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. 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. The surprising bits (which prove light is particle-like):
- 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.
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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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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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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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