The photoelectric effectAQA A-Level Physics: Revision notes

Electromagnetic radiation arrives as photons, packets of energy $E = hf$. In the photoelectric effect, light shone on a metal surface can release electrons called photoelectrons.

Each electron absorbs one photon, and energy from several photons cannot be added up. An electron can escape only if one photon has enough energy.

Below the threshold frequency $f_0$ no electrons are emitted, however intense the light. Above it, emission is immediate, even for dim light.

The work function $\phi$ is the minimum energy needed to remove an electron from the surface of a metal. It depends on the metal.

Energy is conserved when a photon releases an electron:

$hf = \phi + E_{k(max)}$

At the threshold frequency the electron leaves with no kinetic energy, so $hf_0 = \phi$ and $f_0 = \phi / h$. The equation gives the maximum kinetic energy, for electrons released from the surface.

If a reverse potential difference is applied across a photocell, it slows the photoelectrons. The stopping potential $V_s$ is the potential difference at which even the fastest photoelectrons are stopped, so the current is zero.

$eV_s = E_{k(max)}$

Electrons are emitted with a range of kinetic energies up to the maximum. Electrons at the surface leave with the maximum energy, while electrons from deeper in the metal lose energy in collisions on the way out. You do not need to know how to measure the stopping potential.

Experiments show three things that the wave model cannot explain:

• There is a threshold frequency. The wave model predicts that any frequency would work if the light were bright enough
• Emission is immediate, even for dim light. The wave model predicts a delay while energy builds up
• The maximum kinetic energy depends on the frequency, not the intensity

Increasing the intensity at a frequency above the threshold gives more photons per second, so more electrons per second and a larger current, but no change in the maximum kinetic energy.

Light of wavelength 320 nm is shone on a metal of work function 3.6 × 10⁻¹⁹ J.

• Photon energy $E = hc/\lambda = (6.63 \times 10^{-34} \times 3.00 \times 10^8) \div (320 \times 10^{-9}) = 6.2 \times 10^{-19}$ J
• $E_{k(max)} = 6.2 \times 10^{-19} - 3.6 \times 10^{-19} = 2.6 \times 10^{-19}$ J
• $V_s = E_{k(max)} / e = 1.6$ V

Threshold wavelength: $\lambda_0 = hc/\phi = 5.5 \times 10^{-7}$ m. Light of longer wavelength than this releases no electrons.