Explain why electrons emitted from a metal surface in the photoelectric effect have a range of kinetic energies up to a maximum value, rather than a single fixed kinetic energy, even when illuminated with monochromatic light.

IB DP Physics Higher Level (2023 syllabus) — E.2 Quantum physics (HL only) · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

In a photoelectric effect experiment, monochromatic light of a single, well-defined frequency is directed onto a clean metal surface. The emitted electrons are found to have kinetic energies that vary continuously from zero up to a well-defined maximum value.

Model answer (4 marks)

Each photon transfers its energy hf to a single electron in a one‑to‑one interaction. The electron must first overcome the work function φ to leave the metal, so the maximum kinetic energy is hf−φ. Electrons that originate from the surface can escape without losing energy to the lattice and therefore reach this maximum. Electrons that are produced deeper inside the metal must travel to the surface; during this journey they collide with other electrons and lattice vibrations and lose part of their energy. Consequently they emerge with a lower kinetic energy. The energy loss varies continuously with the depth and the number of collisions, giving a continuous range of kinetic energies from zero (for electrons that lose all excess energy before escaping) up to the maximum hf−φ.

Examiner tips

  • Mention the one‑to‑one photon‑electron transfer and the work function first; then explain depth‑dependent energy loss; keep the explanation concise and use the formula hf−φ for the maximum.
  • Use the word "continuous spectrum" to show understanding of the range of energies.

Common mistakes

  • Saying all electrons have the same kinetic energy; ignoring the work function; confusing photon energy with kinetic energy of all electrons.

Mark scheme (4 marks)

  1. Each photon transfers all of its energy to a single electron in a one-to-one interaction, so the energy available per electron is fixed at hf.
  2. A minimum energy equal to the work function φ is required to free an electron from the surface; electrons originating from the surface require the least energy to escape and so retain the maximum kinetic energy.
  3. Electrons deeper within the metal require additional energy to reach the surface because they undergo collisions / lose energy through interactions with the lattice / other electrons before escaping.
  4. The result is a continuous spectrum of kinetic energies from zero (for electrons that just barely escape after many collisions) up to the maximum hf − φ (for electrons emitted directly from the surface with no additional energy loss).

Key terms in this question

photoelectric effect · monochromatic light

Related

More Quantum physics (HL only) questions

▶ Try answering this question with AI marking (free) →