas/media/question-resources/image_Eyq56eh.png"], ["question-resources/image_FjdLy57.png", "/srv/numbas/media/question-resources/image_FjdLy57.png"], ["question-resources/image_fFsskYr.png", "/srv/numbas/media/question-resources/image_fFsskYr.png"], ["question-resources/image_7yxkxrh.png", "/srv/numbas/media/question-resources/image_7yxkxrh.png"], ["question-resources/image_TKd4KFA.png", "/srv/numbas/media/question-resources/image_TKd4KFA.png"], ["question-resources/image_qhno0zh.png", "/srv/numbas/media/question-resources/image_qhno0zh.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}], "tags": [], "metadata": {"description": "The reduced masses are pre-calculated for this question and included in a list. It would be more elegant to program Numbas to permute atoms together to generate diatomic molecules while constraining the permutations to those which are chemically/physically reasonable, so as to allow calculation of each reduced mass directly from the atomic masses- but organising this with high computational efficiency might be a significant programing task (add to \"to do\" list). ", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Given that the moment of inertia, I, of {HTML} is {B_html_output};

", "advice": "

(a) First, calculate the rotational constant, B

\\[B=\\frac{h}{8\\pi^{2}I}\\]

\\[B=\\frac{h}{8\\pi^{2}I}=\\frac{6.626~\\times~10^{-34}{\\rm~J~s}}{8\\pi^{2}~\\times\\var{mantissa_inertia_x}\\times 10^{\\var{log_inertia_x}}~{\\rm kg~m^{2}}}=\\var{B_value2_mantissa}\\times ~10^{\\var {B_value2_log}}~{\\rm Hz}\\]

(b) To calculate the reduced mass in g mol^-1, where m₁ is the mass of the first atom and m₂ is the mass of the second atom, each expressed in units of g mol^-1;

\\[\\frac{m_{1}~\\times~m_{2}}{m{_1}+m_{2}}=\\var{reduced_mass}~\\rm g~mol^{-1}\\]

(c) To calculate the reduced mass in kg molecule^-1, divide the reduced mass in g mol^-1 by (the Avogadro number multiplied by 1000)

(d) To determine the bond length from the moment of inertia and reduced mass;

\\[I=\\mu~r^{2}~~~~~~~~~~{\\rm so}~~~~~~~~~ r=\\sqrt{\\frac{I}{\\mu}}\\]

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Rotational constants data from;

<https://catalog.data.gov/dataset/nist-computational-chemistry-comparison-and-benchmark-database-srd-101>

augmented with reduced masses calculated from IUPAC Green Book.

", "templateType": "json"}, "B_value2_log": {"name": "B_value2_log", "group": "Ungrouped variables", "definition": "floor(log(B_list[1]))", "description": "", "templateType": "anything"}, "B_html": {"name": "B_html", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+{mantissa_inertia_x}+\" \"+\"× \"+\"10\"+\"^{\"+{log_inertia_x}+\"}\"+\" \"+\"kg m²\"+\"\")\n )\n]", "description": "", "templateType": "anything"}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "Molecule_identifiers[randomiser]", "description": "", "templateType": "anything"}, "B_html_output": {"name": "B_html_output", "group": "Ungrouped variables", "definition": "B_html[randomiser_units]", "description": "", "templateType": "anything"}, "randomiser_units": {"name": "randomiser_units", "group": "Ungrouped variables", "definition": "0", "description": "

randomi

", "templateType": "anything"}, "B_list": {"name": "B_list", "group": "Ungrouped variables", "definition": "[\n (siground((get((rot_constants[randomiser]),\"B\",0)),4)),\n (siground((get((rot_constants[randomiser]),\"B\",0))*3*10^10,4))\n]", "description": "", "templateType": "anything"}, "B_value": {"name": "B_value", "group": "Ungrouped variables", "definition": "B_list[randomiser_units]", "description": "", "templateType": "anything"}, "mantissa_inertia_x": {"name": "mantissa_inertia_x", "group": "Ungrouped variables", "definition": "precround(Inertia_x/(10^floor(log(Inertia_x))),3)", "description": "", "templateType": "anything"}, "log_angstroms": {"name": "log_angstroms", "group": "Ungrouped variables", "definition": "-10", "description": "", "templateType": "anything"}, "bond_length_angstroms": {"name": "bond_length_angstroms", "group": "Ungrouped variables", "definition": "siground(((mantissa_inertia_x*10^(log_inertia_x)*10^(20)*1000)/((get((rot_constants[randomiser]),\"reduced mass\",0))/(6.022*10^(23))))^(0.5),5)", "description": "", "templateType": "anything"}, "B_value2_mantissa": {"name": "B_value2_mantissa", "group": "Ungrouped variables", "definition": "B_list[1]/(10^(B_value2_log))", "description": "", "templateType": "anything"}, "reduced_mass_kg": {"name": "reduced_mass_kg", "group": "Ungrouped variables", "definition": "siground((reduced_mass/6.022),3)", "description": "", "templateType": "anything"}, "log_inertia_x": {"name": "log_inertia_x", "group": "Ungrouped variables", "definition": "floor(log(Inertia_x))+(-47)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["randomiser", "Molecule_identifiers", "HTML", "randomiser_units", "B_list", "wavenumber", "B_value", "B_value2_mantissa", "B_value2_log", "B_html", "B_html_output", "Inertia_x", "mantissa_inertia_x", "log_inertia_x", "bond_length_angstroms", "log_angstroms", "reduced_mass", "reduced_mass_kg", "mantissa_reduced_mass_kg", "log_reduced_mass_kg"], "variable_groups": [{"name": "Chemical element masses", "variables": ["rot_constants"]}], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}, "molecule_name": {"parameters": [["atoms", "list"]], "type": "number", "language": "jme", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}, "isotope_name": {"parameters": [["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": false, "unitTests": [], "prompt": "

The rotational constant, B, is [[0]] $\\times$ 10^[[1]]Hz.

What is the reduced mass, $\\mu$, in units of g mol^-1?

The reduced mass, $\\mu$, is [[0]] $\\times$ 10^[[1]] kg molecule^-1.

The bond length, r, is [[0]] $\\times$ 10^[[1]] m.

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{bond_length_angstroms}-{bond_length_angstroms}/50", "maxValue": "{bond_length_angstroms}+{bond_length_angstroms}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{log_angstroms}+{log_angstroms}/50", "maxValue": "{log_angstroms}-{log_angstroms}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}]}, {"name": "Rotational constant and bond length from line spacing", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_DTrtxfw.png", "/srv/numbas/media/question-resources/image_DTrtxfw.png"], ["question-resources/image_gxf2p8m.png", "/srv/numbas/media/question-resources/image_gxf2p8m.png"], ["question-resources/image_YiGalQz.png", "/srv/numbas/media/question-resources/image_YiGalQz.png"], ["question-resources/image_izx86lb.png", "/srv/numbas/media/question-resources/image_izx86lb.png"], ["question-resources/image_EFznxB4.png", "/srv/numbas/media/question-resources/image_EFznxB4.png"], ["question-resources/image_QRX8AOx.png", "/srv/numbas/media/question-resources/image_QRX8AOx.png"], ["question-resources/image_SkqSr5d.png", "/srv/numbas/media/question-resources/image_SkqSr5d.png"], ["question-resources/image_RvwZ0jx.png", "/srv/numbas/media/question-resources/image_RvwZ0jx.png"], ["question-resources/image_jI1pj1c.png", "/srv/numbas/media/question-resources/image_jI1pj1c.png"], ["question-resources/image_m7iIRpR.png", "/srv/numbas/media/question-resources/image_m7iIRpR.png"], ["question-resources/image_e6HMPkZ.png", "/srv/numbas/media/question-resources/image_e6HMPkZ.png"], ["question-resources/image_Hbraekd.png", "/srv/numbas/media/question-resources/image_Hbraekd.png"], ["question-resources/image_fPp87EN.png", "/srv/numbas/media/question-resources/image_fPp87EN.png"], ["question-resources/image_lrBQiRH.png", "/srv/numbas/media/question-resources/image_lrBQiRH.png"], ["question-resources/image_Eyq56eh.png", "/srv/numbas/media/question-resources/image_Eyq56eh.png"], ["question-resources/image_FjdLy57.png", "/srv/numbas/media/question-resources/image_FjdLy57.png"], ["question-resources/image_fFsskYr.png", "/srv/numbas/media/question-resources/image_fFsskYr.png"], ["question-resources/image_7yxkxrh.png", "/srv/numbas/media/question-resources/image_7yxkxrh.png"], ["question-resources/image_TKd4KFA.png", "/srv/numbas/media/question-resources/image_TKd4KFA.png"], ["question-resources/image_qhno0zh.png", "/srv/numbas/media/question-resources/image_qhno0zh.png"], ["question-resources/rot_spectrum.jpg", "/srv/numbas/media/question-resources/rot_spectrum.jpg"], ["question-resources/rot_spectrum_bVm45Fn.jpg", "/srv/numbas/media/question-resources/rot_spectrum_bVm45Fn.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}, {"name": "Hanno Kossen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2434/"}], "tags": [], "metadata": {"description": "The reduced masses are pre-calculated for this question and included in a list. It would be more elegant to program Numbas to permute atoms together to generate diatomic molecules while constraining the permutations to those which are chemically/physically reasonable, so as to allow calculation of each reduced mass directly from the atomic masses- but organising this with high computational efficiency might be a significant programing task (add to \"to do\" list). ", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Given that the interval between two transitions (the {trans_def} transitions) in the microwave spectrum of {HTML} is {line_spacing_output};

\n\n\n\n", "advice": "

First, revise how the interval between rotational transitions in an observed spectrum (bottom of figure), which is sometimes referred as the \"line spacing\", connects with the transitions between energy levels in a molecule (top of figure). Think about how the transitions listed in the question connect with the figure below;

a) If presented with a wavenumber, you will need to start by converting this into a frequency while noting that;

\\[c=\\lambda\\nu\\]

so;

\\[{\\rm{line~spacing}}~{\\rm{in~Hz}}=\\frac{c}{\\lambda}=c ~({\\rm in~cm~s^{-1}})~\\times~{\\rm wavenumber~of~line~spacing~(in~cm^{-1})}\\]

so the line spacing (in Hz) can be calculated as;

\\[2.998 \\times 10^{10}~{\\rm cm~s^{-1}}\\times~\\var{wavenumber_line_spacing}~{\\rm cm^{-1}}=\\var{line_spacing_mantissa}~\\times~10^{\\var{line_spacing_log}}~{\\rm Hz}\\]

Noting that the interval between rotational transitions (the line spacing) in the spectrum is equal to 2B, we can say that;

\\[\\frac{\\rm {line~spacing}}{2} = B\\]

so;

\\[\\frac{\\var{line_spacing_mantissa}~\\times~10^{\\var{line_spacing_log}}~{\\rm Hz}}{2} = \\var{B_value2_mantissa}\\times 10^{\\var{B_value2_log}}~{\\rm Hz}=B\\]

(b) Next, calculate the moment of inertia, I

\\[I=\\frac{h}{8\\pi^{2}B}\\]

(b) To calculate the reduced mass in g mol^-1, where m₁ is the mass of the first atom and m₂ is the mass of the second atom, each expressed in units of g mol^-1;

\\[\\frac{m_{1}~\\times~m_{2}}{m{_1}+m_{2}}=\\var{reduced_mass}~\\rm g~mol^{-1}\\]

(c) To calculate the reduced mass in kg molecule^-1, divide the reduced mass in g mol^-1 by (the Avogadro number multiplied by 1000 g kg^-1)

(d) To determine the bond length from the moment of inertia and reduced mass;

\\[I=\\mu~r^{2}~~~~~~~~~~{\\rm so}~~~~~~~~~ r=\\sqrt{\\frac{I}{\\mu}}\\]

", "rulesets": {"": []}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"bond_length_angstroms": {"name": "bond_length_angstroms", "group": "Ungrouped variables", "definition": "siground(((mantissa_inertia_x*10^(log_inertia_x)*10^(20)*1000)/((get((rot_constants[randomiser]),\"reduced mass\",0))/(6.022*10^(23))))^(0.5),5)", "description": "", "templateType": "anything", "can_override": false}, "units_html": {"name": "units_html", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything", "can_override": false}, "log_inertia_x": {"name": "log_inertia_x", "group": "Ungrouped variables", "definition": "floor(log(Inertia_x))+(-47)", "description": "", "templateType": "anything", "can_override": false}, "Molecule_identifiers": {"name": "Molecule_identifiers", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"H\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"H\"+\"^\"+\"81\"+\"\"+\"Br\"+\"\"),\n html(\"\"+\"H\"+\"I\"+\"\"),\n html(\"\"+\"Na\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"Na\"+\"^\"+\"79\"+\"\"+\"Br\"+\"\"),\n html(\"\"+\"Li\"+\"F\"+\"\"),\n html(\"\"+\"Li\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\"),\n html(\"\"+\"^\"+\"63\"+\"\"+\"Cu\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"63\"+\"\"+\"Cu\"+\"^\"+\"35\"+\"\"+\"Cl\"+\"\")\n )\n]", "description": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n", "templateType": "anything", "can_override": false}, "reduced_mass_kg": {"name": "reduced_mass_kg", "group": "Ungrouped variables", "definition": "siground((reduced_mass/6.022),3)", "description": "", "templateType": "anything", "can_override": false}, "trans_def": {"name": "trans_def", "group": "Ungrouped variables", "definition": "random(\n html(\"\"+\"J = \"+\"3\"+\" → \"+\"2\"+\" and the \"+\"J = \"+\"2\"+\" → \"+\"1\"+\"\"),\n html(\"\"+\"J = \"+\"1\"+\" → \"+\"0\"+\" and the \"+\"J = \"+\"2\"+\" → \"+\"1\"+\"\"),\n html(\"\"+\"J = \"+\"3\"+\" → \"+\"2\"+\" and the \"+\"J = \"+\"4\"+\" → \"+\"3\"+\"\")\n)\n", "description": "", "templateType": "anything", "can_override": false}, "log_reduced_mass_kg": {"name": "log_reduced_mass_kg", "group": "Ungrouped variables", "definition": "floor(log(reduced_mass_kg))+(-26)", "description": "", "templateType": "anything", "can_override": false}, "B_value": {"name": "B_value", "group": "Ungrouped variables", "definition": "B_list[randomiser_units]", "description": "", "templateType": "anything", "can_override": false}, "line_spacing_html": {"name": "line_spacing_html", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+{wavenumber_line_spacing}+\" \"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+{line_spacing_mantissa}+\" \"+\"× \"+\"10\"+\"^{\"+{line_spacing_log}+\"}\"+\" \"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything", "can_override": false}, "log_angstroms": {"name": "log_angstroms", "group": "Ungrouped variables", "definition": "-10", "description": "", "templateType": "anything", "can_override": false}, "mantissa_reduced_mass_kg": {"name": "mantissa_reduced_mass_kg", "group": "Ungrouped variables", "definition": "reduced_mass_kg/(10^(floor(log(reduced_mass_kg))))", "description": "", "templateType": "anything", "can_override": false}, "rot_constants": {"name": "rot_constants", "group": "Chemical element masses", "definition": "json_decode(safe(\"[\\n{\\\"Formula\\\":\\\"H35Cl\\\",\\\"reduced mass\\\":0.979592539,\\\"nu\\\":2990.946,\\\"B\\\":1.059341600000000e+001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647010\\\",\\\"SQUIB\\\":\\\"1979HUB/HER\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"H81Br\\\",\\\"reduced mass\\\":0.995426835,\\\"nu\\\":2648.975,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":8.464880000000001e+000,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10035106\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"HI\\\",\\\"reduced mass\\\":0.999884347,\\\"nu\\\":2309.01,\\\"B\\\":6.426365000000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"6.426365000000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"10034852\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na35Cl\\\",\\\"reduced mass\\\":13.87068615,\\\"nu\\\":366,\\\"B\\\":2.180630000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647145\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Na79Br\\\",\\\"reduced mass\\\":17.80343514,\\\"nu\\\":302,\\\"Comment\\\":\\\"Be\\\",\\\"B\\\":1.512533000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.512533000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7647156\\\",\\\"SQUIB\\\":\\\"webbook\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"LiF\\\",\\\"reduced mass\\\":5.123810029,\\\"Comment\\\":\\\"7Li\\\",\\\"nu\\\":910.34,\\\"B\\\":1.345257590000000e+000,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.345257590000000e+000\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7789244\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"Li35Cl\\\",\\\"reduced mass\\\":5.843574224,\\\"nu\\\":643.31,\\\"B\\\":7.065225000000001e-001,\\\"charge\\\":\\\"0\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7447418\\\",\\\"SQUIB\\\":\\\"2007Iri:389\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63CuF\\\",\\\"reduced mass\\\":14.59283587,\\\"Comment\\\":\\\"Y01\\\",\\\"nu\\\":622.6,\\\"B\\\":3.794029400000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"3.794029400000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"13478416\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linera\\\",\\\"config\\\":\\\"1\\\"},\\n{\\\"Formula\\\":\\\"63Cu35Cl\\\",\\\"reduced mass\\\":22.47814771,\\\"Comment\\\":\\\"63Cu 35Cl\\\",\\\"nu\\\":415.29,\\\"B\\\":1.782489000000000e-001,\\\"charge\\\":\\\"0\\\",\\\"C\\\":\\\"1.782489000000000e-001\\\",\\\"symno\\\":\\\"1\\\",\\\"casno\\\":\\\"7758896\\\",\\\"SQUIB\\\":\\\"NISTdiatomic\\\",\\\"state\\\":\\\"1\\\",\\\"polyatomic\\\":\\\"linear\\\",\\\"config\\\":\\\"1\\\"}\\n]\"))", "description": "

Rotational constants data from;

<https://catalog.data.gov/dataset/nist-computational-chemistry-comparison-and-benchmark-database-srd-101>

augmented with reduced masses calculated from IUPAC Green Book.

\n\n

\n\n\n", "templateType": "json", "can_override": false}, "B_list": {"name": "B_list", "group": "Ungrouped variables", "definition": "[\n (siground((get((rot_constants[randomiser]),\"B\",0)),4)),\n (siground((get((rot_constants[randomiser]),\"B\",0))*3*10^10,4))\n]", "description": "

\n\n\n\n\n\n", "templateType": "anything", "can_override": false}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..8)", "description": "

0 = html(\"\"+\"H\"+\"\"+\"35\"+\"\"+\"Cl\"+\"\"),
1 = html(\"\"+\"H\"+\"\"+\"81\"+\"\"+\"Br\"+\"\"),
2 = html(\"\"+\"H\"+\"I\"+\"\"),
3 = html(\"\"+\"Na\"+\"\"+\"35\"+\"\"+\"Cl\"+\"\"),
4 = html(\"\"+\"Na\"+\"\"+\"79\"+\"\"+\"Br\"+\"\"),
5 = html(\"\"+\"Li\"+\"F\"+\"\"),
6 = html(\"\"+\"Li\"+\"\"+\"35\"+\"\"+\"Cl\"+\"\"),
7 = html(\"\"+\"\"+\"63\"+\"\"+\"Cu\"+\"F\"+\"\"),
8 = html(\"\"+\"\"+\"63\"+\"\"+\"Cu\"+\"\"+\"35\"+\"\"+\"Cl\"+\"\")

\n\n\n\n\n\n\n\n\n\n\n\n", "templateType": "anything", "can_override": false}, "B_value2_mantissa": {"name": "B_value2_mantissa", "group": "Ungrouped variables", "definition": "B_list[1]/(10^(B_value2_log))", "description": "", "templateType": "anything", "can_override": false}, "B_html_rotconst": {"name": "B_html_rotconst", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+{B_value}+\" \"+\"cm\"+\"^\"+\"-1\"+\"\"+\"\"),\n html(\"\"+{B_value2_mantissa}+\" \"+\"× \"+\"10\"+\"^{\"+{B_value2_log}+\"}\"+\" \"+\"Hz\"+\"\")\n )\n]", "description": "", "templateType": "anything", "can_override": false}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "Molecule_identifiers[randomiser]", "description": "

\n\n\n\n\n\n\n\n\n\n\n\n", "templateType": "anything", "can_override": false}, "B_value2_log": {"name": "B_value2_log", "group": "Ungrouped variables", "definition": "floor(log(B_list[1]))", "description": "", "templateType": "anything", "can_override": false}, "Inertia_x": {"name": "Inertia_x", "group": "Ungrouped variables", "definition": "siground((6.626*10^(13))/(8*(3.14^2)*(B_list[1])),4)", "description": "", "templateType": "anything", "can_override": false}, "line_spacing_output": {"name": "line_spacing_output", "group": "Ungrouped variables", "definition": "line_spacing_html[randomiser_units]", "description": "", "templateType": "anything", "can_override": false}, "reduced_mass": {"name": "reduced_mass", "group": "Ungrouped variables", "definition": "siground(get((rot_constants[randomiser]),\"reduced mass\",0),4)", "description": "", "templateType": "anything", "can_override": false}, "wavenumber_line_spacing": {"name": "wavenumber_line_spacing", "group": "Ungrouped variables", "definition": "2*B_list[0]", "description": "", "templateType": "anything", "can_override": false}, "line_spacing_log": {"name": "line_spacing_log", "group": "Ungrouped variables", "definition": "floor(log(line_spacing[1]))", "description": "", "templateType": "anything", "can_override": false}, "B_html_rotconst_output": {"name": "B_html_rotconst_output", "group": "Ungrouped variables", "definition": "B_html_rotconst[randomiser_units]", "description": "", "templateType": "anything", "can_override": false}, "line_spacing": {"name": "line_spacing", "group": "Ungrouped variables", "definition": "[2*B_list[0],2*B_list[1]]", "description": "", "templateType": "anything", "can_override": false}, "mantissa_inertia_x": {"name": "mantissa_inertia_x", "group": "Ungrouped variables", "definition": "precround(Inertia_x/(10^floor(log(Inertia_x))),3)", "description": "", "templateType": "anything", "can_override": false}, "line_spacing_mantissa": {"name": "line_spacing_mantissa", "group": "Ungrouped variables", "definition": "line_spacing[1]/(10^(line_spacing_log))", "description": "", "templateType": "anything", "can_override": false}, "randomiser_units": {"name": "randomiser_units", "group": "Ungrouped variables", "definition": "random(0..1)", "description": "

randomi

\n\n\n\n\n\n", "templateType": "anything", "can_override": false}, "units_output": {"name": "units_output", "group": "Ungrouped variables", "definition": "units_html[randomiser_units]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["randomiser", "Molecule_identifiers", "HTML", "randomiser_units", "B_list", "wavenumber_line_spacing", "B_value", "B_value2_mantissa", "B_html_rotconst_output", "B_html_rotconst", "B_value2_log", "units_html", "units_output", "Inertia_x", "log_inertia_x", "mantissa_inertia_x", "bond_length_angstroms", "log_angstroms", "reduced_mass", "reduced_mass_kg", "mantissa_reduced_mass_kg", "log_reduced_mass_kg", "line_spacing", "line_spacing_mantissa", "line_spacing_log", "line_spacing_html", "line_spacing_output", "trans_def"], "variable_groups": [{"name": "Chemical element masses", "variables": ["rot_constants"]}], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}, "isotope_name": {"parameters": [["atom", "dict"]], "type": "string", "language": "jme", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"^{\"+string(atom[\"isotope\"])+\"}\",\"\")+atom[\"symbol\"])+\"\")"}, "molecule_name": {"parameters": [["atoms", "list"]], "type": "number", "language": "jme", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": false, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Enter the rotational constant, B, in units of Hz;

[[0]] $\\times$ 10^[[1]]

\n\n\n\n", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{B_value2_mantissa}-{B_value2_mantissa}/50", "maxValue": "{B_value2_mantissa}+{B_value2_mantissa}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{B_value2_log}-{B_value2_log}/50", "maxValue": "{B_value2_log}+{B_value2_log}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": false, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The moment of inertia, I, is [[0]] $\\times$ 10^[[1]]kg m².

What is the reduced mass, $\\mu$, in units of g mol^-1?

", "minValue": "{reduced_mass}-{reduced_mass}/50", "maxValue": "{reduced_mass}+{reduced_mass}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The reduced mass, $\\mu$, is [[0]] $\\times$ 10^[[1]] kg molecule^-1.

The bond length, r, is [[0]] $\\times$ 10^[[1]] m.

a) This question requires use of the equation that relates the relative populations of states to the temperature and the energy difference between them;

\\[\\frac{N_u}{N_l}=e^{\\frac{-{\\Delta}E}{kT}}\\]

\\[\\frac{N_u}{N_l}=e^{\\frac{-{\\var{Energy_mantissa}\\times10^\\var{Energy_log}}}{1.38~\\times~10^{-23}~\\times~\\var{temp}}}=\\var{D}\\]

b) To convert the energy of a photon into a frequency;

\\[E=h\\nu~\\]

\\[\\frac{E}{h}=\\nu=\\frac{\\var{Energy_mantissa}~\\times~10^\\var{Energy_log}~\\rm J}{6.626~\\times10^{-34}~\\rm~J~s}=\\var{Freq_mantissa}\\times10^{\\var{Freq_log}}~{\\rm Hz}\\]

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"temp": {"name": "temp", "group": "Ungrouped variables", "definition": "random(5..400)", "description": "", "templateType": "anything", "can_override": false}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(150..300)/100", "description": "", "templateType": "anything", "can_override": false}, "Energy_mantissa": {"name": "Energy_mantissa", "group": "Ungrouped variables", "definition": "siground((random(1..100)/10),3)", "description": "", "templateType": "anything", "can_override": false}, "Energy_log": {"name": "Energy_log", "group": "Ungrouped variables", "definition": "random(-23..-22)", "description": "", "templateType": "anything", "can_override": false}, "int_step2": {"name": "int_step2", "group": "Ungrouped variables", "definition": "Energy_log+34", "description": "", "templateType": "anything", "can_override": false}, "int_step": {"name": "int_step", "group": "Ungrouped variables", "definition": "siground(Energy_mantissa/6.626,3)", "description": "", "templateType": "anything", "can_override": false}, "Freq_log": {"name": "Freq_log", "group": "Ungrouped variables", "definition": "floor(log(int_step*10^(int_step2)))", "description": "", "templateType": "anything", "can_override": false}, "Freq_mantissa": {"name": "Freq_mantissa", "group": "Ungrouped variables", "definition": "int_step*10^(int_step2)/10^(Freq_log)", "description": "", "templateType": "anything", "can_override": false}, "A1": {"name": "A1", "group": "Ungrouped variables", "definition": "siground((-energy_mantissa/(1.38*temp)),3)", "description": "", "templateType": "anything", "can_override": false}, "B1": {"name": "B1", "group": "Ungrouped variables", "definition": "10^(Energy_log+23)", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "siground(exp(A1*B1),3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["temp", "randomiser", "Energy_mantissa", "Energy_log", "int_step2", "int_step", "Freq_log", "Freq_mantissa", "A1", "B1", "D"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the relative populations of an upper quantum state and a lower quantum state, (expressed as the ratio, ($N_u/N_l$)), given a temperature, T, of {temp} K and an energy difference between the states, ${\\Delta}E$, of {Energy_mantissa} $\\times$ 10^{Energy_log}J;

$N_u/N_l$ = [[0]]

A transition occurs between the upper state and the lower state such that a photon is emitted. What is the frequency, $\\nu$, of the photon (in Hz)?

[[0]] $\\times$ 10^[[1]] Hz

a) This question requires use of the equation that relates the relative populations of states to the temperature and the energy difference between them;

\\[\\frac{N_u}{N_l}=e^{\\frac{-{\\Delta}E}{kT}}\\]

\\[{\\rm ln}(\\frac{N_u}{N_l})=\\frac{-{\\Delta}E}{kT}\\]

\\[kT{\\rm ln}(\\frac{N_u}{N_l})={-{\\Delta}E}\\]

\\[-(1.38~\\times~10^{-23}{\\rm~J~K^{-1}}\\times~\\var{temp}~{\\rm K}~\\times~{\\rm{ln}~}\\var{NuNl_rounded})=\\var{Energy_mantissa}\\times10^\\var{Energy_log}{\\rm J}\\]

b) To convert the energy of a photon into a frequency;

\\[E=h\\nu~\\]

\\[\\frac{E}{h}=\\nu=\\frac{\\var{Energy_mantissa}~\\times~10^\\var{Energy_log}~\\rm J}{6.626~\\times10^{-34}~\\rm~J~s}=\\var{Frequency_mantissa}\\times10^{\\var{Frequency_log}}~{\\rm Hz}\\]

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Frequency_log": {"name": "Frequency_log", "group": "Ungrouped variables", "definition": "floor(log(int_step*10^(int_step2)))", "description": "", "templateType": "anything", "can_override": false}, "Frequency_mantissa": {"name": "Frequency_mantissa", "group": "Ungrouped variables", "definition": "int_step*10^(int_step2)/10^(Frequency_log)", "description": "", "templateType": "anything", "can_override": false}, "Energy_mantissa": {"name": "Energy_mantissa", "group": "Ungrouped variables", "definition": "siground(dec(random(1000..5000)/1000),3)", "description": "", "templateType": "anything", "can_override": false}, "temp": {"name": "temp", "group": "Ungrouped variables", "definition": "random(100..350)", "description": "", "templateType": "anything", "can_override": false}, "Energy_log": {"name": "Energy_log", "group": "Ungrouped variables", "definition": "-21", "description": "", "templateType": "anything", "can_override": false}, "int_step": {"name": "int_step", "group": "Ungrouped variables", "definition": "siground(Energy_mantissa/6.626,3)", "description": "", "templateType": "anything", "can_override": false}, "int_step2": {"name": "int_step2", "group": "Ungrouped variables", "definition": "Energy_log+34", "description": "", "templateType": "anything", "can_override": false}, "A1": {"name": "A1", "group": "Ungrouped variables", "definition": "-energy_mantissa/(1.380649*temp)", "description": "", "templateType": "anything", "can_override": false}, "B1": {"name": "B1", "group": "Ungrouped variables", "definition": "10^(Energy_log+23)", "description": "", "templateType": "anything", "can_override": false}, "NuNl": {"name": "NuNl", "group": "Ungrouped variables", "definition": "exp(A1*B1)", "description": "", "templateType": "anything", "can_override": false}, "NuNl_rounded": {"name": "NuNl_rounded", "group": "Ungrouped variables", "definition": "siground(NuNl,3)", "description": "", "templateType": "anything", "can_override": false}, "EfromNuNl": {"name": "EfromNuNl", "group": "Ungrouped variables", "definition": "ln(NuNl)*1.380649*temp", "description": "", "templateType": "anything", "can_override": false}, "EfromNuNl_rounded": {"name": "EfromNuNl_rounded", "group": "Ungrouped variables", "definition": "ln(nunl_rounded)*1.380649*temp", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["temp", "Energy_mantissa", "Energy_log", "Frequency_log", "Frequency_mantissa", "int_step", "int_step2", "A1", "B1", "NuNl", "NuNl_rounded", "EfromNuNl", "EfromNuNl_rounded"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the energy difference, $\\Delta$E, between two states given that the relative populations of these states, $N_u/N_l$={NuNl_rounded} when the temperature, T, is {temp} K. The number of molecules in the upper state is $N_u$ and the number of molecules in the lower state is $N_l$;

${\\Delta}E$ = [[0]] $\\times$ 10^[[1]] J

A transition occurs between the upper state and the lower state such that a photon is emitted. What is the frequency, $\\nu$, of the photon (in Hz)?

[[0]] $\\times$ 10^[[1]] Hz

The answer is a comma-separated list of numbers.

The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.

You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.

", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n if(settings[\"correctAnswerFractions\"],\n map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n ,\n settings[\"correctAnswer\"]\n ),\n settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n \"Enter a list of numbers separated by {settings['separator']}.\",\n \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n true,\n let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n warn(wrong+\" is not a valid number\");\n fail(wrong+\" is not a valid number.\")\n )\n )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n multiply_credit(0.5,\"Not in order\")\n )\n\nincluded:\nmap(\n let(\n num_student,len(filter(x=y,y,interpreted_answer)),\n num_expected,len(filter(x=y,y,expected_numbers)),\n switch(\n num_student=num_expected,\n true,\n num_studentThe separate items in the student's answer

", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "

Is every number in the student's list valid?

", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n true,\n let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n warn(wrong+\" is not a valid number\");\n fail(wrong+\" is not a valid number.\")\n )\n )"}, {"name": "is_sorted", "description": "

Are the student's answers in ascending order?

", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n multiply_credit(0.5,\"Not in order\")\n )"}, {"name": "included", "description": "

Is each number in the expected answer present in the student's list the correct number of times?

", "definition": "map(\n let(\n num_student,len(filter(x=y,y,interpreted_answer)),\n num_expected,len(filter(x=y,y,expected_numbers)),\n switch(\n num_student=num_expected,\n true,\n num_studentHas every number been included the right number of times?

", "definition": "all(included)"}, {"name": "no_extras", "description": "

True if the student's list doesn't contain any numbers that aren't in the expected answer.

", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n true\n ,\n incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n false\n )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n map(\n if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n ,x\n ,bits\n )\n)"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "

Should the answer be considered as a set, so the number of times an element occurs doesn't matter?

", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "

Numbers included in the student's answer that are not in the expected list.

\n\n\n\n\n\n\n\n\n", "preamble": {"js": "", "css": ""}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["gyromag", "randomiser", "Spin_select", "levels", "Nucleus_select", "gyromag_select", "html_out", "html", "level_labels", "labels"], "advice": "

(i) First, retrieve the correct value of the nuclear spin for a {Nucleus_select} nucleus.

The number of levels is given by;

\\[{\\rm~number~of~levels}=2I+1\\]

so;

\\[(2~\\times~\\var{Spin_select})+1=\\var{levels}\\]

(ii) The m_I quantum number represents the projection of the nuclear spin vector onto the z axis and can take values as follows for any given nucleus;

\\[m_{I}=-I,-I+1,-I+2,...I\\]

so the answer for {Nucleus_select} is;

{labels}

", "tags": [], "variable_groups": [], "parts": [{"showFractionHint": true, "useCustomName": false, "marks": 1, "allowFractions": false, "showCorrectAnswer": true, "variableReplacements": [], "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}, "minValue": "{levels}-{levels}/50", "prompt": "

How many nuclear spin levels exist for a {Nucleus_select} nucleus when it is exposed to an applied, external magnetic field?

\n\n\n\n\n\n\n\n\n\n\n\n\n", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "maxValue": "{levels}+{levels}/50", "unitTests": [], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "adaptiveMarkingPenalty": 0, "type": "numberentry", "customName": "", "mustBeReduced": false}, {"useCustomName": false, "showCorrectAnswer": true, "marks": 1, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "adaptiveMarkingPenalty": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "list-of-numbers", "customName": "", "settings": {"correctAnswerFractions": false, "correctAnswer": "{labels}", "allowFractions": false}, "prompt": "

What values of the nuclear spin quantum number, m_I, are available to the {html} nucleus?

\n\n\n\n\n\n\n\n\n"}], "variables": {"levels": {"definition": "(2*Spin_select)+1", "name": "levels", "group": "Ungrouped variables", "templateType": "anything", "description": "

\n\n\n\n\n\n\n\n\n\n\n\n"}, "randomiser": {"definition": "random(0..8)", "name": "randomiser", "group": "Ungrouped variables", "templateType": "anything", "description": "

\n\n\n\n\n\n\n\n

\n\n\n\n\n\n\n\n"}, "gyromag": {"definition": "json_decode(safe(\"[\\n {\\\"Nucleus\\\":\\\"1H\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":267.5},\\n {\\\"Nucleus\\\":\\\"13C\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":67.3},\\n {\\\"Nucleus\\\":\\\"14N\\\",\\\"Spin\\\":1,\\\"gyromagnetic ratio\\\":19.3},\\n {\\\"Nucleus\\\":\\\"19F\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":251.7},\\n {\\\"Nucleus\\\":\\\"31P\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":\\\"Null\\\"},\\n {\\\"Nucleus\\\":\\\"33S\\\",\\\"Spin\\\":1.5,\\\"gyromagnetic ratio\\\":\\\"Null\\\"},\\n {\\\"Nucleus\\\":\\\"59Co\\\",\\\"Spin\\\":3.5,\\\"gyromagnetic ratio\\\":\\\"Null\\\"},\\n {\\\"Nucleus\\\":\\\"87Sr\\\",\\\"Spin\\\":4.5,\\\"gyromagnetic ratio\\\":\\\"Null\\\"},\\n {\\\"Nucleus\\\":\\\"101Ru\\\",\\\"Spin\\\":2.5,\\\"gyromagnetic ratio\\\":\\\"Null\\\"} \\n]\"))", "name": "gyromag", "group": "Ungrouped variables", "templateType": "json", "description": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"}, "level_labels": {"definition": "json_decode(safe(\"[\\n{\\\"Labels\\\":[-0.5,0.5]}, \\n{\\\"Labels\\\":[-0.5,0.5]}, \\n{\\\"Labels\\\":[-1,0,1]},\\n{\\\"Labels\\\":[-0.5,0.5]},\\n{\\\"Labels\\\":[-0.5,0.5]},\\n{\\\"Labels\\\":[-1.5,-0.5,0.5,1.5]},\\n{\\\"Labels\\\":[-3.5,-2.5,-1.5,-0.5,0.5,1.5,2.5,3.5]},\\n{\\\"Labels\\\":[-4.5,-3.5,-2.5,-1.5,-0.5,0.5,1.5,2.5,3.5,4.5]},\\n{\\\"Labels\\\":[-2.5,-1.5,-0.5,0.5,1.5,2.5]}\\n]\\n\"))", "name": "level_labels", "group": "Ungrouped variables", "templateType": "json", "description": "

{\"Nucleus\":\"1H\",\"Spin\":0.5,\"gyromagnetic ratio\":267.5},
{\"Nucleus\":\"13C\",\"Spin\":0.5,\"gyromagnetic ratio\":67.3},
{\"Nucleus\":\"14N\",\"Spin\":1,\"gyromagnetic ratio\":19.3},
{\"Nucleus\":\"19F\",\"Spin\":0.5,\"gyromagnetic ratio\":251.7},
{\"Nucleus\":\"31P\",\"Spin\":0.5,\"gyromagnetic ratio\":\"Null\"},
{\"Nucleus\":\"33S\",\"Spin\":1.5,\"gyromagnetic ratio\":\"Null\"},
{\"Nucleus\":\"59Co\",\"Spin\":3.5,\"gyromagnetic ratio\":\"Null\"},
{\"Nucleus\":\"87Sr\",\"Spin\":4.5,\"gyromagnetic ratio\":\"Null\"},
{\"Nucleus\":\"101Ru\",\"Spin\":2.5,\"gyromagnetic ratio\":\"Null\"}
]

\n\n\n\n\n\n\n\n\n\n\n\n\n"}, "labels": {"definition": "get(level_labels[randomiser],\"Labels\",0)", "name": "labels", "group": "Ungrouped variables", "templateType": "anything", "description": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"}, "gyromag_select": {"definition": "get(gyromag[randomiser],\"gyromagnetic ratio\",0)", "name": "gyromag_select", "group": "Ungrouped variables", "templateType": "anything", "description": "

{gyromag_select

\n\n\n\n\n\n"}, "Nucleus_select": {"definition": "get(gyromag[randomiser],\"Nucleus\",0)", "name": "Nucleus_select", "group": "Ungrouped variables", "templateType": "anything", "description": "

\n\n\n\n\n\n"}, "Spin_select": {"definition": "get(gyromag[randomiser],\"Spin\",0)\n", "name": "Spin_select", "group": "Ungrouped variables", "templateType": "anything", "description": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"}, "html": {"definition": "html_out[randomiser]", "name": "html", "group": "Ungrouped variables", "templateType": "anything", "description": "

\n\n\n"}, "html_out": {"definition": "[\n (\n html(\"\"+\"^\"+\"1\"+\"\"+\"H\"+\"\"),\n html(\"\"+\"^\"+\"13\"+\"\"+\"C\"+\"\"),\n html(\"\"+\"^\"+\"14\"+\"\"+\"N\"+\"\"),\n html(\"\"+\"^\"+\"19\"+\"\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"31\"+\"\"+\"P\"+\"\"),\n html(\"\"+\"^\"+\"33\"+\"\"+\"S\"+\"\"),\n html(\"\"+\"^\"+\"59\"+\"\"+\"Co\"+\"\"),\n html(\"\"+\"^\"+\"87\"+\"\"+\"Sr\"+\"\"),\n html(\"\"+\"^{\"+\"101\"+\"}\"+\"Ru\"+\"\")\n )\n]", "name": "html_out", "group": "Ungrouped variables", "templateType": "anything", "description": "

\n\n\n\n\n\n"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "functions": {}}, {"name": "NMR field", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

List of gyromagnetic ratios, $\\gamma$, for nuclei in units of MHz T^-1;

$\\gamma$(¹H)=268

$\\gamma$(¹³C)=67.3

$\\gamma$(¹⁴N)=19.3

$\\gamma$(¹⁹F)=252

$\\gamma$(³¹P)=108

", "advice": "

(i) First, retrieve the correct value of the gyromagnetic ratio. It can be seen that $\\gamma$ for {Nucleus_select} is equal to {gyromag_select} MHz T^-1.

Next, note that;

\\[\\frac{{\\gamma}Bh}{2\\pi} =h\\nu\\]

which reduces to;

\\[B = \\frac{2\\pi\\nu}{\\gamma}\\]

so;

\\[B = \\frac{2~\\times3.142~\\times~\\var{Frequency_MHz}~{\\rm MHz}}{\\var{gyromag_select}~{\\rm~MHz~T^{-1}}} = {\\var{magfield}~\\rm T}\\]

(ii) Note that;

\\[E=h\\nu\\]

\\[6.62607~\\times~10^{-34}~{\\rm J~s}~\\times\\var{Frequency_MHz}~{\\rm MHz}=\\var{photon_energy_mantissa}\\times10^{\\var{photon_energy_log}} {\\rm J}\\]

because

\\[\\var{Frequency_MHz}~{\\rm MHz} = \\var{Frequency}~{\\rm Hz}\\]

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"gyromag_select": {"name": "gyromag_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"gyromagnetic ratio\",0)", "description": "

{gyromag_select

", "templateType": "anything", "can_override": false}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "templateType": "anything", "can_override": false}, "gyromag": {"name": "gyromag", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\\"Nucleus\\\":\\\"1H\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":268},\\n {\\\"Nucleus\\\":\\\"13C\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":67.3},\\n {\\\"Nucleus\\\":\\\"14N\\\",\\\"Spin\\\":1,\\\"gyromagnetic ratio\\\":19.3},\\n {\\\"Nucleus\\\":\\\"19F\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":252},\\n {\\\"Nucleus\\\":\\\"31P\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":108}\\n]\"))", "description": "", "templateType": "json", "can_override": false}, "photon_energy_mantissa": {"name": "photon_energy_mantissa", "group": "Ungrouped variables", "definition": "siground(photon_energy/10^(photon_energy_log),4)", "description": "", "templateType": "anything", "can_override": false}, "hbar": {"name": "hbar", "group": "Ungrouped variables", "definition": "(6.62607004*10^(-34))/2*3.14159265359\n", "description": "", "templateType": "anything", "can_override": false}, "photon_energy_log": {"name": "photon_energy_log", "group": "Ungrouped variables", "definition": "floor(log(photon_energy))", "description": "", "templateType": "anything", "can_override": false}, "hbar_log": {"name": "hbar_log", "group": "Ungrouped variables", "definition": "floor(log(hbar))\n", "description": "", "templateType": "anything", "can_override": false}, "Nucleus_select": {"name": "Nucleus_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"Nucleus\",0)", "description": "", "templateType": "anything", "can_override": false}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "html_out[randomiser]", "description": "", "templateType": "anything", "can_override": false}, "magfield": {"name": "magfield", "group": "Ungrouped variables", "definition": "siground((random(1..40)/10),5)", "description": "", "templateType": "anything", "can_override": false}, "Frequency": {"name": "Frequency", "group": "Ungrouped variables", "definition": "Frequency_MHz*10^6", "description": "", "templateType": "anything", "can_override": false}, "hbar_mantissa": {"name": "hbar_mantissa", "group": "Ungrouped variables", "definition": "hbar/(10^(hbar_log))", "description": "", "templateType": "anything", "can_override": false}, "levels": {"name": "levels", "group": "Ungrouped variables", "definition": "(2*Spin_select)+1", "description": "", "templateType": "anything", "can_override": false}, "Frequency_MHz": {"name": "Frequency_MHz", "group": "Ungrouped variables", "definition": "siground(((gyromag_select*magfield)/(2*3.14)),3)", "description": "", "templateType": "anything", "can_override": false}, "Spin_select": {"name": "Spin_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"Spin\",0)\n", "description": "", "templateType": "anything", "can_override": false}, "html_out": {"name": "html_out", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"^\"+\"1\"+\"\"+\"H\"+\"\"),\n html(\"\"+\"^\"+\"13\"+\"\"+\"C\"+\"\"),\n html(\"\"+\"^\"+\"14\"+\"\"+\"N\"+\"\"),\n html(\"\"+\"^\"+\"19\"+\"\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"31\"+\"\"+\"P\"+\"\")\n )\n]", "description": "", "templateType": "anything", "can_override": false}, "photon_energy": {"name": "photon_energy", "group": "Ungrouped variables", "definition": "6.626*10^(-34)*frequency", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Spin_select", "levels", "photon_energy_log", "photon_energy_mantissa", "photon_energy", "hbar", "hbar_mantissa", "hbar_log", "magfield", "randomiser", "gyromag", "Nucleus_select", "gyromag_select", "Frequency_MHz", "html_out", "HTML", "Frequency"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the applied magnetic field, B, (in units of T) if the frequency, $\\nu$, of the transition between nuclear spin levels for a {HTML} nucleus is {Frequency_MHz} MHz?

", "minValue": "{magfield}-{magfield}/50", "maxValue": "{magfield}+{magfield}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the energy, E, of a photon of the frequency given in part (i) in units of Joules?

[[0]]$\\times$10^[[1]]

List of gyromagnetic ratios, $\\gamma$, for nuclei in units of MHz T^-1;

$\\gamma$(¹H)=268

$\\gamma$(¹³C)=67.3

$\\gamma$(¹⁴N)=19.3

$\\gamma$(¹⁹F)=252

$\\gamma$(³¹P)=108

", "advice": "

(i) First, retrieve the correct value of the gyromagnetic ratio. It can be seen that $\\gamma$ for {Nucleus_select} is equal to {gyromag_select} MHz T^-1.

Next, note that;

\\[\\frac{{\\gamma}Bh}{2\\pi} =h\\nu\\]

which reduces to;

\\[\\frac{{\\gamma}B}{2\\pi} = \\nu\\]

so;

\\[\\frac{\\var{gyromag_select}~{\\rm~MHz~T^{-1}}\\times~\\var{magfield}~{\\rm T}}{2~\\times~3.1416} = \\var{Frequency_MHz}~{\\rm MHz}\\]

(ii) Note that;

\\[E=h\\nu\\]

\\[6.62607~\\times~10^{-34}~{\\rm J~s}~\\times\\var{Frequency_MHz}~{\\rm MHz}=\\var{photon_energy_mantissa}\\times10^{\\var{photon_energy_log}} {\\rm J}\\]

because

\\[\\var{Frequency_MHz}~{\\rm MHz} = \\var{Frequency}~{\\rm Hz}\\]

{gyromag_select

", "templateType": "anything", "can_override": false}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "templateType": "anything", "can_override": false}, "gyromag": {"name": "gyromag", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\\"Nucleus\\\":\\\"1H\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":268},\\n {\\\"Nucleus\\\":\\\"13C\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":67.3},\\n {\\\"Nucleus\\\":\\\"14N\\\",\\\"Spin\\\":1,\\\"gyromagnetic ratio\\\":19.3},\\n {\\\"Nucleus\\\":\\\"19F\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":252},\\n {\\\"Nucleus\\\":\\\"31P\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":108}\\n]\"))", "description": "", "templateType": "json", "can_override": false}, "photon_energy_mantissa": {"name": "photon_energy_mantissa", "group": "Ungrouped variables", "definition": "siground(6.626*10^(-34)*frequency/10^(floor(log(6.626*10^(-34)*frequency))),4)", "description": "", "templateType": "anything", "can_override": false}, "hbar": {"name": "hbar", "group": "Ungrouped variables", "definition": "(6.62607004*10^(-34))/2*3.14159265359\n", "description": "", "templateType": "anything", "can_override": false}, "photon_energy_log": {"name": "photon_energy_log", "group": "Ungrouped variables", "definition": "floor(log(6.626*10^(-34)*frequency))", "description": "", "templateType": "anything", "can_override": false}, "hbar_log": {"name": "hbar_log", "group": "Ungrouped variables", "definition": "floor(log(hbar))\n", "description": "", "templateType": "anything", "can_override": false}, "Nucleus_select": {"name": "Nucleus_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"Nucleus\",0)", "description": "", "templateType": "anything", "can_override": false}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "html_out[randomiser]", "description": "", "templateType": "anything", "can_override": false}, "magfield": {"name": "magfield", "group": "Ungrouped variables", "definition": "siground(((random(1..40))/10),3)", "description": "", "templateType": "anything", "can_override": false}, "Frequency": {"name": "Frequency", "group": "Ungrouped variables", "definition": "Frequency_MHz*10^6", "description": "", "templateType": "anything", "can_override": false}, "hbar_mantissa": {"name": "hbar_mantissa", "group": "Ungrouped variables", "definition": "hbar/(10^(hbar_log))", "description": "", "templateType": "anything", "can_override": false}, "levels": {"name": "levels", "group": "Ungrouped variables", "definition": "(2*Spin_select)+1", "description": "", "templateType": "anything", "can_override": false}, "Frequency_MHz": {"name": "Frequency_MHz", "group": "Ungrouped variables", "definition": "siground(((gyromag_select*magfield)/(2*3.14)),3)", "description": "", "templateType": "anything", "can_override": false}, "Spin_select": {"name": "Spin_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"Spin\",0)\n", "description": "", "templateType": "anything", "can_override": false}, "html_out": {"name": "html_out", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"^\"+\"1\"+\"\"+\"H\"+\"\"),\n html(\"\"+\"^\"+\"13\"+\"\"+\"C\"+\"\"),\n html(\"\"+\"^\"+\"14\"+\"\"+\"N\"+\"\"),\n html(\"\"+\"^\"+\"19\"+\"\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"31\"+\"\"+\"P\"+\"\")\n )\n]", "description": "

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Spin_select", "levels", "photon_energy_log", "photon_energy_mantissa", "hbar", "hbar_mantissa", "hbar_log", "magfield", "randomiser", "gyromag", "Nucleus_select", "gyromag_select", "Frequency_MHz", "html_out", "HTML", "Frequency"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the frequency, $\\nu$ (in units of MHz) of the transition between nuclear spin levels for a {HTML} nucleus where the applied magnetic field, B, is {magfield} T?

", "minValue": "{Frequency_MHz}-{Frequency_MHz}/50", "maxValue": "{Frequency_MHz}+{Frequency_MHz}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the energy, E,of a photon of the frequency calculated in part (i) in units of Joules?

[[0]]$\\times$10^[[1]]

The Lande g factor of the unpaired electron in an unknown inorganic radical is measured to be {lande_g_factor} in a magnetic field, B, of {magfield} T.

", "advice": "

(i) First, note that;

\\[\\frac{\\Delta E}{h}=\\frac{g\\mu_BB}{h} =\\nu\\]

so;

\\[{\\frac{\\var{Lande_g_factor}~\\times9.274 \\times 10^{-24}{\\rm ~J~T^{-1}}\\times \\var{magfield}{\\rm~T}}{6.62607~\\times~10^{-34}~{\\rm J~s}}=\\var{Frequency_mantissa}~\\times~10^\\var{Frequency_log}~{\\rm~Hz}}\\]

(ii) Note that;

\\[E=h\\nu\\]

\\[6.62607~\\times~10^{-34}~{\\rm J~s}~\\times\\var{Frequency_mantissa}~\\times~10^\\var{Frequency_log}~{\\rm~Hz}=\\var{photon_energy_mantissa}\\times10^{\\var{photon_energy_log}} {\\rm J}\\]

", "rulesets": {}, "variables": {"HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "html_out[randomiser]", "description": "", "templateType": "anything"}, "h_log": {"name": "h_log", "group": "Ungrouped variables", "definition": "floor(log(h))\n", "description": "", "templateType": "anything"}, "Bohr_magneton_mantissa": {"name": "Bohr_magneton_mantissa", "group": "Ungrouped variables", "definition": "9.274009994", "description": "", "templateType": "anything"}, "html_out": {"name": "html_out", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"^\"+\"1\"+\"\"+\"H\"+\"\"),\n html(\"\"+\"^\"+\"13\"+\"\"+\"C\"+\"\"),\n html(\"\"+\"^\"+\"14\"+\"\"+\"N\"+\"\"),\n html(\"\"+\"^\"+\"19\"+\"\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"31\"+\"\"+\"P\"+\"\")\n )\n]", "description": "

", "templateType": "anything"}, "Frequency_MHz": {"name": "Frequency_MHz", "group": "Ungrouped variables", "definition": "Frequency/1000000\n", "description": "", "templateType": "anything"}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "6.62607004*10^(-34)\n", "description": "", "templateType": "anything"}, "Frequency_coeff": {"name": "Frequency_coeff", "group": "Ungrouped variables", "definition": "(lande_g_factor*Bohr_magneton_mantissa*magfield)", "description": "", "templateType": "anything"}, "h_mantissa": {"name": "h_mantissa", "group": "Ungrouped variables", "definition": "h/(10^(h_log))", "description": "", "templateType": "anything"}, "photon_energy_log": {"name": "photon_energy_log", "group": "Ungrouped variables", "definition": "floor(log(6.626*10^(-34)*frequency))", "description": "", "templateType": "anything"}, "magfield": {"name": "magfield", "group": "Ungrouped variables", "definition": "decimal((random(1..40))/10)", "description": "", "templateType": "anything"}, "lande_g_factor": {"name": "lande_g_factor", "group": "Ungrouped variables", "definition": "decimal(random(1900..2100)/1000)", "description": "", "templateType": "anything"}, "Bohr_magneton_log": {"name": "Bohr_magneton_log", "group": "Ungrouped variables", "definition": "-24", "description": "", "templateType": "anything"}, "Frequency_mantissa": {"name": "Frequency_mantissa", "group": "Ungrouped variables", "definition": "Frequency/(10^(Frequency_log))", "description": "", "templateType": "anything"}, "photon_energy_mantissa": {"name": "photon_energy_mantissa", "group": "Ungrouped variables", "definition": "siground(6.626*10^(-34)*frequency/10^(floor(log(6.626*10^(-34)*frequency))),4)", "description": "", "templateType": "anything"}, "Frequency_log": {"name": "Frequency_log", "group": "Ungrouped variables", "definition": "floor(log(Frequency))", "description": "

Frequency_mantissa

", "templateType": "anything"}, "Frequency_powers": {"name": "Frequency_powers", "group": "Ungrouped variables", "definition": "(10^{Bohr_magneton_log})/(6.626*10^-34)\n", "description": "", "templateType": "anything"}, "Frequency": {"name": "Frequency", "group": "Ungrouped variables", "definition": "siground(Frequency_coeff*Frequency_powers,3)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["photon_energy_log", "photon_energy_mantissa", "h", "h_mantissa", "h_log", "magfield", "randomiser", "lande_g_factor", "Frequency_coeff", "Frequency_powers", "Frequency", "html_out", "HTML", "Bohr_magneton_mantissa", "Bohr_magneton_log", "Frequency_MHz", "Frequency_log", "Frequency_mantissa"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the frequency, $\\nu$, of the electron spin resonance transition for the unpaired electron in this radical in units of Hz?

[[0]] $\\times$ 10^[[1]]

What is the energy, E, of a photon of the frequency calculated in part (i) in units of Joules?

[[0]]$\\times$10^[[1]]

The frequency, $\\nu$, of an electron spin transition of an unknown inorganic radical is measured to be {Frequency_MHz} MHz in a magnetic field, B, of {magfield} T.

", "advice": "

(i) First, note that;

\\[\\frac{\\Delta E}{h}=\\frac{g\\mu_BB}{h} =\\nu\\]

in an electron spin resonance experiment. Therefore;

\\[\\frac{h\\nu}{\\mu_BB}=g\\]

so;

\\[\\frac{6.62607~\\times10^{-34}~{\\rm~J~s}~\\times~\\times~\\var{Frequency_mantissa}~\\times~10^\\var{Frequency_log}~{\\rm~Hz}}{9.274 \\times 10^{-24}{\\rm ~J~T^{-1}}\\times \\var{magfield}{\\rm~T}}=\\var{Lande_g}\\]

(ii) Note that;

\\[E=h\\nu\\]

\\[6.62607~\\times~10^{-34}~{\\rm J~s}~\\times\\var{Frequency_mantissa}~\\times~10^\\var{Frequency_log}~{\\rm~Hz}=\\var{photon_energy_mantissa}\\times10^{\\var{photon_energy_log}} {\\rm J}\\]

", "rulesets": {}, "variables": {"Frequency_log": {"name": "Frequency_log", "group": "Ungrouped variables", "definition": "floor(log(Frequency))", "description": "

Frequency_mantissa

", "templateType": "anything"}, "Bohr_magneton_log": {"name": "Bohr_magneton_log", "group": "Ungrouped variables", "definition": "-24", "description": "", "templateType": "anything"}, "magfield": {"name": "magfield", "group": "Ungrouped variables", "definition": "decimal((\n random(1..40))/10)", "description": "", "templateType": "anything"}, "Bohr_magneton_mantissa": {"name": "Bohr_magneton_mantissa", "group": "Ungrouped variables", "definition": "9.274009994", "description": "", "templateType": "anything"}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "html_out[randomiser]", "description": "", "templateType": "anything"}, "h_mantissa": {"name": "h_mantissa", "group": "Ungrouped variables", "definition": "h/(10^(h_log))", "description": "", "templateType": "anything"}, "photon_energy_mantissa": {"name": "photon_energy_mantissa", "group": "Ungrouped variables", "definition": "siground(6.626*10^(-34)*frequency/10^(floor(log(6.626*10^(-34)*frequency))),4)", "description": "", "templateType": "anything"}, "Frequency_MHz": {"name": "Frequency_MHz", "group": "Ungrouped variables", "definition": "Frequency/1000000\n", "description": "", "templateType": "anything"}, "Frequency_coeff": {"name": "Frequency_coeff", "group": "Ungrouped variables", "definition": "(lande_g*Bohr_magneton_mantissa*magfield)", "description": "", "templateType": "anything"}, "html_out": {"name": "html_out", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"^\"+\"1\"+\"\"+\"H\"+\"\"),\n html(\"\"+\"^\"+\"13\"+\"\"+\"C\"+\"\"),\n html(\"\"+\"^\"+\"14\"+\"\"+\"N\"+\"\"),\n html(\"\"+\"^\"+\"19\"+\"\"+\"F\"+\"\"),\n html(\"\"+\"^\"+\"31\"+\"\"+\"P\"+\"\")\n )\n]", "description": "

", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "6.62607004*10^(-34)\n", "description": "", "templateType": "anything"}, "h_log": {"name": "h_log", "group": "Ungrouped variables", "definition": "floor(log(h))\n", "description": "", "templateType": "anything"}, "photon_energy_log": {"name": "photon_energy_log", "group": "Ungrouped variables", "definition": "floor(log(6.626*10^(-34)*frequency))", "description": "", "templateType": "anything"}, "Frequency_mantissa": {"name": "Frequency_mantissa", "group": "Ungrouped variables", "definition": "Frequency/(10^(Frequency_log))", "description": "", "templateType": "anything"}, "lande_g": {"name": "lande_g", "group": "Ungrouped variables", "definition": "decimal(random(1900..2100)/1000)", "description": "", "templateType": "anything"}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "templateType": "anything"}, "Frequency_powers": {"name": "Frequency_powers", "group": "Ungrouped variables", "definition": "(10^{Bohr_magneton_log})/(6.626*10^-34)", "description": "", "templateType": "anything"}, "Frequency": {"name": "Frequency", "group": "Ungrouped variables", "definition": "siground(Frequency_coeff*Frequency_powers,3)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["photon_energy_log", "photon_energy_mantissa", "h", "h_mantissa", "h_log", "magfield", "randomiser", "lande_g", "Frequency_coeff", "Frequency_powers", "Frequency", "html_out", "HTML", "Bohr_magneton_mantissa", "Bohr_magneton_log", "Frequency_MHz", "Frequency_log", "Frequency_mantissa"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the Lande g-factor for the unpaired electron in this radical?

", "minValue": "{lande_g}-{lande_g}/50", "maxValue": "{lande_g}+{lande_g}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_feedback (Feedback on the adjusted significand: mark gap 0):\n feedback(\"Significand:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_significand), gaps[0][\"settings\"],gaps[0][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nexponent_feedback (Feedback on the adjusted exponent: mark gap 1):\n feedback(\"Exponent:\");\n let(result,apply_marking_script(\"numberentry\",string(adjusted_exponent), gaps[1][\"settings\"],gaps[1][\"marks\"]),\n concat_feedback(result[\"mark\"][\"feedback\"],0.5)\n )\n\nmark:\n apply(significand_feedback);\n apply(exponent_feedback)\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the energy, E, of a photon of the frequency calculated in part (i) in units of Joules?

[[0]]$\\times$10^[[1]]

The answer is a comma-separated list of numbers.

The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.

You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.

Is every number in the student's list valid?

Are the student's answers in ascending order?

", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n multiply_credit(0.5,\"Not in order\")\n )"}, {"name": "included", "description": "

Is each number in the expected answer present in the student's list the correct number of times?

", "definition": "all(included)"}, {"name": "no_extras", "description": "

True if the student's list doesn't contain any numbers that aren't in the expected answer.

Should the answer be considered as a set, so the number of times an element occurs doesn't matter?

", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "

Numbers included in the student's answer that are not in the expected list.

", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [["question-resources/image_DTrtxfw.png", "/srv/numbas/media/question-resources/image_DTrtxfw.png"], ["question-resources/image_gxf2p8m.png", "/srv/numbas/media/question-resources/image_gxf2p8m.png"], ["question-resources/image_YiGalQz.png", "/srv/numbas/media/question-resources/image_YiGalQz.png"], ["question-resources/image_izx86lb.png", "/srv/numbas/media/question-resources/image_izx86lb.png"], ["question-resources/image_EFznxB4.png", "/srv/numbas/media/question-resources/image_EFznxB4.png"], ["question-resources/image_QRX8AOx.png", "/srv/numbas/media/question-resources/image_QRX8AOx.png"], ["question-resources/image_SkqSr5d.png", "/srv/numbas/media/question-resources/image_SkqSr5d.png"], ["question-resources/image_RvwZ0jx.png", "/srv/numbas/media/question-resources/image_RvwZ0jx.png"], ["question-resources/image_jI1pj1c.png", "/srv/numbas/media/question-resources/image_jI1pj1c.png"], ["question-resources/image_m7iIRpR.png", "/srv/numbas/media/question-resources/image_m7iIRpR.png"], ["question-resources/image_e6HMPkZ.png", "/srv/numbas/media/question-resources/image_e6HMPkZ.png"], ["question-resources/image_Hbraekd.png", "/srv/numbas/media/question-resources/image_Hbraekd.png"], ["question-resources/image_fPp87EN.png", "/srv/numbas/media/question-resources/image_fPp87EN.png"], ["question-resources/image_lrBQiRH.png", "/srv/numbas/media/question-resources/image_lrBQiRH.png"], ["question-resources/image_Eyq56eh.png", "/srv/numbas/media/question-resources/image_Eyq56eh.png"], ["question-resources/image_FjdLy57.png", "/srv/numbas/media/question-resources/image_FjdLy57.png"], ["question-resources/image_fFsskYr.png", "/srv/numbas/media/question-resources/image_fFsskYr.png"], ["question-resources/image_7yxkxrh.png", "/srv/numbas/media/question-resources/image_7yxkxrh.png"], ["question-resources/image_TKd4KFA.png", "/srv/numbas/media/question-resources/image_TKd4KFA.png"], ["question-resources/image_qhno0zh.png", "/srv/numbas/media/question-resources/image_qhno0zh.png"], ["question-resources/rot_spectrum.jpg", "/srv/numbas/media/question-resources/rot_spectrum.jpg"], ["question-resources/rot_spectrum_bVm45Fn.jpg", "/srv/numbas/media/question-resources/rot_spectrum_bVm45Fn.jpg"]]}