What does the existence of a threshold frequency in the photoelectric effect show about the energy of light?

It shows that energy is exchanged in quanta of size hf, since below a certain frequency no single quantum is large enough to free an electron however bright the light is.

How are the work function and the threshold frequency of a metal related?

The work function equals the Planck constant multiplied by the threshold frequency, φ = hf₀.

A metal has a work function of 2.0 eV. What is its threshold frequency?

The work function is 2.0 × 1.60 × 10⁻¹⁹ = 3.20 × 10⁻¹⁹ J, so f₀ = φ/h = 3.20 × 10⁻¹⁹ / 6.63 × 10⁻³⁴ = 4.8 × 10¹⁴ Hz.

OCR A-Level Physics B H557

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Waves and Quantum Behaviour

Evidence that photons exchange energy in quanta

3 things to know
Components 01, 02 and 03

Overview

Recall questions on threshold frequency, work function and φ = hf₀, the photoelectric equation hf = φ + Eₖ(max) and calculations with it, why intense light below threshold frees no electrons, why the wave model fails, line emission spectra, determining the Planck constant with LEDs, and the limits of the particle and wave models of light.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the photoelectric equation and explain what each term represents.

Key term

Define the work function of a metal.

Key term

Define the threshold frequency for a metal surface.

Questions from this subtopic

Each one with the model answer underneath.

1
What does the existence of a threshold frequency in the photoelectric effect show about the energy of light?
Model answer
It shows that energy is exchanged in quanta of size hf, since below a certain frequency no single quantum is large enough to free an electron however bright the light is.
2
Define the work function of a metal.
Model answer
The work function is the minimum energy needed to remove an electron from the surface of that metal.
3
Define the threshold frequency for a metal surface.
Model answer
The threshold frequency is the lowest frequency of radiation that can release electrons from that surface.
4
How are the work function and the threshold frequency of a metal related?
Model answer
The work function equals the Planck constant multiplied by the threshold frequency, φ = hf₀.
5
State the photoelectric equation and explain what each term represents.
Model answer
The equation is hf = φ + Eₖ(max), where hf is the energy of the incident photon, φ the work function of the metal and Eₖ(max) the greatest kinetic energy an emitted electron can have.
6
A metal has a work function of 2.0 eV. What is its threshold frequency?
Model answer
The work function is 2.0 × 1.60 × 10⁻¹⁹ = 3.20 × 10⁻¹⁹ J, so f₀ = φ/h = 3.20 × 10⁻¹⁹ / 6.63 × 10⁻³⁴ = 4.8 × 10¹⁴ Hz.

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