Photoelectric Effect

Overview

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

It provided strong evidence that light can behave as particles called photons.

This topic is a key part of Quantum Physics.

Definition

The photoelectric effect is the emission of photoelectrons from a metal when incident photons transfer sufficient energy to electrons at the surface.

Why It Matters

This phenomenon is important because it:

• showed the limits of classical wave theory
• supported the photon model of light
• introduced threshold frequency and work function ideas
• provides one of the clearest links between light and quantised energy

Key Representations

Experimental Setup

A typical photoelectric tube contains:

• clean metal cathode
• anode collector plate
• evacuated glass tube
• variable potential difference
• microammeter to measure current
• monochromatic light source

Process:

1. light shines on the cathode
2. electrons are emitted from the metal surface
3. emitted electrons move to the anode
4. current is measured

Key Observations

1. Threshold Frequency Exists

Below a certain frequency:

• no electrons are emitted
• regardless of intensity

2. Immediate Emission

When frequency is above threshold:

• electrons may be emitted almost instantly

3. Maximum Kinetic Energy Depends on Frequency

For a fixed metal and frequency above threshold, higher incident frequency gives higher maximum electron kinetic energy.

4. Photocurrent Depends on Intensity

At fixed frequency above threshold:

• increasing intensity increases the emitted-electron rate
• photocurrent increases

Why Classical Wave Theory Failed

Classical wave theory predicted:

• energy delivered continuously
• brighter light should eventually eject electrons at any frequency
• delay before emission possible

But experiments showed:

• threshold frequency
• no delay
• kinetic energy depends on frequency

Hence a new model was needed.

Photon Model of Light

Light consists of photons.

Each photon carries energy:

$$E=hf$$

where:

• $h$ = Planck constant
• $f$ = frequency

One photon transfers energy to one electron.

Threshold Frequency

Minimum frequency required for emission:

$$f_0$$

If:

$$f<f_0$$

then no emission occurs.

If:

$$f>f_0$$

electrons can be emitted.

Work Function

The minimum energy needed to remove an electron from the metal surface is called the work function.

Symbol:

$$\Phi$$

Relation with threshold frequency:

$$\Phi =h{f}_0$$

Different metals have different work functions.

Photoelectric Equation

Einstein’s photoelectric equation:

$$hf=\Phi +K{E}_{\max }$$

where:

• $hf$ = photon energy
• $\Phi$ = work function
• $K{E}_{\max }$ = maximum kinetic energy of emitted electrons

Meaning of the Equation

Photon energy is used for:

1. overcoming attraction within the metal
2. the remaining energy becomes electron kinetic energy

Hence:

• for a fixed metal, higher frequency gives larger $K{E}_{\max }$
• higher intensity alone does not increase $K{E}_{\max }$

Stopping Potential

A reverse potential difference can stop emitted electrons reaching the anode.

When current just becomes zero:

$$K{E}_{\max }=e{V}_s$$

where:

• $e$ = elementary charge
• $V_s$ = stopping potential

Thus:

$$hf=\Phi +e{V}_s$$

Graph Interpretation

1. $K{E}_{\max }$ vs Frequency

Using:

$$K{E}_{\max }=hf-\Phi$$

The graph is a straight line:

• gradient = $h$
• x-intercept = threshold frequency $f_0$
• y-intercept = $-\Phi$

2. Photocurrent vs Voltage

As anode voltage increases:

• more electrons are collected
• current rises
• the current reaches saturation

With reverse voltage:

• current decreases
• becomes zero at $V_s$

3. Photocurrent vs Intensity

At fixed frequency above threshold:

• greater intensity gives more emitted electrons per second
• larger photocurrent

Intensity vs Frequency Distinction

Frequency determines:

• photon energy
• whether emission occurs
• maximum kinetic energy for a fixed metal

Intensity determines:

• number of photons arriving each second
• number of electrons emitted
• photocurrent

This distinction is heavily tested.

Summary

The photoelectric effect shows that light behaves as photons.

Core equations:

$$E=hf$$ $$hf=\Phi +K{E}_{\max }$$ $$K{E}_{\max }=e{V}_s$$

Key conclusions:

• threshold frequency exists
• emission can be immediate
• intensity affects photocurrent
• frequency affects electron energy

Links

• Quantum Physics
• Wave-Particle Duality
• Quantum Physics Common Exam Traps