randomi
", "definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "randomiser_units"}, "units_output": {"description": "", "definition": "units_list[randomiser_units]", "templateType": "anything", "group": "Ungrouped variables", "name": "units_output"}, "frequency_randomiser": {"description": "", "definition": "random(2000..8000)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "frequency_randomiser"}, "units_list": {"description": "", "definition": "[\n (\n html(\"\"+\"{wavenumber}\"+\" \"+\"cm\"+\"\"+\"-1\"+\"\"+\"\"),\n html(\"\"+\"{frequency_mantissa}\"+\" \"+\"× \"+\"10\"+\"\"+\"{frequency_log}\"+\"\"+\" \"+\"Hz\"+\"\")\n )\n]", "templateType": "anything", "group": "Ungrouped variables", "name": "units_list"}, "frequency": {"description": "", "definition": "10^(8+frequency_randomiser)", "templateType": "anything", "group": "Ungrouped variables", "name": "frequency"}, "frequency_log": {"description": "", "definition": "floor(log(frequency))", "templateType": "anything", "group": "Ungrouped variables", "name": "frequency_log"}, "wavelength_log_cm": {"description": "", "definition": "wavelength_log+2", "templateType": "anything", "group": "Ungrouped variables", "name": "wavelength_log_cm"}, "wavelength_log": {"description": "", "definition": "floor(log(wavelength))", "templateType": "anything", "group": "Ungrouped variables", "name": "wavelength_log"}, "quantity_label": {"description": "", "definition": "[\"wavenumber\",\"frequency\"][randomiser_units]", "templateType": "anything", "group": "Ungrouped variables", "name": "quantity_label"}, "wavelength_mantissa": {"description": "", "definition": "siground((wavelength/(10^(wavelength_log))),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "wavelength_mantissa"}, "Energy_mantissa": {"description": "", "definition": "Energy/10^{Energy_log}", "templateType": "anything", "group": "Ungrouped variables", "name": "Energy_mantissa"}, "Energy": {"description": "", "definition": "siground(frequency*(6.626*10^(-34)),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "Energy"}, "wavenumber": {"description": "", "definition": "siground((1/(wavelength*100)),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "wavenumber"}, "Energy_log": {"description": "", "definition": "floor(log(Energy))", "templateType": "anything", "group": "Ungrouped variables", "name": "Energy_log"}}, "extensions": ["formula", "permutations"], "parts": [{"extendBaseMarkingAlgorithm": false, "scripts": {}, "type": "gapfill", "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]", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "numberentry", "showFractionHint": true, "customMarkingAlgorithm": "", "useCustomName": false, "mustBeReducedPC": 0, "minValue": "{wavelength_mantissa}-{wavelength_mantissa}/50", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "marks": 1, "mustBeReduced": false, "maxValue": "{wavelength_mantissa}+{wavelength_mantissa}/50", "allowFractions": false, "unitTests": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacements": [], "customName": "", "showFeedbackIcon": true, "correctAnswerFraction": false}, {"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "numberentry", "showFractionHint": true, "customMarkingAlgorithm": "", "useCustomName": false, "mustBeReducedPC": 0, "minValue": "{wavelength_log}+{wavelength_log}/50", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "marks": 1, "mustBeReduced": false, "maxValue": "{wavelength_log}-{wavelength_log}/50", "allowFractions": false, "unitTests": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacements": [], "customName": "", "showFeedbackIcon": true, "correctAnswerFraction": false}], "sortAnswers": false, "unitTests": [], "customName": "", "marks": 0, "variableReplacements": [], "prompt": "the wavelength, $\\lambda$, is [[0]] $\\times$ 10[[1]] m;
", "showCorrectAnswer": true, "showFeedbackIcon": true}, {"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "gapfill", "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]", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "numberentry", "showFractionHint": true, "customMarkingAlgorithm": "", "useCustomName": false, "mustBeReducedPC": 0, "minValue": "{Energy_mantissa}-{Energy_mantissa}/50", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "marks": 1, "mustBeReduced": false, "maxValue": "{Energy_mantissa}+{Energy_mantissa}/50", "allowFractions": false, "unitTests": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacements": [], "customName": "", "showFeedbackIcon": true, "correctAnswerFraction": false}, {"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "numberentry", "showFractionHint": true, "customMarkingAlgorithm": "", "useCustomName": false, "mustBeReducedPC": 0, "minValue": "{Energy_log}+{Energy_log}/50", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "marks": 1, "mustBeReduced": false, "maxValue": "{Energy_log}-{Energy_log}/50", "allowFractions": false, "unitTests": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacements": [], "customName": "", "showFeedbackIcon": true, "correctAnswerFraction": false}], "sortAnswers": false, "unitTests": [], "customName": "", "marks": 0, "variableReplacements": [], "prompt": "What is the energy, E, of a single photon in units of Joules?
\n[[0]] $\\times$ 10[[1]]
", "showCorrectAnswer": true, "showFeedbackIcon": true}, {"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "numberentry", "showFractionHint": true, "customMarkingAlgorithm": "", "useCustomName": false, "mustBeReducedPC": 0, "minValue": "{energy_molar}-{energy_molar}/50", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "marks": 1, "mustBeReduced": false, "maxValue": "{energy_molar}+{energy_molar}/50", "allowFractions": false, "unitTests": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacements": [], "customName": "", "showFeedbackIcon": true, "correctAnswerFraction": false}], "sortAnswers": false, "unitTests": [], "customName": "", "marks": 0, "variableReplacements": [], "prompt": "the energy, E, of one mole of photons is [[0]] kJ mol-1.
", "showCorrectAnswer": true, "showFeedbackIcon": true}], "statement": "Given that the {quantity_label} of a transition is {units_output};
", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"": []}, "functions": {"": {"definition": "", "type": "number", "parameters": [], "language": "jme"}, "isotope_name": {"definition": "(\"\"+(if(atom[\"isotope\"]<>\"\",\"\"+string(atom[\"isotope\"])+\"\",\"\")+atom[\"symbol\"])+\"\")", "type": "string", "parameters": [["atom", "dict"]], "language": "jme"}, "molecule_name": {"definition": "html(join(map(isotope_name(atom),atom,atoms),\"\"))", "type": "number", "parameters": [["atoms", "list"]], "language": "jme"}}, "preamble": {"js": "", "css": ""}, "advice": "a) To determine a wavelength when given a frequency in Hz;
\n\\[c=\\lambda\\nu\\]
\nso;
\n\\[\\frac{c}{\\nu}=\\lambda=\\frac{3.0~\\times~10^{8}~{\\rm~m~s^{-1}}}{\\var{Frequency_mantissa}~\\times~10^{\\var{Frequency_log}}~{\\rm Hz}}=\\var{wavelength_mantissa}~\\times~10^{\\var{wavelength_log}}~{\\rm~m}\\]
\n\nb) Calculate 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", "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"], "variablesTest": {"condition": "", "maxRuns": "200"}, "tags": [], "variable_groups": [], "name": "Interchange frequency, wavelength, wavenumber.", "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/"}]}