List of gyromagnetic ratios, $\\gamma$, for nuclei in units of MHz T-1;
\n$\\gamma$(1H)=268
\n$\\gamma$(13C)=67.3
\n$\\gamma$(14N)=19.3
\n$\\gamma$(19F)=252
\n$\\gamma$(31P)=108
", "advice": "(i) First, retrieve the correct value of the gyromagnetic ratio. It can be seen that $\\gamma$ for {Nucleus_select} is equal to {gyromag_select} MHz T-1.
\nNext, note that;
\n\\[\\frac{{\\gamma}Bh}{2\\pi} =h\\nu\\]
\nwhich reduces to;
\n\\[\\frac{{\\gamma}B}{2\\pi} = \\nu\\]
\nso;
\n\\[\\frac{\\var{gyromag_select}~{\\rm~MHz~T^{-1}}\\times~\\var{magfield}~{\\rm T}}{2~\\times~3.1416} = \\var{Frequency_MHz}~{\\rm MHz}\\]
\n\n(ii) Note that;
\n\\[E=h\\nu\\]
\nso
\n\\[6.62607~\\times~10^{-34}~{\\rm J~s}~\\times\\var{Frequency_MHz}~{\\rm MHz}=\\var{photon_energy_mantissa}\\times10^{\\var{photon_energy_log}} {\\rm J}\\]
\nbecause
\n\\[\\var{Frequency_MHz}~{\\rm MHz} = \\var{Frequency}~{\\rm Hz}\\]
", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"gyromag_select": {"name": "gyromag_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"gyromagnetic ratio\",0)", "description": "{gyromag_select
", "templateType": "anything", "can_override": false}, "randomiser": {"name": "randomiser", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "templateType": "anything", "can_override": false}, "gyromag": {"name": "gyromag", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\\"Nucleus\\\":\\\"1H\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":268},\\n {\\\"Nucleus\\\":\\\"13C\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":67.3},\\n {\\\"Nucleus\\\":\\\"14N\\\",\\\"Spin\\\":1,\\\"gyromagnetic ratio\\\":19.3},\\n {\\\"Nucleus\\\":\\\"19F\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":252},\\n {\\\"Nucleus\\\":\\\"31P\\\",\\\"Spin\\\":0.5,\\\"gyromagnetic ratio\\\":108}\\n]\"))", "description": "", "templateType": "json", "can_override": false}, "photon_energy_mantissa": {"name": "photon_energy_mantissa", "group": "Ungrouped variables", "definition": "siground(6.626*10^(-34)*frequency/10^(floor(log(6.626*10^(-34)*frequency))),4)", "description": "", "templateType": "anything", "can_override": false}, "hbar": {"name": "hbar", "group": "Ungrouped variables", "definition": "(6.62607004*10^(-34))/2*3.14159265359\n", "description": "", "templateType": "anything", "can_override": false}, "photon_energy_log": {"name": "photon_energy_log", "group": "Ungrouped variables", "definition": "floor(log(6.626*10^(-34)*frequency))", "description": "", "templateType": "anything", "can_override": false}, "hbar_log": {"name": "hbar_log", "group": "Ungrouped variables", "definition": "floor(log(hbar))\n", "description": "", "templateType": "anything", "can_override": false}, "Nucleus_select": {"name": "Nucleus_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"Nucleus\",0)", "description": "", "templateType": "anything", "can_override": false}, "HTML": {"name": "HTML", "group": "Ungrouped variables", "definition": "html_out[randomiser]", "description": "", "templateType": "anything", "can_override": false}, "magfield": {"name": "magfield", "group": "Ungrouped variables", "definition": "siground(((random(1..40))/10),3)", "description": "", "templateType": "anything", "can_override": false}, "Frequency": {"name": "Frequency", "group": "Ungrouped variables", "definition": "Frequency_MHz*10^6", "description": "", "templateType": "anything", "can_override": false}, "hbar_mantissa": {"name": "hbar_mantissa", "group": "Ungrouped variables", "definition": "hbar/(10^(hbar_log))", "description": "", "templateType": "anything", "can_override": false}, "levels": {"name": "levels", "group": "Ungrouped variables", "definition": "(2*Spin_select)+1", "description": "", "templateType": "anything", "can_override": false}, "Frequency_MHz": {"name": "Frequency_MHz", "group": "Ungrouped variables", "definition": "siground(((gyromag_select*magfield)/(2*3.14)),3)", "description": "", "templateType": "anything", "can_override": false}, "Spin_select": {"name": "Spin_select", "group": "Ungrouped variables", "definition": "get(gyromag[randomiser],\"Spin\",0)\n", "description": "", "templateType": "anything", "can_override": false}, "html_out": {"name": "html_out", "group": "Ungrouped variables", "definition": "[\n \n html(\"\"+\"\"+\"1\"+\"\"+\"H\"+\"\"),\n html(\"\"+\"\"+\"13\"+\"\"+\"C\"+\"\"),\n html(\"\"+\"\"+\"14\"+\"\"+\"N\"+\"\"),\n html(\"\"+\"\"+\"19\"+\"\"+\"F\"+\"\"),\n html(\"\"+\"\"+\"31\"+\"\"+\"P\"+\"\")\n \n]", "description": "What is the frequency, $\\nu$ (in units of MHz) of the transition between nuclear spin levels for a {HTML} nucleus where the applied magnetic field, B, is {magfield} T?
", "minValue": "{Frequency_MHz}-{Frequency_MHz}/50", "maxValue": "{Frequency_MHz}+{Frequency_MHz}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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 photon of the frequency calculated in part (i) in units of Joules?
\n[[0]]$\\times$10[[1]]
", "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": "{photon_energy_mantissa}-{photon_energy_mantissa}/50", "maxValue": "{photon_energy_mantissa}+{photon_energy_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": "{photon_energy_log}+{photon_energy_log}/50", "maxValue": "{photon_energy_log}-{photon_energy_log}/50", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}