// Numbas version: finer_feedback_settings
{"name": "Core Exercise Resit", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], []], "questions": [{"name": "Diffraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Calculate the $2\\theta$ angles of various Bragg peaks</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"lambda": {"name": "lambda", "group": "Ungrouped variables", "definition": "random(1.36 .. 1.36#0.02)", "description": "", "templateType": "randrange", "can_override": false}, "a0": {"name": "a0", "group": "Ungrouped variables", "definition": "random(4.24 .. 4.24#0.02)", "description": "", "templateType": "randrange", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "[[1,0,0],[1,1,0],[1,1,1],[3,2,1]]", "description": "<p>list of [h,k,l] values</p>", "templateType": "anything", "can_override": false}, "Qvec": {"name": "Qvec", "group": "Ungrouped variables", "definition": "[ b0*sqrt(q[0][0]^2+q[0][1]^2+q[0][2]^2),\n  b0*sqrt(q[1][0]^2+q[1][1]^2+q[1][2]^2),\n  b0*sqrt(q[2][0]^2+q[2][1]^2+q[2][2]^2),\n  b0*sqrt(q[3][0]^2+q[3][1]^2+q[3][2]^2)]", "description": "<p>Q vector</p>", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "2*pi/lambda", "description": "", "templateType": "anything", "can_override": false}, "b0": {"name": "b0", "group": "Ungrouped variables", "definition": "2*pi/a0", "description": "", "templateType": "anything", "can_override": false}, "twotheta": {"name": "twotheta", "group": "Ungrouped variables", "definition": "[ 2*180/pi*arcsin(Qvec[0]/2/k),\n  2*180/pi*arcsin(Qvec[1]/2/k),\n  2*180/pi*arcsin(Qvec[2]/2/k),\n  2*180/pi*arcsin(Qvec[3]/2/k)]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": ["lambda", "a0", "q", "Qvec", "k", "b0", "twotheta"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>X-rays with a wavelength, {lambda} &Aring; are incident on a cubic crystal with a lattice parameter, $a_0=${a0} &Aring;.</p>"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the $2\\theta$ scattering angles for the following Bragg reflections. Give your answers in degrees.</p>\n<p>$(h,k,l)$=({q[0][0]},{q[0][1]},{q[0][2]}): $2\\theta$=[[0]]</p>\n<p>$(h,k,l)$=({q[1][0]},{q[1][1]},{q[1][2]}): $2\\theta$=[[1]]</p>\n<p>$(h,k,l)$=({q[2][0]},{q[2][1]},{q[2][2]}): $2\\theta$=[[2]]</p>\n<p>$(h,k,l)$=({q[3][0]},{q[3][1]},{q[3][2]}): $2\\theta$=[[3]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "twotheta[0]", "maxValue": "twotheta[0]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": "0", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "0", "precisionMessage": "You have not given your 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"custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Calculate various properties of an FCC crystal given the lattice parameter and atomic weight.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a0": {"name": "a0", "group": "Ungrouped variables", "definition": "4.5", "description": "<p>lattice parameter</p>", "templateType": "number", "can_override": false}, "w0": {"name": "w0", "group": "Ungrouped variables", "definition": "random(30 .. 30#1)", "description": "<p>atomic weight</p>", "templateType": "randrange", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "[random(0),random(-1),random(2)]", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "[random(0),random(1),random(2)]", "description": "", "templateType": "anything", "can_override": false}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "[random(-1),random(-1),random(-1)]", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "[random(2),random(1),random(1)]", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "[random(0),random(1),random(-1)]", "description": "", "templateType": "anything", "can_override": false}, "z2": {"name": "z2", "group": "Ungrouped variables", "definition": "[random(0),random(-2),random(2)]", "description": "", "templateType": "anything", "can_override": false}, "angle0": {"name": "angle0", "group": "Ungrouped variables", "definition": "180/3.1415927*arccos((x1[0]*x2[0]+y1[0]*y2[0]+z1[0]*z2[0])/sqrt(x1[0]^2+y1[0]^2+z1[0]^2)/sqrt(x2[0]^2+y2[0]^2+z2[0]^2))", "description": "", "templateType": "anything", "can_override": false}, "angle1": {"name": "angle1", "group": "Ungrouped variables", "definition": "180/3.1415927*arccos((x1[1]*x2[1]+y1[1]*y2[1]+z1[1]*z2[1])/sqrt(x1[1]^2+y1[1]^2+z1[1]^2)/sqrt(x2[1]^2+y2[1]^2+z2[1]^2))", "description": "", "templateType": "anything", "can_override": false}, "angle2": {"name": "angle2", "group": "Ungrouped variables", "definition": "180/3.1415927*arccos((x1[2]*x2[2]+y1[2]*y2[2]+z1[2]*z2[2])/sqrt(x1[2]^2+y1[2]^2+z1[2]^2)/sqrt(x2[2]^2+y2[2]^2+z2[2]^2))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a0", "w0", "x1", "y1", "z1", "x2", "y2", "z2", "angle0", "angle1", "angle2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A particular element crystallises in the FCC structure with a single atom basis. The lattice constant is {{a0}}&Aring; and the atomic weight is {w0} a.m.u.</p>"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Deduce the number of nearest- and next-nearest-neighbour atoms and their separations.</p>\n<p>Number of nearest neighbours [[0]]. NN distance [[1]] &Aring;.</p>\n<p>Number of next-nearest neighbours [[2]]. NNN distance [[3]] &Aring;.</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": "12", "maxValue": "12", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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": "a0/sqrt(2)", "maxValue": "a0/sqrt(2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": 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": "6", "maxValue": "6", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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": "a0", "maxValue": "a0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the mass density of the material: [[0]] amu per &Aring;$^{3}$ = [[1]] kg.m$^{-3}$ (Round your answers to 3 significant figures)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "4*w0/a0^3", "maxValue": "4*w0/a0^3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "4*w0/a0^3*10000/6.022", "maxValue": "4*w0/a0^3*10000/6.022", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the angle beween the directions [{x1[0]},{y1[0]},{z1[0]}] and [{x2[0]},{y2[0]},{z2[0]}] in degrees:[[0]]</p>\n<p>Determine the angle beween the directions [{x1[1]},{y1[1]},{z1[1]}] and [{x2[1]},{y2[1]},{z2[1]}] in degrees:[[1]]</p>\n<p>Determine the angle beween the directions [{x1[2]},{y1[2]},{z1[2]}] and [{x2[2]},{y2[2]},{z2[2]}] in degrees:[[2]]</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "angle0", "maxValue": "angle0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "0", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "angle1", "maxValue": "angle1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "0", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "angle2", "maxValue": "angle2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "0", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "reciprocal lattice", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Calculate the reciprocal lattice vectors give a real space lattice.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a0": {"name": "a0", "group": "Ungrouped variables", "definition": "random(4.7 .. 4.7#0.01)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a0"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A cubic crystal with a lattice parameter, $a_0$ has real space lattice vectors given by</p>\n<p>$\\mathbf{a}_1=a_0\\mathbf{i}$</p>\n<p>$\\mathbf{a}_2=a_0\\mathbf{j}$</p>\n<p>$\\mathbf{a}_3=a_0\\mathbf{k}$</p>\n<p>where $\\mathbf{i},\\mathbf{j}$ and $\\mathbf{k}$ are the cartesian unit vectors.</p>\n<p></p>"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $a_0=$ {a0}, what are the reciprocal lattice vectors?</p>\n<p>$\\mathbf{b}_1=$[[0]]$\\mathbf{i}+$[[1]]$\\mathbf{j}+$[[2]]$\\mathbf{k}$</p>\n<p>$\\mathbf{b}_2=$[[3]]$\\mathbf{i}+$[[4]]$\\mathbf{j}+$[[5]]$\\mathbf{k}$</p>\n<p>$\\mathbf{b}_3=$[[6]]$\\mathbf{i}+$[[7]]$\\mathbf{j}+$[[8]]$\\mathbf{k}$</p>\n<p>Give all answers to 3 significant figures in &Aring;$^{-1}$</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": "2*pi/a0", "maxValue": "2*pi/a0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "2*pi/a0", "maxValue": "2*pi/a0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "2*pi/a0", "maxValue": "2*pi/a0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "PA2230 U2 Q2.1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Steve Leach", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19398/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Valence electrons in a one-dimensional chain of atoms experience a periodic potential of period $a$, the atomic spacing. In a very approximate model, this potential is zero between the atomic sites and at each atomic site consists of a rectangular well of width $w$ where the potential falls to $-V_0$, where $V_0 &gt; 0$. Express the potential as a complex exponential Fourier series and find an expression for the Fourier components. <strong>NOTE</strong>: Fill in the missing terms from this list: $V_g, a, x, g, i, w$, * as multiplier.</p>\n<p>Fourier series:<br/>$V(x)=\\sum_{g}\\:$[[0]]&nbsp;exp([[1]])</p>\n<p>Fourier components:<br/>$V_g=(-2V_0/$[[2]] $)\\sin($ [[3]] $/2)$</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "i", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "V_g", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "v_g", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "ii", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "i*g*x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "g", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "iii", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "g*a", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "a", "value": ""}, {"name": "g", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "iv", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "g*w", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "g", "value": ""}, {"name": "w", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The lowest band gap of this system can be estimated with the nearly-free electron approximations as 2|$V_g$| where $V_g$ is a Fourier component of the potential. Use the appropriate Fourier component to show that the gap approaches zero like $w/a$ in the large $a$ regime where $a &gt;&gt; w$. <strong>NOTE</strong>: Fill in the missing terms from this list: $V_0, a, w$, * as multiplier, factor 2.</p>\n<p>$E_g\\approx$ [[0]]&nbsp;</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Band gap", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "2*V_0*w/a", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "a", "value": ""}, {"name": "v_0", "value": ""}, {"name": "w", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The electron wave function in the nearly-free electron approximation is a superposition of two plane waves. Explain physically why the exact wave function has a more complicated form <strong>AND</strong> state this general form. Choose the <strong>ONE</strong> correct description:</p>\n<p>[[0]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["The wave-function is a superposition of a plane wave and a diffracted wave. In reality the electron wave undergoes multiple diffraction events. The most general form in 1-D is $\\exp(ikx) u(x)$", "The wave-function is a superposition of two waves travelling in opposite directions. In reality the electron wave undergoes diffraction. The most general form in 1-D is $\\exp(ikx) u(x)$", "The wave-function is a superposition of two waves travelling in opposite directions. In reality the electron wave undergoes diffraction. The most general form in 1-D is $\\exp(2\\pi ikx) u(x)$", "The wave-function is a superposition of a plane wave and a diffracted wave. In reality the electron wave undergoes multiple diffraction events. The most general form in 1-D is $\\exp(2\\pi ikx) u(x)$", "The wave-function is a diffracted wave. In reality the electron wave undergoes multiple diffraction events. The most general form in 1-D is $\\exp(2\\pi ikx) u(x)$", "The wave-function is a diffracted wave. In reality the electron wave undergoes multiple diffraction events. The most general form in 1-D is $\\exp(ikx) u(x)$", "The wave-function is a superposition of two waves travelling in opposite directions. In reality the electron wave undergoes diffraction. The most general form in 1-D is $\\exp(\\pi ikx) u(x)$", "The wave-function is a superposition of two waves travelling in opposite directions. The most general form in 1-D is $\\exp(-ikx) \\exp(ikx)$", "The wave-function is a superposition of two plane waves. In reality the electron wave undergoes attenuation. The most general form in 1-D is $\\exp(ikx) u(x)$", "The wave-function is a superposition of two plane waves. In reality the electron wave undergoes attenuation. The most general form in 1-D is $\\exp(-ikx) \\exp(ikx)$"], "matrix": ["3", 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "PA2230 U2 Q2.2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Steve Leach", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19398/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the reciprocal lattice vectors of an fcc lattice with edge length $a$. Hence show that the lattice reciprocal to fcc is bcc</p>\n<p>Select the <strong>ONE</strong> correct answer:</p>\n<p>[[0]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "i", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\underline a* = (2\\pi/a) (1, 1, -1)$&nbsp; &nbsp; &nbsp;$\\underline b* = (2\\pi/a) (-1, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (2\\pi/a) (1, -1, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l/2)(\\pm 1, \\pm 1, \\pm 1)$. Therefore bcc lattice with edge length $4\\pi/a)$", "$\\underline a* = (2\\pi/a) (1, 1, 0)$&nbsp; &nbsp; &nbsp;$\\underline b* = (2\\pi/a) (0, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (2\\pi/a) (1, 0, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l/2)(\\pm 0/1, \\pm 0/1, \\pm 0/1)$. Therefore bcc lattice with edge length $4\\pi/a)$", "$\\underline a* = (\\pi/a) (1, 1, -1)$&nbsp; &nbsp; &nbsp;$\\underline b* = (\\pi/a) (-1, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (\\pi/a) (1, -1, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l^2/2)(\\pm 1, \\pm 1, \\pm 1)$. Therefore bcc lattice with edge length $4\\pi/a)$", "$\\underline a* = (\\pi/a) (1, 1, 0)$&nbsp; &nbsp; &nbsp;$\\underline b* = (\\pi/a) (0, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (\\pi/a) (1, 0, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l^2/4)(\\pm 1, \\pm 1, \\pm 1)$. Therefore bcc lattice with edge length $4\\pi/a)$", "$\\underline a* = (a/2) (1, 1, -1)$&nbsp; &nbsp; &nbsp;$\\underline b* = (a/2) (-1, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (a/2) (1, -1, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l^2/4)(\\pm 1, \\pm 1, \\pm 1)$. Therefore bcc lattice with edge length $4\\pi/a)$", "$\\underline a* = (a/2) (1, 1, 0)$&nbsp; &nbsp; &nbsp;$\\underline b* = (a/2) (0, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (a/2) (1, 0, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l^2/2)(\\pm 0/1, \\pm 0/1, \\pm 0/1)$. Therefore bcc lattice with edge length $4\\pi/a)$", "$\\underline a* = (a^2/2) (1, 1, 0)$&nbsp; &nbsp; &nbsp;$\\underline b* = (a^2/2) (0, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (a^2/2) (1, 0, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l/4)(\\pm 0/1, \\pm 0/1, \\pm 0/1)$. Therefore bcc lattice with edge length $4\\pi/a)$", "$\\underline a* = (a/4) (1, 1, 0)$&nbsp; &nbsp; &nbsp;$\\underline b* = (a/4) (0, 1, 1)$&nbsp; &nbsp; &nbsp; &nbsp; $\\underline c* = (a/4) (1, 0, 1)$<br/>The primative vectors of a bcc lattice constant $l$ are $(l/4)(\\pm 0/1, \\pm 0/1, \\pm 0/1)$. Therefore bcc lattice with edge length $4\\pi/a)$"], "matrix": ["8", 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Identify the $k$-vectors at which the first <strong>AND</strong> second energy gaps occur in an fcc empty lattice model.</p>\n<p>Select the <strong>ONE</strong> correct answer:</p>\n<p>[[0]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "ii", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$|k|=\\sqrt3 \\pi/a$&nbsp; &nbsp; &nbsp;<strong>AND</strong>&nbsp; &nbsp; &nbsp; $|k|=2\\pi/a$", "$|k|=\\pi/a$&nbsp; &nbsp; <strong>AND</strong> &nbsp; &nbsp; &nbsp;$|k|=2\\pi/a$", "$|k|=\\sqrt3 \\pi/a$&nbsp; &nbsp; <strong>AND</strong> &nbsp; &nbsp; &nbsp;$|k|=\\pi/a$", "$|k|=\\sqrt3/a$&nbsp; &nbsp; <strong>AND</strong> &nbsp; &nbsp; &nbsp;$|k|=2/a$", "$|k|=\\sqrt3 \\pi/a^2$&nbsp; &nbsp; <strong>AND</strong> &nbsp; &nbsp; &nbsp;$|k|=2\\pi/a^2$", "$|k|=\\sqrt2 \\pi/a$&nbsp; &nbsp; <strong>AND</strong> &nbsp; &nbsp; &nbsp;$|k|=4\\pi/a$", "$|k|=\\sqrt2 \\pi/a^2$&nbsp; &nbsp; <strong>AND</strong> &nbsp; &nbsp; &nbsp;$|k|=4\\pi/a^2$", "$|k|=\\sqrt3 \\pi^2/a$&nbsp; &nbsp; <strong>AND</strong> &nbsp; &nbsp; &nbsp;$|k|=4\\pi^2/a$"], "matrix": ["6", 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hence sketch an $E(k)$ plot to show how overlapping bands may occur in fcc alkaline earth metals, Ca and Sr.</p>\n<p>Choose the <strong>ONE</strong> best description from the seven options:</p>\n<p>[[0]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "i", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<ul>\n<li>A sketch showing $E(k)$ versus $k$</li>\n<li>Shaded areas showing filled electron states</li>\n<li>Fermi Energy line ($E_F$) illustrated with some states for $-k$ above $E_F$ and some states for $+k$ below $E_F$</li>\n<li>Zone boundry at $-2\\pi/a$</li>\n<li>Zone boundry at $+\\sqrt3\\pi/a$</li>\n<li>Minima at $k=0$ and&nbsp;Maxima at zone boundaries</li>\n<li>Overlapping energy bands illustrating material is a metal</li>\n</ul>", "<ul>\n<li>A sketch showing $E(k)$ versus $k$</li>\n<li>Shaded areas showing filled electron states</li>\n<li>Fermi Energy line ($E_F$) illustrated mid-way in energy band</li>\n<li>Zone boundry at $-\\pi/a$</li>\n<li>Zone boundry at $+\\pi/a$</li>\n<li>Minima at $k=0$ and Maxima at zone boundaries</li>\n<li>Overlapping energy bands illustrating material is a metal</li>\n</ul>", "<ul>\n<li>A sketch showing $E(k)$ versus $k$</li>\n<li>Shaded areas showing filled electron states</li>\n<li>Fermi Energy line ($E_F$) illustrated with some states for $-k$ above $E_F$ and some states for $+k$ below $E_F$</li>\n<li>Zone boundry at $-\\pi/a$</li>\n<li>Zone boundry at $+\\pi/a$</li>\n<li>Minima at $k=0$ and&nbsp;Maxima at zone boundaries</li>\n<li>Overlapping energy bands illustrating material is a metal</li>\n</ul>", "<ul>\n<li>A sketch showing $E(k)$ versus $k$</li>\n<li>Part shaded areas showing filled electron states</li>\n<li>Fermi Energy line ($E_F$) illustrated mid-way in energy band</li>\n<li>Zone boundry at $-2\\pi/a$</li>\n<li>Zone boundry at $+\\sqrt3\\pi/a$</li>\n<li>Minima at $k=0$ and&nbsp;Maxima at zone boundaries</li>\n<li>Some empty energy bands illustrating material is a metal</li>\n</ul>", "<ul>\n<li>A sketch showing $E(k)$ versus $k$</li>\n<li>Shaded areas showing forbidden energy states</li>\n<li>Zone boundry at $-\\pi/a$</li>\n<li>Zone boundry at $+\\pi/a$</li>\n<li>Minima at $k=0$ and&nbsp;Maxima at zone boundaries</li>\n<li>Splitting energy states illustrating material is a metal</li>\n</ul>", "<ul>\n<li>A sketch showing $E(k)$ versus $k$</li>\n<li>Parabola with broken sections at zone boundaries</li>\n<li>Shaded areas showing forbidden energy states</li>\n<li>Zone boundry at $-\\pi/a$</li>\n<li>Zone boundry at $+\\pi/a$</li>\n<li>Minima at $k=0$</li>\n<li>Splitting energy states illustrating material is a metal</li>\n</ul>", "<ul>\n<li>A sketch showing $E(k)$ versus $k$</li>\n<li>Parabola with broken sections at zone boundaries</li>\n<li>Shaded areas showing forbidden energy states</li>\n<li>Zone boundry at $-2\\pi/a$</li>\n<li>Zone boundry at $+\\sqrt3\\pi/a$</li>\n<li>Minima at $k=0$</li>\n<li>Small 1st energy gap illustrating material is a metal</li>\n</ul>"], "matrix": ["6", 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "PA2230 U2 Q2.3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Steve Leach", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19398/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In a particular direction in a crystal, within the first Brillouin zone the energy $E$ of an electron varies with wavevector $k$ according to $E=Ak^2+Bk^4$ . If the effective mass equals the free electron mass $m$ at low values of $k$, determine the value of the effective mass as a fraction of $m$, at the first Brillouin zone boundary $k = \\pi/a$.</p>\n<p><strong>NOTE</strong>: Fill in the missing terms from this list: $hbar^2, a, m, \\pi^2, $, * as multiplier, factor 2, factor 4 and -.</p>\n<p>$A$ = [[0]]&nbsp; &nbsp; $B$ = [[1]]&nbsp; &nbsp; $m^*$ = [[2]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "i", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "hbar^2/(2*m)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "hbar", "value": ""}, {"name": "m", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "ii", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-hbar^2*a^2/(4*m*pi^2)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "a", "value": ""}, {"name": "hbar", "value": ""}, {"name": "m", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "iii", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-m/2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "m", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "PA2230 U3 Q1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Lapington", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28937/"}, {"name": "Steve Baker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9244/"}], "tags": [], "metadata": {"description": "", "licence": null}, "statement": "<p>The semiconducting element silicon (Si) has the following properties.</p>\n<p>Energy gap $E$$_g$ = $1.1$ eV; electron mobility $\\mu$$_e$ = $0.16$ m$^{2}$V$^{-1}$s$^{-1}$; hole mobility $\\mu$$_h$ = $0.05$&nbsp;m$^{2}$V$^{-1}$s$^{-1}$; effective electron mass $m$$_e$$^{*}$ = $0.26$$m$;&nbsp;effective&nbsp;hole mass $m$$_h$$^{*}$ = $0.50$$m$. [$m$ is the free electron mass].</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In an <em>intrinsic</em> semiconductor, which of the following statements is true?</p>\n<p>[[0]]</p>", "gaps": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["The electron concentration in the conduction band is approximately equal to the hole concentration in the valence band.", "The concentration of electrons in the conduction band is exactly equal to the concentration of holes in the valence band at high temperatures, and approximately so at temperatures close to absolute zero.", "The concentrations of electrons and holes in the conduction and valence bands respectively are equal at all temperatures.", "At room temperature, the hole contribution to the electrical conductivity is approximately equal to the electron contribution to the conductivity."], "matrix": [0, 0, "1", "1"], "distractors": ["", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate&nbsp; the charge carrier concentration $n$$_i$ of intrinsic silicon at room temperature. [Take room temperature to be $300$ K]. Give your answer to two significant figures, using scientific E notation e.g. for 6,300,000 input 6.3E+6, for 0.00056 input 5.6E-4 etc.</p>\n<p>$n$$_i$ =[[0]]m$^{-3}$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "2.9*10^{15}", "maxValue": "3.5*10^{15}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the electrical conductivity $\\sigma$ of intrinsic silicon at room temperature. [Take room temperature to be $300$ K]. Give your answer to two sigificant figures.</p>\n<p>$\\sigma$&nbsp;=[[0]]$\\Omega$$^{-1}$ m$^{-1}$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1.0*10^{-4}", "maxValue": "1.2*10^{-4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $10$$^{20}$ atoms m$^{-3}$ of phosphorus&nbsp;impurities are now added to the silicon sample, what will the electron concentration $n$$_c$ in the conduction band be at room temperature, assuming complete ionisation of the phosphorus donor impurities at room temperature? Give your answer using scientific E notation.</p>\n<p>$n$$_c$ =[[0]]m$^{-3}$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "10^{20}", "maxValue": "10^{20}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>For the sample in part (d) above. what will the hole concentration $p$$_v$ in the valence band be, assuming complete ionisation of the phosphorus donor impurities at room temperature? Give your answer to two significant figures, using scientific E notation.</p>\n<p>$p$$_v$ =[[0]]m$^{-3}$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.90*10^{11}", "maxValue": "1.10*10^{11}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "PA2230 U3 Q2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Lapington", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28937/"}, {"name": "Steve Baker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9244/"}], "tags": [], "metadata": {"description": "", "licence": null}, "statement": "<p>A sample of germanium (Ge) has the following values of resistance at the temperatures given:</p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td>$T$ (K)</td>\n<td>$310$</td>\n<td>$321$</td>\n<td>$339$</td>\n<td>$360$</td>\n<td>$383$</td>\n<td>$405$</td>\n<td>$434$</td>\n</tr>\n<tr>\n<td>$R$ (Ohms)</td>\n<td>$13.5$</td>\n<td>$9.10$</td>\n<td>$4.95$</td>\n<td>$2.41$</td>\n<td>$1.22$</td>\n<td>$0.74$</td>\n<td>$0.37$</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Estimate the energy gap $E$$_g$ in Ge. In your written (scanned) answer, state any assumptions that you make. Give your answer to two significant figures.</p>\n<p>$E$$_g$ =[[0]]eV</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.67", "maxValue": "0.69", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A concentration of $0.0001$% arsenic (As) donor impurities is added to a pure Ge sample to form an <em>n</em>-type Ge sample. At a temperature of $300$ K, what percentage of the donor impurities are ionised? (Note: the donor energy levels for As impurities in Ge are $0.013$ eV below the bottom edge of the conduction band). Give your answer to the nearest whole number.</p>\n<p>Percentage&nbsp; =[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "42", "maxValue": "46", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If the concentration of As impurities is $4.4$*$10$$^{22}$ m$^{-3}$, and the electron mobility $\\mu$$_e$ in Ge is $0.39$ m$^{2}$V$^{-1}$s$^{-1}$, what is the electrical conductivity $\\sigma$in the sample? Give your answer to three significant figures. Give your answer to the nearest whole number.</p>\n<p>$\\sigma$&nbsp;=[[0]]$\\Omega$$^{-1}$m$^{-1}$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1205", "maxValue": "1215", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "PA2230 U3 Q3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jon Lapington", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28937/"}, {"name": "Steve Baker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9244/"}], "tags": [], "metadata": {"description": "", "licence": null}, "statement": "<table border=\"2\">\n<tbody>\n<tr>\n<td></td>\n<td>Si</td>\n<td>Ge</td>\n</tr>\n<tr>\n<td>Band Gap $E$$_g$ (eV)</td>\n<td>$1.11$</td>\n<td>$0.67$</td>\n</tr>\n<tr>\n<td>Intrinsic Charge Carrier Concentration $n$$_i$ (cm$^{-3}$)</td>\n<td>$1.4$*$10$$^{10}$</td>\n<td>$2.4$*$10$$^{13}$</td>\n</tr>\n<tr>\n<td>Electron Mobility&nbsp;$\\mu$$_e$ (cm$^{2}$V$^{-1}$s$^{-1}$)&nbsp;</td>\n<td>$1350$</td>\n<td>$3900$</td>\n</tr>\n<tr>\n<td>Hole Mobility&nbsp;$\\mu$$_h$ (cm$^{2}$V$^{-1}$s$^{-1}$)</td>\n<td>$480$</td>\n<td>$1900$</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p>Use the room temperature data given above to answer the following questions.</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the ratio of the room temperature conductivity of Si to that of Ge. Give your answer to three significant figures.</p>\n<p>Ratio =[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.000183", "maxValue": "0.000185", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>By writing the equilibrium carrier concentrations in terms of the effective masses, calculate the ratio of the product $m$$_e$$^{*}$$m$$_h$$^{*}$ for Si to that for Ge. 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