// Numbas version: exam_results_page_options {"name": "Interchange frequency, wavelength, wavenumber_2", "extensions": ["permutations"], "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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Interchange frequency, wavelength, wavenumber_2", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

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": {"": []}, "extensions": ["permutations"], "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;

", "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": "{frequency_mantissa}-{frequency_mantissa}/50", "maxValue": "{frequency_mantissa}+{frequency_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": "{frequency_log}-{frequency_log}/50", "maxValue": "{frequency_log}+{frequency_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, of a single photon?

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

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