The photoelectric effect and photons - TCE Physics (Tasmania)

What this dot point is asking

The photoelectric effect was one of the first experiments to reveal the quantum nature of light, and it earned Einstein his Nobel Prize. It is central to Unit 4's story of how classical physics gave way to quantum ideas.

The experiment

When light shines on a clean metal surface, electrons can be ejected. These ejected electrons are called photoelectrons. Careful measurements revealed three features that classical wave theory could not explain:

1. There is a threshold frequency below which no electrons are emitted, no matter how bright (intense) the light.
2. The maximum kinetic energy of the emitted electrons depends on the frequency of the light, not its intensity.
3. Emission is essentially instantaneous, even for very dim light above the threshold frequency.

Classical theory predicts that any frequency should work given enough intensity or time, so these results demanded a new model.

The photon model

Einstein proposed that light energy is carried in discrete quanta, now called photons. Each photon has energy proportional to the frequency $f$ of the light:

where $h = 6.63 \times 10^{-34}\ \text{J s}$ is Planck's constant and $\lambda$ is the wavelength. One photon interacts with one electron in a single, all-or-nothing event, which is why emission is instantaneous and why the energy of each electron depends on the energy of a single photon.

Work function and threshold frequency

To escape the metal, an electron must be given at least a minimum energy called the work function $\phi$, a property of the metal. The threshold frequency $f_0$ is the lowest frequency whose photon energy just equals the work function:

If the photon energy $hf$ is less than $\phi$, no electron escapes, however intense the beam. This neatly explains feature 1: it is the energy per photon, not the total energy delivered, that decides whether an electron escapes.

Einstein's photoelectric equation

Energy conservation for one photon ejecting one electron gives Einstein's photoelectric equation:

The photon supplies energy $hf$. Part of it ($\phi$) is used to free the electron, and the rest becomes the maximum kinetic energy of the photoelectron. Increasing the frequency raises $E_{k,\text{max}}$ linearly, while increasing the intensity only increases the number of photoelectrons. A graph of $E_{k,\text{max}}$ against $f$ is a straight line of gradient $h$ and horizontal intercept $f_0$, so plotting experimental data both confirms the theory and lets you measure Planck's constant.

The stopping voltage

In practice the maximum kinetic energy is measured by applying a reverse voltage that just stops the most energetic electrons. At the stopping voltage $V_\text{stop}$ the work done against the field equals the maximum kinetic energy, so $E_{k,\text{max}} = eV_\text{stop}$. This gives a clean experimental route to $E_{k,\text{max}}$ in electronvolts, as used in the calcium question above.

In the exam, watch your units: energies are often quoted in electronvolts, where $1\ \text{eV} = 1.6 \times 10^{-19}\ \text{J}$. Convert to joules before substituting, and use the linear graph of $E_{k,\text{max}}$ against $f$ to extract Planck's constant or the work function when asked.