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Photoelectric Effect

Understand the photoelectric effect, work function, threshold frequency, and stopping potential, with graph explanations and a worked frequency-change example.

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Tutorial Content

Photoelectric Effect

The photoelectric effect occurs when light transfers enough energy to electrons in a material for them to escape. The emitted electrons are called photoelectrons. If they are collected in a circuit, they produce a photocurrent.

In the diagram, the cathode is the illuminated emitting surface; the anode collects electrons. The voltmeter measures the applied potential difference, and the ammeter measures the photocurrent.

1. Why frequency matters

Increasing the intensity of light does not, by itself, guarantee electron emission. In the usual single-photon model, one photon transfers energy $h\nu$ to one electron. That energy must be sufficient to overcome the material's work function, $W_0$.

The work function is the minimum energy needed to remove an electron from the surface. It depends on the material and its surface condition. The threshold frequency is

Below this frequency, the model predicts no emission, even if the light is made brighter. At the threshold, the maximum kinetic energy is zero. Above it, the excess photon energy can become kinetic energy.

2. Einstein's photoelectric equation

• $h$ is Planck's constant.
• $\nu$ and $\lambda$ are the frequency and wavelength of the incident light.
• $c$ is the speed of light.
• $E_{k,\max}$ is the greatest kinetic energy of an emitted electron, not the energy of every emitted electron.

In the non-relativistic model, $E_{k,\max}=\frac12 mv_{\max}^2$. If $h\nu<W_0$, a negative value from the equation means that emission is not possible under these assumptions; it is not a negative electron kinetic energy.

3. Reading the graphs

Maximum kinetic energy against frequency

The slope is $h$ when the energy and frequency units are chosen consistently. The horizontal intercept is $\nu_0$. Extending the straight line back to the vertical axis gives $-W_0$.

The dashed section below zero is only an extrapolation. It does not represent emitted electrons with negative kinetic energy.

Photocurrent against applied voltage

At a sufficiently positive collecting voltage, essentially all emitted electrons reach the collector and the current reaches its saturation value.

A reverse voltage opposes the electrons' motion. Let $U_c$ denote the positive magnitude of the stopping potential and $e$ the positive elementary charge. Then

On the signed voltage axis shown above, the intercept is $-U_c$. Do not insert that negative coordinate into an equation that uses the positive magnitude.

For the same metal at a fixed frequency above threshold, increasing intensity increases the photon arrival rate and usually raises the saturation current. It does not increase the energy per photon, the maximum kinetic energy, or the stopping potential in this model. Changing the frequency or the work function can change the stopping potential.

4. Keep energy units consistent

Useful approximate values are

For light with wavelength $400\ \mathrm{nm}$, the photon energy is approximately $1240/400=3.10\ \mathrm{eV}$. Subtract the work function in the same energy unit before finding the maximum kinetic energy. Use the constants and rounding instructions supplied in the question.

5. Worked example: doubling the frequency

Light of frequency $\nu$ produces a stopping-potential magnitude $U_c$ from a metal with work function $W_0$. Assume the same metal and surface conditions when the frequency doubles.

Initially,

At frequency $2\nu$,

Therefore,

Since $W_0>0$, the new stopping-potential magnitude is more than twice the original. Doubling the frequency doubles the photon energy, but the work function is subtracted only once in each emission event.

Further reading

• OpenStax University Physics: Photoelectric effect

Content reviewed: 9 September 2026.