Energy and momentum of a photon

Physics A2 · Quantum physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Electromagnetic radiation does not only behave as a wave. It also arrives in separate packets of energy, so it has a particulate nature. Each packet is a photon: a quantum of electromagnetic energy.

The energy of one photon depends only on the frequency of the radiation. A brighter beam of the same frequency has more photons per second, not bigger photons.

Photon energies are tiny, so they are often given in electronvolts. One electronvolt is the energy gained by an electron moved through a p.d. of one volt. A photon has no mass but it does have momentum, so light exerts a small force on a surface it hits.

Rules to remember

Common mistake

Students think a brighter beam has photons of higher energy. Intensity changes the number of photons per second; only frequency changes the energy of each one. Change nm to m before using E = hc/λ.

Worked example

Ultraviolet radiation has a wavelength of 250 nm. What is the energy of one photon in electronvolts, and what is its momentum?

  1. E = hc ÷ λ = (6.63 × 10−34 × 3.00 × 108) ÷ (250 × 10−9) = 7.96 × 10−19 J.
  2. In eV: 7.96 × 10−19 ÷ 1.60 × 10−19 = 4.97 eV.
  3. p = E ÷ c = 7.96 × 10−19 ÷ 3.00 × 108 = 2.65 × 10−27 N s.

Answer: 4.97 eV and 2.65 × 10−27 N s

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