Monochromatic light is incident on a metal surface and electrons are emitted instantaneously from the surface.

Explain why

(i) the emission of the electrons is instantaneous.

(ii) the energy of the emitted electrons does not depend on the intensity of the incident light.

The wavelength of the incident light in (a) is 420 nm and the work function of the metal is 3.4×10^–19J.

(i) Determine, in joules, the maximum kinetic energy of an emitted electron.

(ii) The metal surface has dimensions of 1.5 mm×2.0 mm. The intensity of the light incident on the surface is 4.5×10^–6 W m^–2. On average, one electron is emitted for every 300 photons that are incident on the surface. Determine the initial electric current leaving the metal surface.

(i) mention of photons;
of quantized energy / energy is hf;
one to one correspondence with electrons and photons / OWTTE;
(so arrival of light causes emission straightaway)

(ii) intensity is a measure of the number of photons not the individual photon energy;

(i) \(E = \frac{{hc}}{{4.2 \times {{10}^{ - 7}}}}\);
4.7×10^–19J;
so maximum energy (4.7×10⁻¹⁹-3.4×10⁻¹⁹=)1.3×10⁻¹⁹J;

(ii) energy arriving per second=3×10^–6×4.5×10^–6(=1.35×10⁻¹¹W);
so arrival rate of photons \( = \frac{{1.35 \times {{10}^{ - 11}}}}{{4.7 \times {{10}^{ - 19}}}}\) } (allow ECF from (b)(i))
(=2.9×10⁷ photons s^–1);
and a current of \(\left( {\frac{{2.9 \times {{10}^7} \times 1.6 \times {{10}^{ - 19}}}}{{300}} = } \right)1.5 \times {10^{ - 14}}{\rm{A}}\);