What Is the Work Function of a Metal?

The work function of a metal is the minimum energy required to remove an electron from its surface, represented by $\Phi$ and measured in joules (J) or electronvolts (eV). A photoelectron can escape only when one incident photon supplies at least this energy.

The Photoelectric Mechanism

This is part of E.2 Quantum physics, which is HL-only. In the photoelectric effect, electromagnetic radiation reaches the metal as photons, each carrying energy

$$E = hf$$

where $h$ is the Planck constant and $f$ is the radiation's frequency. One photon transfers its energy to one electron. The work function is a property of the material and its surface condition; it is not determined by the incident light.

The electron must use at least $\Phi$ to escape. Any remaining energy becomes the maximum kinetic energy of the emitted photoelectron:

$$E_{\text{max}} = hf - \Phi$$

At the threshold frequency $f_0$, electrons are just released with zero maximum kinetic energy. Therefore,

$$\Phi = hf_0$$

For example, suppose a metal has $\Phi = 2.2\,\text{eV}$. Converting to joules gives

$$\Phi = 2.2(1.60 \times 10^{-19}) = 3.52 \times 10^{-19}\,\text{J}$$

Thus,

$$f_0 = \frac{\Phi}{h} = \frac{3.52 \times 10^{-19}}{6.63 \times 10^{-34}} = 5.3 \times 10^{14}\,\text{Hz}$$

This corresponds to high-frequency visible or ultraviolet radiation, depending on the metal.

A common misconception is that sufficiently intense low-frequency radiation will release electrons. This is incorrect: if $hf < \Phi$, each photon has insufficient energy. Energy from several low-frequency photons is not normally accumulated by one electron in the standard photoelectric model.

If a stopping potential $V_s$ is given, the fastest electrons are stopped when $eV_s = E_{\text{max}}$, giving .

Exam Technique

For an IB Calculate question, show the equation, substitution, unit conversion and final answer. Keep $\Phi$ and (hf) in the same energy unit, and distinguish between photon energy, work function and maximum kinetic energy.