All subjects · Physics · WPH12 (Unit 2)

The photoelectric effect

Shining light on a metal can release electrons. The way this depends on frequency, not brightness, is strong evidence that light comes in photons.

What is observed

A clean zinc plate on a negatively charged electroscope loses its charge when ultraviolet light shines on it, but not with visible light, however bright. In general:

The photon explanation

Each photon gives all its energy to one electron. An electron needs a minimum energy, the work function φ, to escape the metal surface. Any energy left over becomes kinetic energy:

hf = φ + (1/2)mv2_max

At the threshold frequency, the kinetic energy is zero: hf0 = φ, so f0 = φ / h.

Why the wave model fails

If light were only a wave, energy would arrive continuously, so:

None of these happens. The photoelectric effect is evidence for the particle (photon) nature of light.

Worked example

Light of wavelength 400 nm falls on a metal with work function 2.3 eV. Find the maximum kinetic energy of the photoelectrons.

  1. Photon energy = hc / λ = 4.97 x 10-19 J = 3.11 eV
  2. E_k max = 3.11 - 2.3

Answer: E_k max = 0.81 eV (1.3 x 10-19 J)

Key idea: hf = φ + (1/2)mv2_max; f0 = φ/h. One photon frees one electron: frequency sets the energy, intensity sets the number.

Check yourself

  1. A metal has a work function of 4.3 eV. Find its threshold frequency, in units of 1015 Hz, to 3 s.f.
    Show answer

    1.04 x 1015 Hz. f0 = φ / h = 4.3 x 1.60 x 10-19 / 6.63 x 10-34 = 1.04 x 1015 Hz.

  2. Photons of energy 5.0 eV fall on a metal with work function 3.2 eV. Find the maximum kinetic energy of the photoelectrons in eV.
    Show answer

    1.8 eV. E_k max = hf - φ = 5.0 - 3.2 = 1.8 eV.

  3. A photoelectron has a kinetic energy of 1.8 eV. Find its speed, in units of 105 m/s, to 3 s.f.
    Show answer

    7.95 x 105 m/s. E_k = 1.8 x 1.60 x 10-19 = 2.88 x 10-19 J; v = sqrt(2 x 2.88 x 10-19 / 9.11 x 10-31) = 7.95 x 105 m/s.

  4. The threshold wavelength for a metal is 540 nm. Find its work function in eV, to 3 s.f.
    Show answer

    2.30 eV. φ = hc / λ0 = 1.989 x 10-25 / 540 x 10-9 = 3.68 x 10-19 J = 2.30 eV.

  5. Light above the threshold frequency is made more intense. What happens?
    • The photoelectrons have a higher maximum kinetic energy
    • More photoelectrons are emitted per second, with the same maximum kinetic energy
    • The threshold frequency falls
    • No photoelectrons are emitted
    Show answer

    More photoelectrons are emitted per second, with the same maximum kinetic energy. More photons per second release more electrons, but each photon's energy hf is unchanged.

  6. Why does very bright light below the threshold frequency release no electrons?
    • The light is reflected by the metal
    • The electrons need time to absorb enough energy
    • Bright light has a shorter wavelength
    • Each photon has too little energy, and one photon interacts with one electron
    Show answer

    Each photon has too little energy, and one photon interacts with one electron. No single photon has enough energy to overcome the work function, and electrons cannot save up energy from several photons.

  7. What is the work function of a metal?
    • The energy of the most energetic photoelectron
    • The minimum energy needed to remove an electron from the metal's surface
    • The frequency below which emission happens
    • The p.d. across the metal
    Show answer

    The minimum energy needed to remove an electron from the metal's surface. It is the energy barrier at the surface.

  8. The photoelectric effect is evidence for
    • the particle nature of light
    • the wave nature of light
    • the wave nature of electrons
    • the transverse nature of light
    Show answer

    the particle nature of light. It can only be explained if light arrives in photons.

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Last updated 7 November 2026. Spotted a mistake? Tell us.