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Learn9702Paper 4 · A Level Structured QuestionsQuantum physicsPhotons and the photoelectric effect
Quantum physics · Subtopic 1 of 3

Photons and the Photoelectric Effect

Light comes in quanta called photons, each of energy E=hf=hcλE=hf=\dfrac{hc}\lambda (h=6.63×10−34h=6.63\times10^{-34} J s) and momentum p=Ecp=\dfrac Ec. When photons hit a metal, each can release one electron if its energy exceeds the work function Φ\Phi: hf=Φ+12mvmax⁡2hf=\Phi+\tfrac12mv_{\max}^2. Below the threshold frequency f0=Φhf_0=\dfrac\Phi h, no electrons are emitted, however bright the light. Brighter light means more photons, so more electrons, but not faster ones.

Cambridge 9702 Paper 4Edexcel YPH11 WPH12AQA 7408 Paper 1≈ 40 minRevision 7 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Use E=hfE=hf, the electronvolt and p=Ecp=\dfrac Ec.
  • Describe the photoelectric effect and define threshold frequency and work function.
  • Use hf=Φ+12mvmax⁡2hf=\Phi+\tfrac12mv_{\max}^2.
  • Explain the effects of frequency and intensity using the photon model.
Pause and think

Very bright red light shone on zinc releases no electrons, but dim ultraviolet does. How can dimmer light do more?

Section 2 of 14

Core idea

Start hereBright red light does nothing

Shine the brightest red lamp on a zinc plate: no electrons come out. Shine a faint ultraviolet lamp: electrons fly off instantly. Waves can't explain this. Light must arrive in packets, each with an energy set by its frequency.

The big idea

E=hf=hcλE=hf=\frac{hc}\lambda. One photon frees at most one electron: hf=Φ+12mvmax⁡2hf=\Phi+\frac12mv_{\max}^2. Threshold f0=Φhf_0=\frac\Phi h.

1. Evidence for photons

  • Emission is instant, even in dim light.
  • Max KE depends on frequency, not intensity.
  • Intensity only changes the number of electrons per second.
  • Wave theory predicts none of these.

2. Einstein's equation

Maximum kinetic energy of photoelectrons against frequency
2468101214−4−2240frequency (×10¹⁴ Hz)max KE (×10⁻¹⁹ J)gradient = hthreshold f₀intercept −Φ
A straight line: gradient h=6.63×10−34h=6.63\times10^{-34} J s for every metal; the intercept on the energy axis is −Φ-\Phi, different for each metal.
Energy bookkeeping for one photon
  1. hfhf
    Energy delivered by one photon, all to one electron.
  2. hf=Φ+Ek,max⁡hf=\Phi+E_{k,\max}
    At least Φ\Phi is needed to escape; the rest is kinetic (maximum for surface electrons).
  3. eVs=Ek,max⁡eV_s=E_{k,\max}
    Stopping potential just halts the fastest electrons.
  4. Ek,max⁡=0⇒f0=ΦhE_{k,\max}=0\Rightarrow f_0=\frac\Phi h
    Threshold frequency.
Worked example250 nm UV on zinc

Φ=4.3\Phi=4.3 eV.

Goal
Photon energy; max KE; threshold wavelength.
Strategy
E=hc/λE=hc/\lambda in eV.
  1. (6.63×10−34)(3.0×108)2.5×10−7=7.96×10−19 J=4.97 eV\frac{(6.63\times10^{-34})(3.0\times10^8)}{2.5\times10^{-7}}=7.96\times10^{-19}\text{ J}=4.97\text{ eV}
    ÷ 1.6×10−191.6\times10^{-19}.
  2. Ek,max⁡=4.97−4.3=0.67 eVE_{k,\max}=4.97-4.3=0.67\text{ eV}
    Stopping potential 0.67 V.
  3. λ0=hcΦ=289 nm\lambda_0=\frac{hc}\Phi=289\text{ nm}
    Longer wavelengths emit nothing.
Answer4.974.97 eV; 0.670.67 eV; 289289 nm.
✓ Check250<289250<289: emission occurs ✓.
Worked examplePhotons from a laser

1.0 mW at 500 nm.

Goal
Photons per second.
Strategy
Power ÷ energy per photon.
  1. E=hc5.0×10−7=3.98×10−19 JE=\frac{hc}{5.0\times10^{-7}}=3.98\times10^{-19}\text{ J}
    One photon.
  2. 1.0×10−33.98×10−19=2.5×1015 s−1\frac{1.0\times10^{-3}}{3.98\times10^{-19}}=2.5\times10^{15}\text{ s}^{-1}
    Rate.
Answer2.5×10152.5\times10^{15} per second.
✓ CheckHuge numbers: why light seems continuous ✓.
Common misconceptionIntensity raises KE Brighter light means more photons, not more energetic ones.

Summary

  • E=hfE=hf.
  • hf=Φ+Ek,max⁡hf=\Phi+E_{k,\max}.
  • 1 eV =1.6×10−19=1.6\times10^{-19} J.
Key words
Work function
Minimum energy to free an electron.
Photon
Quantum of EM energy.
HistoryEinstein's Nobel Prize. Einstein won the 19211921 Nobel Prize not for relativity but for his 19051905 explanation of the photoelectric effect. Robert Millikan spent ten years trying to disprove Einstein's equation and ended up confirming it precisely, measuring Planck's constant along the way.
Fun factSolar sails. Photons carry momentum, so sunlight pushes on anything it hits. Japan's IKAROS spacecraft in 20102010 unfurled a 1414 m sail and was propelled by sunlight alone, the pressure being about the weight of a few grains of sand.
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