The Photoelectric Effect

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

This phenomenon cannot be explained using classical wave theory — it was one of the key experiments that led to the development of quantum physics.

The Gold-Leaf Electroscope Demonstration

A classic demonstration uses a zinc plate mounted on a gold-leaf electroscope:

1. Charge the electroscope negatively: The gold leaf rises due to repulsion between like charges
2. Shine UV light on the zinc plate: The leaf collapses — electrons are being emitted from the zinc
3. Shine visible light on the zinc plate: Nothing happens (even with very bright light)
4. Charge the electroscope positively: UV light has no effect — positive charge holds electrons in the metal

The Photon Model of Light

To explain the photoelectric effect, Einstein proposed that light consists of discrete packets of energy called photons. Each photon has energy proportional to its frequency:

Where:

• h = 6.63 × 10⁻³⁴ J s — Planck's constant
• f — frequency of the electromagnetic radiation (Hz)
• c = 3.00 × 10⁸ m s⁻¹ — speed of light
• λ — wavelength (m)

The electronvolt is often used as a convenient unit:

When light shines on a metal surface in a vacuum tube, several key observations emerge that challenge wave theory:

Why Wave Theory Fails

Classical wave theory predicts:

• Energy depends on intensity (amplitude²), not frequency → contradicts observations 2 and 3
• Electrons should accumulate energy over time → contradicts observation 1 (instantaneous emission)
• Any frequency should work if intense enough → contradicts observation 2 (threshold frequency)

Einstein explained the photoelectric effect using the photon model, for which he won the Nobel Prize in 1921.

Key Principles

1. One-to-one interaction: Each photon interacts with a single surface electron. Either the photon has enough energy to eject the electron, or it doesn't.
2. Energy quantisation: A photon's energy depends only on its frequency (E = hf), not on intensity.
3. Work function: An electron needs a minimum energy to escape the metal surface. This is called the work function φ (phi) of the metal.
4. Energy conservation: If hf > φ, the excess energy becomes the electron's kinetic energy.

Where:

• hf — energy of the incident photon
• φ — work function of the metal (minimum energy to escape)
• KE_max — maximum kinetic energy of emitted photoelectrons

Threshold Frequency

At the threshold frequency f₀, photoelectrons are emitted with zero kinetic energy:

Below this frequency, no photoelectrons are emitted regardless of intensity.

Why KE is Independent of Intensity

Each photon has energy hf. The intensity only affects how many photons arrive per second, not the energy of each photon. Since the interaction is one-to-one, a brighter light just means more photoelectrons (higher current), not faster ones.

The stopping potential V_s is the minimum reverse voltage needed to stop the most energetic photoelectrons from reaching the collector plate.

How It Works

Photoelectrons are emitted from the metal surface with kinetic energy up to KE_max. If we apply a reverse voltage (collector negative relative to emitter), the photoelectrons must do work against the electric field. The stopping potential is reached when:

Where e = 1.60 × 10⁻¹⁹ C is the elementary charge.

Measuring Stopping Potential

1. Shine monochromatic light on the metal surface
2. Vary the reverse voltage until the photocurrent drops to zero
3. This voltage equals the stopping potential V_s
4. KE_max can then be calculated: KE_max = eV_s

Understanding the graphical relationships is crucial for exam questions.

KE_max vs Frequency

Plotting maximum kinetic energy against frequency gives a straight line:

• Equation: KE_max = hf - φ (compare to y = mx + c)
• Gradient: h (Planck's constant)
• y-intercept: -φ (negative of work function)
• x-intercept: f₀ (threshold frequency)

Photocurrent vs Intensity

For frequencies above the threshold:

• Photocurrent is directly proportional to intensity
• This is because intensity determines the number of photons per second
• More photons = more photoelectrons = higher current

Photocurrent vs Stopping Potential

As the stopping potential is approached:

• Current decreases gradually, then reaches zero at V_s
• This is because electrons have a range of energies up to KE_max
• At V_s, even the most energetic electrons cannot reach the collector

Different metals have different work functions, affecting their threshold frequencies and photoelectric behaviour: