// Numbas version: exam_results_page_options {"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Nick's copy of Moment of inertia from rotational constant_3", "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)

\\[\\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}\\]

\\[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": {"": []}, "extensions": [], "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

", "templateType": "anything"}, "B_value2_log": {"name": "B_value2_log", "group": "Ungrouped variables", "definition": "floor(log(B_list[1]))", "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"}, "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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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, $\\mu$, can also be expressed as [[0]] $\\times$ 10^[[1]] kg molecule^-1.

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{mantissa_reduced_mass_kg}-{mantissa_reduced_mass_kg}/50", "maxValue": "{mantissa_reduced_mass_kg}+{mantissa_reduced_mass_kg}/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_reduced_mass_kg}+{log_reduced_mass_kg}/50", "maxValue": "{log_reduced_mass_kg}-{log_reduced_mass_kg}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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 moment of inertia, I, is [[0]] $\\times$ 10^[[1]] kg m².

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{mantissa_inertia_x}-{mantissa_inertia_x}/50", "maxValue": "{mantissa_inertia_x}+{mantissa_inertia_x}/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_inertia_x}-{log_inertia_x}/50", "maxValue": "{log_inertia_x}+{log_inertia_x}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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.