The photoelectric effect Cambridge International AS & A Level Physics revision
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In plain words
Shine ultraviolet light on zinc and electrons come off. Shine red light on it, however bright, and nothing happens. A wave can't explain that. Einstein's answer was that each electron is knocked out by one photon acting alone: either that one packet has enough energy, or it doesn't.
4 things to know
- Photoelectric emission: electrons are released from a metal surface when radiation of a high enough frequency shines on it. Each electron absorbs one photon.
- The work function φ is the minimum energy needed to free an electron from the surface. The threshold frequency f₀ is the lowest frequency that frees any: hf₀ = φ. (The threshold wavelength is the longest wavelength that works.)
- Einstein's equation: hf = φ + ½mv²max. The photon's energy pays the work function, and what is left over is the electron's maximum kinetic energy.
- Making the light brighter at the same frequency means more photons each second, so more electrons each second (a bigger photoelectric current), but their maximum kinetic energy stays the same.
Worked example
Light of wavelength 400 nm falls on a metal with a work function of 2.0 eV. Find the maximum kinetic energy of the photoelectrons.
- Photon energy = hc ÷ λ = 6.63 × 10⁻³⁴ × 3.00 × 10⁸ ÷ 4.00 × 10⁻⁷ = 4.97 × 10⁻¹⁹ J.
- In electronvolts: 4.97 × 10⁻¹⁹ ÷ 1.60 × 10⁻¹⁹ = 3.1 eV.
- Maximum kinetic energy = 3.1 − 2.0 = 1.1 eV (1.8 × 10⁻¹⁹ J).
Tips and tricks
- Intensity decides how many electrons. Frequency decides how energetic they are. Keep the two apart.
- Have the photon energy and the work function in the same units, both joules or both electronvolts, before you subtract.
It lands in your notebook with its questions as flashcards.
The photoelectric effect: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the work function of a metal?
Photons with less energy than this free nothing.
Light above the threshold frequency is made brighter. What happens?
More photons arrive, and each one can free one electron.
The frequency of the light is increased, above the threshold. What happens to the photoelectrons?
Each photon brings more energy, and the work function is unchanged.
Which observation shows that light behaves as particles?
The others are evidence that light is a wave.
Light below the threshold frequency is made much brighter. What happens?
No single photon has enough energy.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
The photoelectric effect
Cambridge International AS & A Level Physics 9702 · 8 marks · papermunch.org
Name ______________________________ Date ______________
A metal has a work function of 3.2 × 10⁻¹⁹ J. Find its threshold frequency.[2]
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4.8 × 10¹⁴ Hz. 3.2 × 10⁻¹⁹ ÷ 6.63 × 10⁻³⁴.
Light of frequency 1.0 × 10¹⁵ Hz falls on a metal with a work function of 4.0 × 10⁻¹⁹ J. Find the maximum kinetic energy of the electrons emitted.[3]
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2.6 × 10⁻¹⁹ J. The photon energy is 6.63 × 10⁻¹⁹ J.
Explain why light below the threshold frequency releases no electrons, however bright it is.[3]
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Each electron absorbs a single photon. Below the threshold frequency every photon has less energy than the work function, so no electron can escape. Brighter light only means more photons, not more energy in each one.
Answers: The photoelectric effect
- 1. 4.8 × 10¹⁴ Hz. 3.2 × 10⁻¹⁹ ÷ 6.63 × 10⁻³⁴.
- 2. 2.6 × 10⁻¹⁹ J. The photon energy is 6.63 × 10⁻¹⁹ J.
- 3. Each electron absorbs a single photon. Below the threshold frequency every photon has less energy than the work function, so no electron can escape. Brighter light only means more photons, not more energy in each one.