(b) a one-to-one interaction between a photon and a surface electron

The idea

The photoelectric effect is explained by treating light as a stream of photons, each carrying energy E = hf, where h is the Planck constant and f the frequency. Emission occurs when a single photon is absorbed by a single electron at or near the metal surface in a one-to-one interaction. All the photon energy is transferred to that electron; it is not shared among many electrons and does not accumulate over time. The electron uses energy equal to the work function φ to escape the surface, and any surplus becomes kinetic energy. If hf is below φ, no emission occurs however intense the beam, because intensity means more photons, not more energetic ones. A useful check is to compare hf with φ for one photon and one electron.

What earns the marks

• A photon is a quantum of electromagnetic radiation carrying energy E = hf, where h is the Planck constant and f is the frequency.
• In the photoelectric effect one photon interacts with one surface electron, so the interaction is one-to-one rather than spread over many electrons.
• The whole photon energy hf is transferred to that single electron; energy is not shared or accumulated over time.
• Emission requires hf to be at least the work function φ; surplus energy appears as kinetic energy of the emitted electron.
• Increasing intensity increases the number of photons per second, so it increases the rate of emission, not the energy delivered per photon.

Common mistakes and how to put them right

• Thinking that many photons can combine their energies to release one electron.

  Put it right: The interaction is one-to-one, so a single photon must supply at least the work function.

• Believing that a very intense low-frequency beam will eventually cause emission.

  Put it right: If hf is less than φ, no single photon has enough energy, so no emission occurs at any intensity.

• Assuming the electron gradually absorbs energy from the wave until it escapes.

  Put it right: Absorption is a single instantaneous photon-electron event, not a gradual build-up.

Exam tips

• State explicitly that one photon interacts with one electron, then use E = hf to justify whether emission is possible.
• When a question mentions intensity, translate it into photons per second and link that to emission rate rather than to electron energy.
• Check the frequency against the threshold before discussing kinetic energy, so your reasoning follows the one-to-one condition.