the wavelength, $\\lambda$ is [[0]] $\\times$ 10[[1]] m;
", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": false, "variableReplacements": [], "showFeedbackIcon": true, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}}, {"unitTests": [], "type": "gapfill", "gaps": [{"marks": 1, "unitTests": [], "allowFractions": false, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "maxValue": "{Energy_mantissa}+{Energy_mantissa}/50", "mustBeReducedPC": 0, "minValue": "{Energy_mantissa}-{Energy_mantissa}/50", "customName": "", "correctAnswerFraction": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}, {"marks": 1, "unitTests": [], "allowFractions": false, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "maxValue": "{Energy_log}-{Energy_log}/50", "mustBeReducedPC": 0, "minValue": "{Energy_log}+{Energy_log}/50", "customName": "", "correctAnswerFraction": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}], "sortAnswers": false, "customName": "", "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]", "prompt": "What is the energy, E, of a single photon in units of Joules?
\n[[0]] $\\times$ 10[[1]] J
", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}}, {"unitTests": [], "type": "gapfill", "gaps": [{"marks": 1, "unitTests": [], "allowFractions": false, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "maxValue": "{energy_molar}+{energy_molar}/50", "mustBeReducedPC": 0, "minValue": "{energy_molar}-{energy_molar}/50", "customName": "", "correctAnswerFraction": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}], "sortAnswers": false, "customName": "", "customMarkingAlgorithm": "", "prompt": "the energy, E, of one mole of photons is [[0]] kJ mol-1.
", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"maxRuns": "200", "condition": ""}, "variable_groups": [], "extensions": ["formula", "permutations"], "preamble": {"css": "", "js": ""}, "variables": {"randomiser_units": {"name": "randomiser_units", "description": "randomi
", "templateType": "anything", "group": "Ungrouped variables", "definition": "0"}, "quantity_label": {"name": "quantity_label", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "[\"wavenumber\",\"frequency\"][randomiser_units]"}, "wavelength_mantissa": {"name": "wavelength_mantissa", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "siground((wavelength/(10^(wavelength_log))),4)"}, "wavelength_log_cm": {"name": "wavelength_log_cm", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "wavelength_log+2"}, "frequency_randomiser": {"name": "frequency_randomiser", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2000..8000)/1000"}, "frequency_log": {"name": "frequency_log", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "floor(log(frequency))"}, "units_list": {"name": "units_list", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "[\n (\n html(\"\"+\"{wavenumber}\"+\" \"+\"cm\"+\"\"+\"-1\"+\"\"+\"\"),\n html(\"\"+\"{frequency_mantissa}\"+\" \"+\"× \"+\"10\"+\"\"+\"{frequency_log}\"+\"\"+\" \"+\"Hz\"+\"\")\n )\n]"}, "Energy_log": {"name": "Energy_log", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "floor(log(Energy))"}, "wavelength": {"name": "wavelength", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "(3*10^8)/frequency"}, "Energy_molar": {"name": "Energy_molar", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "siground(frequency*(6.626*10^(-34))*6.022*10^(23)/1000,3)"}, "Energy_mantissa": {"name": "Energy_mantissa", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "Energy/10^{Energy_log}"}, "units_output": {"name": "units_output", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "units_list[randomiser_units]"}, "wavelength_log": {"name": "wavelength_log", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "floor(log(wavelength))"}, "wavenumber": {"name": "wavenumber", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "siground((1/(wavelength*100)),4)"}, "frequency_mantissa": {"name": "frequency_mantissa", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "siground((frequency/(10^(frequency_log))),4)"}, "frequency": {"name": "frequency", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "10^(8+frequency_randomiser)"}, "Energy": {"name": "Energy", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "siground(frequency*(6.626*10^(-34)),3)"}}, "advice": "a) If you are given a quantity in wavenumbers, convert this into a wavelength;
\n\\[[\\frac{1}{\\lambda}={\\rm wavenumber}]~{\\rm and~therefore}~[\\frac{1}{\\rm wavenumber}={\\lambda}]\\]
\nIf you specify wavenumbers in cm-1, you will obtain the wavelength in centimetres ;
\n\\[\\frac{1}{\\var{wavenumber}~\\rm cm^{-1}}={\\var{wavelength_mantissa}~\\times~10^{\\var{wavelength_log_cm}}~\\rm cm}\\]
\nYou need to divide a wavelength defined in centimetres by 100 cm m-1 (ie the number of centimetres in 1 metre) to obtain a wavelength in metres.
\n\\[\\frac{{\\var{wavelength_mantissa}~\\times~10^{\\var{wavelength_log_cm}}~\\rm cm}}{100~\\rm cm~m^{-1}}=\\var{wavelength_mantissa}~\\times~10^{\\var{wavelength_log}}~{\\rm m}\\]
\n\nb) Note that;
\n\\[c=\\lambda\\nu\\]
\nso;
\n\\[\\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}\\]
\nCalculate the energy of a single photon using;
\n\\[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}\\]
\n\nc) Then, multiply by the Avogadro number, and divide by 1000 J kJ-1 to convert this into an energy in kJ mol-1;
\n\\[\\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}}\\]
\n", "name": "Interchange frequency, wavelength, wavenumber_3", "statement": "Given that the {quantity_label} of a transition is {units_output};
", "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"], "functions": {"": {"parameters": [], "language": "jme", "type": "number", "definition": ""}, "molecule_name": {"parameters": [["atoms", "list"]], "language": "jme", "type": "number", "definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))"}, "isotope_name": {"parameters": [["atom", "dict"]], "language": "jme", "type": "string", "definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"\"+string(atom[\"isotope\"])+\"\",\"\")+atom[\"symbol\"])+\"\")"}}, "type": "question", "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}]}]}], "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}]}