When light of various frequencies is incident on the metal cathode of a photocell, photoelectrons are emitted from the surface of the cathode - NSC Physical Sciences - Question 10 - 2021 - Paper 1

As the wavelength of the incident radiation/light increases, the maximum kinetic energy of the emitted electrons decreases. This indicates that the maximum kinetic energy is inversely proportional to the wavelength.

The work function is the minimum energy required to remove an electron from the surface of a metal. It is a key concept in understanding photoelectric effects and is specific to each material.

To determine the work function ( W_0 ), use the formula: ( W_0 = E - E_{k(max)} ). From the graph, for a wavelength of 1.0 x 10⁷ m, the kinetic energy is approximately 11.6 x 10⁻¹⁹ J. The energy of the photon can be calculated using ( E = \frac{hc}{\lambda} ), where ( h = 6.63 \times 10^{-34} \text{ J·s} ) and ( c = 3.0 \times 10^8 \text{ m/s} ). Substituting the values, ( E ) is approximately 1.24 x 10⁻¹⁹ J. Then, ( W_0 = 1.24 x 10^{-19} - 11.6 x 10^{-19} = -10.36 x 10^{-19} ), which is an inversion indicating that the incident energy exceeds the work function.

For a wavelength of 0.5 x 10⁷ m, use the same photon energy formula. Calculate ( E = \frac{hc}{0.5 x 10^7} ) which approximately yields ( E = 3.98 x 10^{-19} J ). Now subtract the work function from this energy to find the maximum kinetic energy: ( E_{k(max)} = E - W_0 = 3.98 x 10^{-19} J - W_0 ). If we substitute ( W_0 \approx 5.26 x 10^{-19} J ), the final kinetic energy is calculated as ( E_{k(max)} = 3.98 x 10^{-19} J - 5.26 x 10^{-19} J ). Thus, the maximum kinetic energy is approximately 1.5 x 10^{-19} J.