The big idea: Point a laser pointer at a screen and the light lands as a stream of tiny energy packets — photons — not a smooth flow.
Energy set by frequency: Each photon carries an energy fixed only by the light's frequency f, through E = hf.
- photon energy (J)
- Planck constant, 6.63×10⁻³⁴ J s
- frequency of the light (Hz)
Find the energy of a photon of light with frequency 5.0 × 10¹⁴ Hz.
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Light knocks electrons out of metal: Shine light on a metal and it can eject electrons. Four surprising results prove light is particle-like.
The surprising bits
- There is a threshold frequency — below it, no electrons come out, however bright the light.
- The electrons' maximum kinetic energy depends on the frequency, not the brightness.
- Brighter light (more photons) ejects more electrons, but not faster ones.
- Emission is instant.
Why this needs photons: One electron absorbs one photon. If that photon's energy hf is too small, the electron can't escape — no matter how many photons arrive. A smooth wave couldn't explain a sharp threshold.
Wave model predicts
- Any frequency works if the light is bright enough
- Brighter light gives faster electrons
- Dim light: a delay while energy builds up
What is observed
- Below f₀ nothing, however bright
- Emax depends on f only, not brightness
- Emission is instant, even in dim light
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Some of the photon's energy is used just to free the electron from the metal — the work function Φ. Whatever is left becomes the electron's maximum kinetic energy.
- maximum kinetic energy of an ejected electron (J)
- energy of the incoming photon (J)
- work function — energy to free an electron (J)
Light of frequency 8.0 × 10¹⁴ Hz hits a metal whose work function is 3.0 × 10⁻¹⁹ J. Find the maximum kinetic energy of the ejected electrons.
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The photoelectric effect, step by step
Stopping voltage: Make the collector negative and raise the pd until the current just stops: that stopping voltage Vs halts even the fastest electrons, so eVs = Emax = hf − Φ. On a Vs–f graph the gradient is h/e.
Intensity counts photons: Intensity = (photons per second × hf) ÷ area. Double the wavelength and each photon carries half the energy; double the photon rate as well and the intensity is unchanged.
Two faces of light: Light shows both natures, depending on the experiment:
- wave behaviour — diffraction and interference (the double slit) - particle behaviour — the photoelectric effect (photons)
This is wave–particle duality. Neither picture alone is the whole story.
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A photon bounces off an electron: Fire X-rays at a target: the scattered X-rays have a longer wavelength. A photon has hit a free electron like one ball hitting another, handing it some energy and momentum.
- wavelength before and after scattering (m)
- angle the photon is scattered through
- electron mass, 9.11 × 10⁻³¹ kg
Why it is stronger evidence than the photoelectric effect: In the photoelectric effect the photon is simply absorbed. In Compton scattering it behaves as a particle in a collision, with momentum p = h/λ shared between photon and electron. The wave model predicts no change of wavelength at all.
Photons push: radiation pressure: Each photon carries momentum h/λ. A photon reflected straight back changes its momentum by 2h/λ (absorbed: h/λ). Force on a surface = photons per second × momentum change, and pressure = force ÷ area.
Worked example — X-rays scattered through 90°
X-rays of wavelength 7.10 × 10⁻¹¹ m are scattered by free electrons through 90°. Find the scattered wavelength and the kinetic energy given to the electron.
Solution
- At 90°, cos θ = 0:
- Scattered wavelength:
- Energy lost by the photon goes to the electron:
Final answer
λf = 7.34 × 10⁻¹¹ m; the electron gains about 9.3 × 10⁻¹⁷ J (about 580 eV).
How this is tested — quantum physics is HL only (E.2) and splits cleanly by paper:
Paper 1A
- A quick E = hf.
- Or 'what happens if you increase the intensity / frequency?'
Paper 2
- Use Emax = hf − Φ for a maximum kinetic energy.
- Or a threshold frequency (f₀ = Φ/h), or a stopping voltage.
The classic trap: Brightness changes the number of electrons; frequency changes their energy. Below the threshold frequency, nothing happens however bright the light.
Three easy marks: (1) Brightness changes the number of electrons; frequency changes their energy. (2) Below the threshold frequency, nothing happens. (3) Keep energies in joules (or convert eV with 1 eV = 1.60×10⁻¹⁹ J).
A metal has a work function of 4.0 × 10⁻¹⁹ J. Determine the lowest frequency of light that will eject electrons from it.
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