| Date | May 2013 | Marks available | 4 | Reference code | 13M.2.HL.TZ1.1 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Deduce, Explain, and Suggest | Question number | 1 | Adapted from | N/A |
Question
Data analysis question.
A particular semiconductor device generates an emf, which varies with light intensity. The diagram shows the experimental arrangement which a student used to investigate the variation with distance d of the emf ε. The power output of the lamp was constant. (The power
supply for the lamp is not shown.)
The table shows how ε varied with d.
The student hypothesises that there may be an exponential relationship between ε and d of the form shown below, where a and k are constants.
ε = ae−kd
(i) Deduce a suitable unit for k.
(ii) Suggest the graph that the student should plot in order to get a straight-line graph if the hypothesis is valid.
(iii) Explain how k can be obtained from the graph in (d)(ii).
Markscheme
(i) metre–1;
Allow any SI prefix
(ii) one axis loge ε /loge (ε /a);
other axis d;
(iii) k=–gradient/−reciprocal of gradient;
Minus sign must be seen.
Do not allow ECF from incorrect answer to (d)(ii).
Examiners report
(i) There were good attempts at finding the unit of k but many candidates failed to recognise that the power in an exponential is dimensionless, giving k the units of d-1 (i.e. m-1 or cm-1).
(ii) Although most candidates appeared to be able to perform the appropriate logarithm function to the equation many failed to take the next step and actually state what values needed to be plotted on the graph (that is, logeε vs. d).
(iii) Again, showing that the gradient was equal to –k, most ignored the minus sign and incorrectly stated that the gradient was k.
