The photoelectric effectEdexcel International A Level Physics: Revision notes

When electromagnetic radiation of high enough frequency strikes a metal surface, electrons are emitted. These are photoelectrons. Each electron absorbs one photon and gains energy $hf$ in a single event.

Observations:

• no emission below a threshold frequency, however intense the radiation
• emission is instantaneous
• the maximum kinetic energy of photoelectrons increases with frequency but not with intensity
• the number of photoelectrons per second is proportional to intensity (for frequencies above the threshold)

The work function $\phi$ is the minimum energy needed to remove an electron from the surface of a metal. An electron that absorbs a photon of energy $hf$ uses $\phi$ to escape, and the rest is kinetic energy:

$hf = \phi + \tfrac{1}{2}mv_{max}^2$

At the threshold frequency the electron has no kinetic energy left, so $hf_0 = \phi$ and $f_0 = \phi / h$.

A graph of maximum kinetic energy against frequency is a straight line of gradient h, with intercept on the frequency axis at $f_0$.

The electronvolt (eV) is the energy gained by an electron moving through a potential difference of 1 V:

$1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$

To convert eV to J, multiply by 1.60 × 10⁻¹⁹. To convert J to eV, divide.

For example, a work function of 2.3 eV is 2.3 × 1.60 × 10⁻¹⁹ = 3.7 × 10⁻¹⁹ J.

Light of wavelength 400 nm falls on sodium (work function 2.3 eV).

Photon energy = hc/λ = 6.63 × 10⁻³⁴ × 3.00 × 10⁸ / 400 × 10⁻⁹ = 5.0 × 10⁻¹⁹ J.

φ = 2.3 × 1.60 × 10⁻¹⁹ = 3.7 × 10⁻¹⁹ J.

Maximum kinetic energy = 5.0 × 10⁻¹⁹ − 3.7 × 10⁻¹⁹ = 1.3 × 10⁻¹⁹ J.

Threshold frequency = φ/h = 3.7 × 10⁻¹⁹ / 6.63 × 10⁻³⁴ = 5.6 × 10¹⁴ Hz.

The wave model predicts a gradual build-up of energy, so any frequency should work at high intensity, with a delay. The observations contradict this.

The photon model explains them:

• one photon is absorbed by one electron, giving energy hf
• if hf is less than $\phi$ no electron escapes, whatever the number of photons
• more intense radiation means more photons per second, so more electrons per second but not faster ones

This is evidence that electromagnetic radiation is quantised: it comes in packets.