Part 1: Core observations

The photoelectric effect is the emission of electrons from the surface of a metal when electromagnetic radiation of sufficiently high frequency is incident on it. The emitted electrons are called photoelectrons.

Experiments showed three key facts:

1. There is a minimum frequency needed for emission.
2. Above that minimum frequency, the number of electrons emitted each second depends on intensity.
3. Emission begins without any measurable delay once suitable radiation reaches the surface.

The minimum frequency is called the threshold frequency.

Below the threshold frequency, no photoelectrons are emitted however intense the radiation is. Above the threshold frequency, increasing the intensity increases the number of photons arriving each second, so more electrons can be emitted each second.

The apparatus sketch below shows the observation to notice: ultraviolet radiation can discharge the electroscope by ejecting electrons, whereas visible light below the threshold frequency leaves the leaf raised.

[DIAGRAM: asset_name: 2.2.1 - The Photoelectric Effect - Diagram 1; asset_slug: 2.2.1 - The Photoelectric Effect - Diagram 1; recommended_method: retained_png; description: A zinc plate on a gold-leaf electroscope. UV radiation falls on the plate and electrons leave the surface, causing the gold leaf to fall. A second label shows that visible light below threshold does not eject electrons.]

These observations were a major problem for classical wave theory, because a wave picture suggests that energy is spread continuously across the surface.

Part 2: Einstein's photon explanation

Einstein explained the observations by proposing that light arrives in discrete packets called photons, not as a continuously spread-out energy supply.

Here $h$ is the Planck constant, $f$ is the frequency, $c$ is the speed of light, and $\lambda$ is the wavelength. The crucial idea is that one surface electron absorbs one photon.

This immediately explains the threshold frequency. If a photon's energy $hf$ is smaller than the minimum energy needed to free an electron, that electron cannot escape. It does not matter how many other low-energy photons arrive.

The photon model also explains the lack of a time delay. Once a photon with enough energy is absorbed, the electron can escape straight away. There is no need for the electron to "save up" energy from many weak wavefronts.

The comparison below shows what matters in Einstein's model: one photon transfers its energy to one electron, whereas a classical wave picture would smear the energy across many electrons.

[DIAGRAM: asset_name: 2.2.1 - The Photoelectric Effect - Diagram 2; asset_slug: 2.2.1 - The Photoelectric Effect - Diagram 2; recommended_method: retained_png; description: A single photon of energy $hf$ striking one surface electron and ejecting it. A crossed-out comparison diagram shows a wave spreading energy over many electrons.]

Part 3: Work function and the photoelectric equation

Different metals hold their electrons with different strengths. The minimum energy needed to release an electron from a particular metal is called the work function, $\phi$.

When a photon is absorbed, some of its energy is used to overcome the work function. Any remaining energy becomes the kinetic energy of the emitted electron. The most energetic photoelectrons have the maximum kinetic energy, written $E_{K(\text{max})}$.

At the threshold frequency, the photon only just frees the electron, so $E_{K(\text{max})} = 0$ and therefore

This means the threshold frequency depends on the metal because the work function depends on the metal.

If you rearrange the photoelectric equation to

then a graph of $E_{K(\text{max})}$ against $f$ is a straight line with gradient $h$, $y$-intercept $-\phi$, and $x$-intercept $f_0$.

The graph below is worth learning visually, so notice the positive gradient $h$, the x-axis crossing at $f_0$, and the y-axis crossing at $-\phi$.

[DIAGRAM: asset_name: 2.2.1 - The Photoelectric Effect - Diagram 3; asset_slug: 2.2.1 - The Photoelectric Effect - Diagram 3; recommended_method: retained_png; description: A graph of $E_{K(\text{max})}$ on the y-axis against frequency $f$ on the x-axis. The line has positive gradient, crosses the x-axis at $f_0$, and the y-axis at $-\phi$.]

Part 4: Stopping potential

The emitted photoelectrons do not all leave the surface with the same kinetic energy. The fastest ones have the maximum kinetic energy, and that is what the stopping potential measures.

If a photoelectron of charge $e$ is just stopped, its maximum kinetic energy equals the electrical energy transfer $eV_s$.

Combining this with the photoelectric equation gives

You are not required to know the experimental method for determining stopping potential, but you must know what it means and how to use it in calculations.

The calculation below uses that direct link between stopping potential and the maximum kinetic energy of the emitted electrons.

Part 5: Frequency versus intensity

Students often mix up the effect of changing frequency with the effect of changing intensity. The safest approach is to link frequency to the energy of each photon and intensity to the number of photons arriving each second.

The important correction here is that "same intensity" does not mean "same number of photons". If the frequency rises while the intensity stays fixed, each photon carries more energy, so fewer photons are needed each second to deliver the same total power.

Explaining Threshold Behaviour

You now have the full exam toolkit for this topic: threshold frequency tells you whether emission can happen, the work function sets the energy barrier, the photoelectric equation tracks the energy balance, and the stopping potential tells you the maximum kinetic energy.