The big idea: Light is not delivered smoothly — it comes in tiny packets of energy called photons. Each photon carries an energy set only by the light's frequency f.
- photon energy (J)
- Planck constant, 6.63×10⁻³⁴ J s
- frequency of the light (Hz)
Worked example — energy of a photon
Find the energy of a photon of light with frequency 5.0 × 10¹⁴ Hz.
Solution
- Write the given formula first:
- Substitute h = 6.63 × 10⁻³⁴ J s:
- Work it out — keep the unit:
Final answer
E = 3.3 × 10⁻¹⁹ J.
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)
Worked example — maximum kinetic energy
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.
Solution
- Write the given formula first:
- Substitute (hf = 6.63×10⁻³⁴ × 8.0×10¹⁴ = 5.3×10⁻¹⁹ J):
- Work it out:
Final answer
Emax = 2.3 × 10⁻¹⁹ J.
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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Where it shows up: Quantum physics is HL only (E.2):
- Paper 1A — a quick E = hf, or 'what happens if you increase intensity / frequency?'. - Paper 2 — use E_max = hf − Φ to find a maximum kinetic energy, a threshold frequency (f₀ = Φ/h), or a stopping voltage.
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).
IB-style question — finding the threshold frequency
A metal has a work function of 4.0 × 10⁻¹⁹ J. Determine the lowest frequency of light that will eject electrons from it.
Solution
- At the threshold the electron just escapes with zero KE, so Emax = 0 in the given equation:
- Substitute:
- Work it out:
Final answer
f₀ = 6.0 × 10¹⁴ Hz — below this, no electrons are emitted.