The photoelectric effect, explained with examples

By The STEM-Tutor team · Updated October 2026

When light shines on a metal surface, it can knock electrons out. The details of how this happens could not be explained by treating light as a wave, and explaining them earned Einstein his Nobel Prize.

What happens

When electromagnetic radiation of high enough frequency shines on a clean metal surface, electrons are emitted from the surface. These are called photoelectrons. A classic demonstration uses a gold-leaf electroscope with a zinc plate on top. Charge the plate negatively, and the gold leaf rises. Shine ultraviolet light on the zinc, and the leaf falls as electrons are emitted. Shine bright visible light instead, even for a long time, and nothing happens.

The key observations

1. Electrons are only emitted if the frequency of the light is above a certain minimum, the threshold frequency f₀, which depends on the metal.
2. Below the threshold, no electrons are emitted however intense the light is or however long it shines.
3. Above the threshold, emission is instantaneous.
4. The maximum kinetic energy of the photoelectrons depends on the frequency of the light, not its intensity.
5. Increasing the intensity increases the number of electrons emitted per second, but not their maximum kinetic energy.

Why wave theory fails

If light were only a wave, its energy would be spread continuously across the surface and would depend on intensity. A bright enough light of any frequency should eventually give electrons enough energy to escape, and dim light should cause a delay while electrons gathered energy. Neither prediction matches what happens. The threshold frequency and the instant emission are both unexplained by wave theory.

Einstein's photon explanation

Einstein proposed that light is made of discrete packets of energy called photons, each with energy

E = hf = hc/λ

where h = 6.63 × 10⁻³⁴ J s is the Planck constant. Each electron absorbs the energy of exactly one photon, all at once. To escape, an electron needs at least a minimum energy called the work function, φ, of the metal. If hf < φ, no electron can escape, no matter how many photons arrive. That explains the threshold: f₀ = φ/h. Higher intensity means more photons per second, so more electrons per second, but each photon still has the same energy.

Einstein's photoelectric equation

hf = φ + E_k(max)

The photon's energy is used to free the electron (the work function) and any leftover becomes the electron's kinetic energy. Electrons from deeper in the metal need more than φ to escape, so they leave with less kinetic energy; that is why we talk about the maximum kinetic energy.

Electronvolts

Energies at this scale are often given in electronvolts (eV). One electronvolt is the energy gained by an electron accelerated through a potential difference of 1 V: 1 eV = 1.60 × 10⁻¹⁹ J. To convert from eV to J, multiply by 1.60 × 10⁻¹⁹; to convert from J to eV, divide.

Worked examples

Example 1: photon energy

Find the energy of a photon of ultraviolet light with wavelength 250 nm, in joules and electronvolts.

• E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸)/(250 × 10⁻⁹) ≈ 7.96 × 10⁻¹⁹ J.
• In eV: 7.96 × 10⁻¹⁹/1.60 × 10⁻¹⁹ ≈ 4.97 eV.

Example 2: maximum kinetic energy

Zinc has a work function of 4.3 eV. Find the maximum kinetic energy of electrons emitted by the 250 nm light.

• E_k(max) = hf − φ = 4.97 − 4.3 = 0.67 eV, or about 1.1 × 10⁻¹⁹ J.

Example 3: threshold frequency

Find the threshold frequency for zinc.

• φ = 4.3 × 1.60 × 10⁻¹⁹ = 6.88 × 10⁻¹⁹ J.
• f₀ = φ/h = 6.88 × 10⁻¹⁹/6.63 × 10⁻³⁴ ≈ 1.04 × 10¹⁵ Hz, in the ultraviolet. That is why visible light does not release electrons from zinc.

Example 4: will emission happen?

Red light of wavelength 700 nm falls on a metal with work function 2.3 eV. Are electrons emitted?

• Photon energy = hc/λ ≈ 2.84 × 10⁻¹⁹ J ≈ 1.78 eV.
• 1.78 eV < 2.3 eV, so no electrons are emitted, however bright the light.

Example 5: maximum speed

Electrons leave a surface with maximum kinetic energy 1.2 × 10⁻¹⁹ J. Find their maximum speed. (m_e = 9.11 × 10⁻³¹ kg)

• v = √(2E_k/m) = √(2.4 × 10⁻¹⁹/9.11 × 10⁻³¹).
• v ≈ 5.1 × 10⁵ m/s.

Stopping potential and the graph

The maximum kinetic energy can be measured by applying a reverse potential difference that slows the electrons. The smallest voltage that stops all of them is the stopping potential V_s, where eV_s = E_k(max). A graph of E_k(max) against frequency is a straight line with gradient h, an x-intercept at the threshold frequency f₀, and a y-intercept of −φ. Every metal gives a parallel line with the same gradient, because h is a universal constant, but a different intercept.

Why it matters

The photoelectric effect was key evidence that light behaves as particles as well as waves, the idea of wave-particle duality. Diffraction and interference show light's wave nature; the photoelectric effect shows its particle nature. Solar cells and light sensors work on closely related principles, and the same photon idea explains line spectra and energy levels in atoms.

Common mistakes

• Saying brighter light gives electrons more energy; it gives more electrons, not more energetic ones.
• Forgetting to convert between eV and J.
• Using nm without converting to metres.
• Thinking one electron can absorb several photons to escape; at A level, it is one photon per electron.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is the photoelectric effect in AS or A level Physics?

It is usually a first-year topic, in the particles and quantum phenomena section. Check your specification.

Is the photoelectric effect in AP Physics?

It is part of modern physics in AP Physics 2.

Key takeaways

• Light is made of photons with energy E = hf.
• Electrons are emitted only if hf is at least the work function.
• hf = φ + E_k(max).
• Intensity changes the number of electrons, not their maximum energy.
• 1 eV = 1.60 × 10⁻¹⁹ J.

Related guides

• A level Physics topics
• A level Physics formula sheet
• The electromagnetic spectrum