(i)     Explain, with reference to the Einstein model of the photoelectric effect, the existence of the threshold frequency.

(ii)     State, with reference to your answer in (a)(i), the reason why the threshold frequency is different for different metals.

(i)     Show that the maximum kinetic energy of the emitted electrons is \(3.4 \times {10^{ - 19}}{\text{ J}}\).

(ii)     Determine the de Broglie wavelength of the electrons in (b)(i).

(i)     light consists of photons/quanta;

a certain minimum amount of energy (the work function) is required to remove an electron from the metal;

if the photon energy is below this energy/work function no electrons will be emitted;

the energy of the photons is proportional to the frequency / \(E = hf\) (with terms defined);

If work function is mentioned it must be defined to award [4].

(ii)     different metals need a different amount of minimum energy for electrons to be removed;

Accept answers in terms of work function if defined either here or in (a)(i).

(i)     \(K{E_{\max }} = hf - \phi \);

\( = 6.6 \times {10^{ - 34}} \times 1.0 \times {10^{15}} - 3.2 \times {10^{ - 19}}\);

\( = 3.4 \times {10^{ - 19}}{\text{ J}}\)

(ii)     use of \(E = \frac{{{p^2}}}{{2m}}\) and \(p = \frac{h}{\lambda }\)\(\,\,\,\,\,\)or\(\,\,\,\,\,\)use of \(v = \sqrt {\frac{{2E}}{m}} \) and \(p = mv = \frac{h}{\lambda }\);

to give \(\lambda  = \frac{h}{{\sqrt {2mE} }}\);

\(\lambda  = 8.4 \times {10^{ - 10}}{\text{ m}}\);

In (a) (i) many candidates showed clearly that they understood the concept of the Einstein model and the existence of a threshold frequency. However, a significant minority of candidates had very little understanding of the topic. Those who answered (i) well had no problem in answering part (ii) correctly.

The problem on maximum kinetic energy was often done well but the standard calculation of the de Broglie wavelength was often done poorly with many candidates unable to make a start.