7.2.3. Photoelectric Effect

Table of Contents

Light Can Remove Electrons from Matter

The photoelectric effect is the emission of electrons from a material, usually a metal, when light shines on it. These emitted electrons are called photoelectrons. This phenomenon was one of the key discoveries that showed light does not behave only like a wave. It also revealed that light transfers energy in small packets.

In classical wave ideas, brighter light should simply deliver more energy to electrons, and after enough time electrons should escape from the metal. But experiments showed something very different. Electrons were emitted only if the light had a high enough frequency. Even very bright light of low frequency could fail to eject any electrons at all.

This result was surprising and important. It suggested that the energy of light depends on its frequency, not only on its intensity.

Experimental Setup

A simple photoelectric experiment uses a metal surface inside a vacuum tube. Light shines on the metal, and electrons are emitted. These electrons are collected by another electrode, creating a current.

If a battery is connected, the electric potential between the electrodes can help or oppose the motion of the emitted electrons. By changing this potential, we can study the energy of the photoelectrons.

Rendering scientific sketch…

Basic photoelectric effect setup

What Experiments Show

Several important observations come from the photoelectric effect.

First, there is a threshold frequency. Below a certain frequency, no electrons are emitted, no matter how intense the light is.

Second, when the frequency is above the threshold, electrons can be emitted almost immediately. There is no noticeable delay.

Third, increasing the intensity of the light increases the number of emitted electrons, so the photoelectric current increases.

Fourth, increasing the frequency of the light increases the maximum kinetic energy of the emitted electrons.

These results could not be explained well by a purely classical wave picture.

The key experimental rule is this: electrons are emitted only if the light frequency is greater than a threshold frequency $f_0$.

Einstein's Explanation

Einstein explained the photoelectric effect by proposing that light consists of discrete packets of energy called photons. Each photon carries energy

$$
E = hf
$$

where $h$ is Planck's constant and $f$ is the frequency of the light.

A single electron in the metal absorbs energy from a single photon. Part of that energy is used to free the electron from the metal. The minimum energy needed to remove an electron is called the work function, written as $\phi$.

If the photon energy is greater than the work function, the electron escapes and the remaining energy becomes kinetic energy.

This gives the photoelectric equation:

$$
hf = \phi + K_{\max}
$$

where $K_{\max}$ is the maximum kinetic energy of the emitted electron.

Einstein's photoelectric equation is
$$
hf = \phi + K_{\max}
$$
This is the central formula of the photoelectric effect.

Work Function and Threshold Frequency

The work function $\phi$ depends on the material. Different metals hold their electrons with different strengths. A material with a larger work function requires higher-frequency light to emit electrons.

At the threshold frequency, the emitted electron has zero kinetic energy, so

$$
hf_0 = \phi
$$

Thus the threshold frequency is

$$
f_0 = \frac{\phi}{h}
$$

This explains why low-frequency light cannot eject electrons if its photon energy is too small.

Threshold condition:
$$
hf_0 = \phi
$$
If $f < f_0$, no photoelectrons are emitted.

Maximum Kinetic Energy

When the photon energy is more than enough to free the electron, the extra energy becomes kinetic energy. The maximum possible value is

$$
K_{\max} = hf - \phi
$$

This means that photoelectrons become more energetic when the light frequency increases.

It is important to notice that intensity does not appear in this equation. Intensity changes how many photons arrive each second, but the energy of each photon depends only on frequency.

Stopping Potential

To measure the maximum kinetic energy, experimenters apply a reverse voltage that opposes the motion of the emitted electrons. As this voltage increases, fewer electrons reach the collector. At a certain value, even the fastest electrons are stopped. This is called the stopping potential $V_s$.

The electric potential energy needed to stop an electron is

$$
eV_s = K_{\max}
$$

where $e$ is the magnitude of the electron charge.

Combining this with the photoelectric equation gives

$$
eV_s = hf - \phi
$$

$$
V_s = \frac{h}{e}f - \frac{\phi}{e}
$$

This is a straight-line relation between stopping potential and frequency.

Stopping potential relation:
$$
eV_s = K_{\max} = hf - \phi
$$
So the stopping potential increases linearly with light frequency.

Role of Intensity

Intensity affects the number of emitted electrons, provided the frequency is already above threshold. Brighter light means more photons arrive per second. More photons can eject more electrons, so the current increases.

But intensity does not increase the maximum kinetic energy of the electrons. That depends only on frequency.

This is one of the most important ideas of the photoelectric effect.

Quantity changed	Main effect
Increase frequency	Increases photon energy, increases $K_{\max}$
Increase intensity	Increases number of emitted electrons, increases current
Frequency below threshold	No emission, regardless of intensity

Why the Classical Wave Picture Failed

In a classical wave description, light energy is spread continuously across the wavefront. An electron should be able to collect energy gradually from the wave. Then intense light of any frequency should eventually eject electrons.

But experiments showed immediate emission only above a threshold frequency. This means energy transfer is not continuous in this process. Instead, electrons receive energy in single packets from photons.

The photoelectric effect therefore provided strong evidence for the quantum nature of light.

A Simple Energy Picture

You can think of the metal as having an energy barrier that electrons must overcome to escape. The work function is the height of that barrier. A photon brings a fixed amount of energy, $hf$. If that amount is too small, the electron stays trapped. If it is large enough, the electron escapes with the leftover energy.

Rendering scientific sketch…

Energy diagram for the photoelectric effect

Importance in Physics

The photoelectric effect was a turning point in modern physics. It showed that light cannot be understood only as a classical wave. In some experiments, light behaves as if it is made of particles, photons, each carrying energy $hf$.

This discovery helped launch quantum physics. It also led to practical devices such as photoelectric sensors, light detectors, and solar cells, though the detailed operation of such devices belongs to later study.

Summary

The photoelectric effect is the emission of electrons from a material when light of sufficiently high frequency shines on it. The main facts are explained by the photon model of light. Each photon has energy $E = hf$. A minimum energy, the work function $\phi$, is needed to free an electron. The remaining energy becomes kinetic energy.

Essential formulas:
$$
E = hf
$$
$$
hf = \phi + K_{\max}
$$
$$
hf_0 = \phi
$$
$$
K_{\max} = hf - \phi
$$
$$
eV_s = K_{\max}
$$

The photoelectric effect showed that frequency controls the energy of emitted electrons, while intensity controls how many electrons are emitted. This was one of the clearest early pieces of evidence for quantum theory.

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