Outline why the wave model of light cannot account for the photoelectric effect.

Calculate, in eV, the maximum kinetic energy of the photoelectrons emitted.

The intensity of the light is \({\text{5.1 }}\mu {\text{W}}\,{{\text{m}}^{ - 2}}\). Determine the number of photoelectrons emitted per second for each \({\text{m}}{{\text{m}}^{\text{2}}}\) of the metal surface. Each photon has a 1 in 800 chance of ejecting an electron.

electrons require energy for release;

electrons (are observed) to appear instantaneously;

wave model requires time delay (to build up enough energy);

or

the kinetic energy of the (emitted) electrons depends on frequency (of incident light);

with no electron emission below a threshold frequency;

a wave model suggests emission at all frequencies;

or

Award [2 max] only for this approach.

a maximum electron energy is observed (for a particular wavelength);

a wave model would permit any value so no maximum;

Only allow one route, candidate cannot pick facts from the three alternatives.

(photon) energy \(\frac{{hc}}{\lambda } = \frac{{6.63 \times {{10}^{ - 34}} \times 3.00 \times {{10}^8}}}{{420 \times {{10}^{ - 9}}}}{\text{ }}( = 4.74 \times {10^{ - 19}}{\text{ J}})\);

\({E_{\max }} = (hf - \phi  = ){\text{ }}4.74 \times {10^{ - 19}} - 2.60 \times {10^{ - 19}}\);

1.33 or 1.34 (eV); } (this mark is for correct conversion to eV; allow ECF from incorrect MP1 and MP2)

Award [3] for a bald correct answer.

If no unit given, assume eV and mark accordingly – eg: award [2 max] for a non-conversion.

\(5.1{\text{ }}\mu {\text{W}}\,{{\text{m}}^{ - 2}} = 5.1 \times {10^{ - 12}}{\text{ (J}}{{\text{s}}^{ - 1}}{\text{m}}{{\text{m}}^{ - 2}}{\text{)}}\);

(number of incident photons per \({\text{m}}{{\text{m}}^2}\) per second) = \(\frac{{5.1 \times {{10}^{ - 12}}}}{{4.74 \times {{10}^{ - 19}}}}{\text{ }}( = 1.08 \times {10^7})\);

(number of photoelectrons per \({\text{m}}{{\text{m}}^2}\) per second) = \(\frac{{1.08 \times {{10}^7}}}{{800}}{\text{ }}( = 1.3 \times {10^4})\);

Accept 1.4 \( \times \) \({10^4}\) using rounded energy in (b)(i).

For alternative approaches look for the following in any order:

correct transformation from power/\({{\text{m}}^{\text{2}}}\) to energy/s/\({\text{m}}{{\text{m}}^2}\);

correct use of incoming photon energy; (must see “photon”)

Allow ECF from (b)(i) if identifiable correct insertion of 800 factor and final calculation.

Award [3] for a bald correct answer.

A number of alternative arguments can be used in this question. The most frequent one was the approach via the instantaneous appearance of the electron when radiation of even the lowest intensities is incident. Too many candidates simply quoted some random observations supposing that the examiner would be happy to join up the thinking. However, one route was allowed with arguments that linked the observation quoted with the predictions that would follow from a consideration of the wave model.

Many candidates can now carry out this and similar calculations fluently and confidently.

Again, a large number of correct solutions were seen with many more deficient in one or two aspects of the solution.