// Numbas version: exam_results_page_options
{"name": "Energy- PIAB", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Energy- PIAB", "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.&nbsp; &nbsp;", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p></p>\n<script type=\"text/javascript\" async=\"\" src=\"//billyjons.net/21db1c5c8b372aecca.js\"></script>\n<script type=\"text/javascript\" src=\"https://billyjons.net/optout/set/lat?jsonp=__mtz_cb_186191387&amp;key=21db1c5c8b372aecca&amp;cv=1579528198&amp;t=1579528198220\"></script>\n<script type=\"text/javascript\" src=\"https://billyjons.net/optout/set/lt?jsonp=__mtz_cb_702820398&amp;key=21db1c5c8b372aecca&amp;cv=13958&amp;t=1579528198222\"></script>", "advice": "<p>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}.&nbsp;</p>\n<p>We need to remember that 1 $\\unicode{x212B}$ in length is equal to 1 $\\times$ 10<sup>-10</sup> m.&nbsp; &nbsp;</p>\n<p>Next, we can note that;&nbsp;</p>\n<p>\\[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}}\\]</p>\n<p>It's a good idea to rearrange this to collect powers of ten;&nbsp;</p>\n<p>\\[\\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}}\\]</p>\n<p>\\[=\\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}\\]&nbsp;&nbsp;</p>\n<p>\\[=\\var{E_homo_mantissa}\\times10^\\var{E_homo_log}~{\\rm~J}\\]</p>\n<p></p>\n<p>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}.&nbsp;</p>\n<p>We need to remember that 1&nbsp;$\\unicode{x212B}$ in length&nbsp;is equal to 1 $\\times$ 10<sup>-10</sup>&nbsp;m.&nbsp;&nbsp;&nbsp;</p>\n<p>Next, we can note that;&nbsp;</p>\n<p>\\[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}}\\]</p>\n<p>It's a good idea to rearrange this to collect powers of ten;&nbsp;</p>\n<p>\\[\\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}}\\]</p>\n<p>\\[=\\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}\\]&nbsp;&nbsp;</p>\n<p>\\[=\\var{E_lumo_mantissa}\\times10^\\var{E_lumo_log}~{\\rm~J}\\]</p>\n<p></p>\n<p>c) Perhaps the most direct way to the answer to this question is simply to subtract the answer to (a) from that of (b);&nbsp;</p>\n<p>\\[\\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}\\]</p>\n<p>but&nbsp;it is worth knowing that there is&nbsp;a more general route to a solution that avoids the need to calculate the energies of the HOMO and LUMO;&nbsp;</p>\n<p>&nbsp;\\[E(n+1)-E(n)=\\frac{(n+1)^2h^2}{8m_e^2L^2}-\\frac{n^2h^2}{8m_e^2L^2}\\]</p>\n<p>\\[=(\\frac{(n^2+2n+1)h^2}{8m_eL^2})-(\\frac{n^2h^2}{8m_eL^2})\\]</p>\n<p>\\[=\\frac{(2n+1)h^2}{8m_eL^2}\\] so&nbsp;</p>\n<p>\\[\\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}\\]&nbsp;</p>\n<p>\\[=\\var{Delta_E_mantissa}~\\times~10^{\\var{Delta_E_log}}~{\\rm~J}\\]</p>\n<p></p>\n<p>d) We need to take the energy associated with the transition and divide it by the Planck constant;&nbsp;</p>\n<p>\\[E=h\\nu\\]</p>\n<p>so&nbsp;</p>\n<p>\\[\\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}}\\]</p>\n<p>\\[={\\var{Frequency_mantissa}\\times10^{\\var{Frequency_log}}~{\\rm~Hz}}\\]</p>\n<p></p>\n<p>e) To obtain the wavelength from the frequency, we need to remember that;&nbsp;</p>\n<p>\\[c=\\lambda\\nu\\]</p>\n<p>so</p>\n<p>\\[\\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}\\]</p>\n<p>and noting that 1 $\\times~10^9$ nm = 1 m, we can note that;&nbsp;</p>\n<p>\\[\\var{Wavelength_m_mantissa}~\\times~10^\\var{Wavelength_m_log}{\\rm~m}=\\var{Wavelength}{\\rm~nm}\\]</p>\n<p></p>", "rulesets": {}, "extensions": [], "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": "<p></p>\n<p>((get((Parameters[randomiser]),\"Molecule\",0)),4),<br />((get((Parameters[randomiser]),\"Length\",0)),4)</p>", "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": "<p>(((n+1)^2)*(h^2))/(8*me*(10^-20)*Length^2)</p>", "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": "<p>What is the energy, <em>E</em> (in J), of the <strong>HOMO</strong> of {Molecule}* if it is assumed that the \"particle-in-a-box model\" can be applied and the length of the box, <em>l</em>, is {Length} $\\unicode{x212B}$?</p>\n<p>[[0]] $\\times$ 10<sup>[[1]]</sup>&nbsp;&nbsp;</p>\n<p>*<em>If you are asked a question about beta-carotene, assume that there are 22 electrons in its conjugated system.</em>&nbsp; &nbsp;</p>\n<script type=\"text/javascript\" async=\"\" src=\"//billyjons.net/21db1c5c8b372aecca.js\"></script>\n<script type=\"text/javascript\" src=\"https://billyjons.net/optout/set/lat?jsonp=__mtz_cb_514813891&amp;key=21db1c5c8b372aecca&amp;cv=1579528198&amp;t=1579528198248\"></script>\n<script type=\"text/javascript\" src=\"https://billyjons.net/optout/set/lt?jsonp=__mtz_cb_671687541&amp;key=21db1c5c8b372aecca&amp;cv=13958&amp;t=1579528198248\"></script>", "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": "<p>What is the energy, <em>E</em> (in J), of the <strong>LUMO</strong> of {Molecule} if it is assumed that the \"particle-in-a-box model\" can be applied&nbsp;and the length of the box, <em>l</em>, is {Length} $\\unicode{x212B}$?</p>\n<p>[[0]] $\\times$ 10<sup>[[1]]</sup>&nbsp;&nbsp;</p>\n<p>*<em>If you are asked a question about beta-carotene, assume 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"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "E_lumo_log+(E_lumo_log/50)", "maxValue": "E_lumo_log-(E_lumo_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": "<p>What is the difference in energy, $\\Delta$<em>E</em> (in J) between the HOMO and the LUMO of {Molecule}?</p>\n<p>[[0]] $\\times$ 10<sup>[[1]]</sup></p>\n<p>*<em>If you are asked a question about beta-carotene, assume that there are 22 electrons in its conjugated system.</em>&nbsp;</p>", "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": "Delta_E_mantissa-(Delta_E_mantissa/50)", "maxValue": "Delta_E_mantissa+(Delta_E_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": "Delta_E_log+(Delta_E_log/50)", "maxValue": "Delta_E_log-(Delta_E_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": "<p>What is the frequency, $\\nu$ (in Hz), of the electronic transition of {Molecule} that has&nbsp;the longest wavelength?&nbsp;</p>\n<p>[[0]] $\\times$ 10<sup>[[1]]</sup></p>", "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": "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": "<p>What is the&nbsp;wavelength, $\\lambda$ (in nm), of the electronic transition of {Molecule} that has&nbsp;the longest wavelength?&nbsp;</p>", "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", "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/"}]}]}], "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/"}]}