Cambridge A Level Physics 9702 — 2011 May/June Paper 5 · Variant 1

1 When light is incident on the front of a photocell, an e.m.f. is generated in the photocell. For Examiner’s A student wishes to investigate the effect of adding various thicknesses of glass in front of Use a photocell. This may be carried out in the laboratory by varying the number of identical thin glass sheets between a light source and the front of the photocell. It is suggested that the e.m.f. V is related to the number n of glass sheets by the equation V = V0e –αnt where t is the thickness of one sheet, α is the absorption coefficient of glass and V0 is the e.m.f. for n = 0. Design a laboratory experiment to determine the absorption coefficient of glass. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. 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Defining the Methods of Method of Safety Additional For problem data collection analysis considerations detail Examiner’s Use

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P1 n is the independent variable and V is the dependent variable or vary n and measure V [1] P2 Keep distance from light to photocell constant [1] P3 Keep intensity of light constant. Allow constant voltage across lamp/current through lamp/brightness. Do not allow ‘same lamp/output’. [1] Methods of data collection (5 marks) M1 Labelled diagram of apparatus: lamp, glass sheet and photocell in line. [1] M2 Voltmeter connected to photocell. Penalise unworkable photocell circuit. [1] M3 Use micrometer (screw gauge) to measure thickness of glass sheet. [1] M4 Take many readings of thickness and average. [1] M5 Perform experiment in a dark room or shield apparatus. [1] Method of analysis (2 marks) A1 Plot a graph of ln V against n. Allow ln V against nt [1] A2 α = (–)gradient / t. (ln V against nt then α = (–)gradient) [1] Safety considerations (1 mark) S Reasoned method to prevent burns from hot source, e.g. use gloves Reasoned method to prevent eye damage from bright/intense source, e.g. shield lamp/ dark glasses/do not look at source directly Reasoned method to prevent cuts from glass e.g. use gloves. [1] Additional detail (4 marks) D Relevant points might include [4] 1 Use small distance/high intensity to gain large reading. 2 Method to check output of lamp is constant e.g. measure current through/p.d. across lamp/regularly check V0 with no glass. 3 Reasoned method to ensure output of lamp is constant e.g. workable circuit diagram with variable resistor or variable power supply. 4 Clean sheets of glass before use. 5 Direction of light is perpendicular to glass sheets/constant orientation. 6 ln V = –αnt + ln V0. 7 Further safety consideration. Do not allow vague computer methods. [Total: 15] GCE AS/A LEVEL – May/June 2011 9702 51

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2 A student is investigating how a volume of nitrogen gas is affected by the pressure exerted For on it. Examiner’s Use A sample of nitrogen gas is trapped in a vertical tube of uniform cross-sectional area by a small volume of oil. Pressure is applied by a pump. The applied pressure is measured on a gauge, as shown in Fig. 2.1. nitrogen h pressure gauge oil pump air Fig. 2.1 The temperature T of the nitrogen is 290 K. An experiment is carried out to investigate how the height h of nitrogen trapped in the tube varies with the pressure p. Question 2 continues on the next page. It is suggested that p and h are related by the equation For Examiner’s pAh = NkT Use where A is the cross-sectional area of the tube, k is the Boltzmann constant and N is the number of molecules of nitrogen gas. 1 (a) A graph is plotted of p on the y-axis against on the x-axis. Express the gradient in h terms of N. gradient = ..................................................[1] (b) Values of p and h are given in Fig. 2.2. p / 105 Pa h / 10–3 m 1.10 400 ± 5 1.22 360 ± 5 1.38 320 ± 5 1.57 280 ± 5 1.83 240 ± 5 2.09 210 ± 5 Fig. 2.2 1 1 Calculate and record values of in Fig. 2.2. Include the absolute uncertainties in . h h [3] 1 1(c) (i) Plot a graph of p / 105 Pa against / m–1. Include error bars for [2] h h. (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the uncertainty in your answer. gradient = ..................................................[2] 2.1 For Examiner’s Use 2.0 1.9 p / 105 Pa 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 1 / m–1 h

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 NkT/A 290Nk/A (b) T1 1 Column heading. Allow equivalent unit. / m–1 h e.g. h–1 / m–1 T2 2.5 or 2.50 A mixture of 2sf and 3sf is allowed. 2.8 or 2.78 3.1 or 3.13 3.6 or 3.57 4.2 or 4.17 4.8 or 4.76 U1 From ± 0.03 to ± 0.1, ± 0.11 or ± 0.12 Allow more than one significant figure. (c) (i) G1 Six points plotted correctly Check second and fifth plots and other anomalous plots. Must be less than half a small square. Ecf allowed from table. U2 1 Half square or greater loses the mark. Ecf All error bars in plotted correctly h allowed from table. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (2.20, 1.0) and (2.30, 1.0) and upper end of line should pass between (4.75, 2.1) and (4.85, 2.1). Allow ecf from points plotted incorrectly – examiner judgement. G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Steepest or shallowest possible line Should pass from top of top error bar to that passes through all the error bars. bottom of bottom error bar or bottom of top error bar to top of bottom error bar. Mark scored only if error bars are plotted. (iii) C1 Gradient of best fit line The triangle used should be at least half the length of the drawn line. Check the read offs. Work to half a small square. Do not penalise POT. U3 Uncertainty in gradient Method of determining absolute uncertainty Difference in worst gradient and gradient. (d) C2 gradient × A Gradient must be used. Value of N = Allow ecf from (c)(iii) but penalise POT. kT U4 Determines uncertainty in N Method required. Do not check calculation. (e) (i) C3 Method to determine h NkT −20 h = = 1.111 × 10 × N ; T = 278 K pA Must use answer from (d). C4 Between 0.361 and 0.391 given to 2 or Must be in range. Allow 0.36, 0.37, 0.38 or 3 sf 0.39. Assume metres unless otherwise specified. (ii) U5 Percentage uncertainty % uncertainty in N + % uncertainty in T) [Allow ∆T to be 0.5 or 1] [Total: 15] GCE AS/A LEVEL – May/June 2011 9702 51 Uncertainties in Question 2 (c) (iii) Gradient [U3] Uncertainty = gradient of line of best fit – gradient of worst acceptable line Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (d) [U4] Uncertainty = worst N – N ∆m ∆N = × N m A ∆N = ∆m × kT (e) [U5] ∆h Percentage uncertainty = × 100 h Percentage uncertainty = percentage uncertainty in N + percentage uncertainty in T

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