# 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

> 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.

## 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

- [photoelectric effect](https://www.gradenine.co.uk/glossary/photoelectric-effect)
- [monochromatic light](https://www.gradenine.co.uk/glossary/monochromatic-light)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-electrons-emitted-from-a-ed660f2f) · Published by Druglandscape Ltd.