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4.11.1Electrons, Waves and Photons

The Photon

5 min read 6 parts Lesson 18 of 62 Unit quiz

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Part 1 of 6The Photon Model

4.11.1 The Photon
Quantum of energy
  • A photon is a discrete packet of electromagnetic energy that travels at the speed of light.
Energy formula
  • The energy of a photon is E = hf, where h is the Planck constant and f is the frequency.
Wavelength form
  • Because c = fλ, the energy can also be written E = hc/λ.
Size of the energy
  • Photon energies are tiny, of the order of 10⁻¹⁹ J for visible light, so we need very large numbers of photons.

Part 2 of 6Dependence on the Waves

Dependence on the Waves
Higher frequency
  • Photons of higher frequency carry more energy, so ultraviolet photons are more energetic than infrared photons.
Shorter wavelength
  • Energy is inversely proportional to wavelength, so a shorter wavelength means more energy per photon.
Intensity
  • For a given frequency, intensity depends on the number of photons passing per second, not on photon energy.
Spectrum
  • Gamma photons are the most energetic and radio photons the least energetic in the electromagnetic spectrum.
RadiationFrequencyPhoton energy
RadioLowSmallest
VisibleMediumIntermediate
GammaHighestGreatest

Part 3 of 6Evidence for Photons

1
Wave behaviour such as diffraction and interference shows electromagnetic radiation acts as a wave.
2
The photoelectric effect cannot be explained by waves but is explained by photons.
3
Atomic line spectra can be explained by atoms emitting photons of fixed energies.
4
Taken together, the evidence shows that radiation has both wave and particle properties.
5
Radiation therefore shows wave-particle duality, behaving as both.

Part 4 of 6Power and Photon Rate

Total power
  • The power of a beam equals the number of photons per second multiplied by the energy of each photon.
Photon rate
  • The number of photons per second is found by dividing the power by the energy of one photon.
Light bulb
  • Only a small fraction of the power of a bulb comes out as visible photons, so rates must use the right power.
Units
  • Use joules for energy, watts for power and metres for wavelength before calculating.

Part 5 of 6Worked Example

Question

  • A laser emits light of wavelength 600 nm with a power of 5.0 mW.
  • Calculate the energy of one photon and the number of photons emitted each second.
  • (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m/s)

  1. Photon energy E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (600 × 10⁻⁹) = 3.32 × 10⁻¹⁹ J.
  2. Power = 5.0 × 10⁻³ W, which is 5.0 × 10⁻³ J each second.
  3. Photons per second = 5.0 × 10⁻³ / 3.32 × 10⁻¹⁹ = 1.5 × 10¹⁶.

Answer One photon has energy 3.3 × 10⁻¹⁹ J, and about 1.5 × 10¹⁶ photons are emitted each second.

Part 6 of 6Exam Checklist & Tips

4.11.1 – Key Points for the Exam

  • Photon A quantum of electromagnetic radiation carrying energy hf.
  • Planck constant Constant linking photon energy and frequency, 6.63 × 10⁻³⁴ J s.
  • Wave-particle duality The ability of radiation and matter to show both wave and particle behaviour.
  • Quantum The smallest discrete amount of a quantity that can be exchanged.
  • Electromagnetic spectrum The family of radiation from radio waves to gamma rays.

Common Mistakes

  • Using wavelength in nanometres without converting to metres.
  • Saying brighter light has more energetic photons; it has more photons per second.
  • Forgetting that E = hc/λ shows energy is inversely proportional to wavelength.
  • Confusing the power of the source with the energy of a single photon.
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