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Mass, energy and antimatter Edexcel International A Level Physics revision

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In plain words

Mass is a very concentrated form of energy. Give a photon enough energy and it can turn into an electron and its antimatter twin. Bring the twins back together and they vanish in a flash of light. Einstein's equation keeps the accounts.

5 things to know

  1. ΔE = c²Δm: mass can be turned into energy, and energy into mass.
  2. Annihilation: a particle meets its antiparticle and their mass becomes the energy of photons. Pair production: a photon with enough energy creates a particle and its antiparticle.
  3. Particle masses are often given in MeV/c² or GeV/c². A mass of 1 MeV/c² has a rest energy of 1 MeV. 1 MeV = 1.60 × 10⁻¹³ J and 1 GeV = 1.60 × 10⁻¹⁰ J.
  4. High energies are needed to study the structure of nucleons. More energy means more momentum and so a shorter de Broglie wavelength, which can pick out finer detail.
  5. An unstable particle moving close to the speed of light lives longer, as we measure it, than the same particle at rest. So fast, short-lived particles travel much further before they decay than you would expect.

Worked example

An electron and a positron annihilate at rest. Find the energy of each of the two photons produced. (Mass of an electron = 9.11 × 10⁻³¹ kg.)

  1. Mass converted = 2 × 9.11 × 10⁻³¹ = 1.82 × 10⁻³⁰ kg.
  2. Energy = c²Δm = (3.00 × 10⁸)² × 1.82 × 10⁻³⁰ = 1.64 × 10⁻¹³ J.
  3. Shared equally between two photons: 8.2 × 10⁻¹⁴ J each (0.51 MeV).

Tips and tricks

  • To turn MeV/c² into kilograms, multiply by 1.60 × 10⁻¹³ and divide by c², which is 9.00 × 10¹⁶.
  • Annihilation at rest gives two photons, not one. A single photon could not conserve momentum.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Mass, energy and antimatter: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What happens in annihilation?
    • A particle and its antiparticle turn into photons. (the answer)
    • A photon turns into two particles.
    • A nucleus splits in two.
    • An electron is absorbed by a nucleus.

    Their mass becomes the energy of the photons.

  2. An electron has a mass of 0.511 MeV/c². What is its rest energy?
    • 0.511 MeV (the answer)
    • 0.511 J
    • 0.511 eV
    • 511 MeV

    That is what the unit means.

  3. Why are two photons produced when an electron and a positron annihilate at rest?
    • so that momentum is conserved (the answer)
    • so that charge is conserved
    • because photons always come in pairs
    • because each particle makes one photon of its own

    The total momentum was zero, so the photons must travel in opposite directions.

  4. What is 1 GeV in joules?
    • 1.60 × 10⁻¹⁹ J
    • 1.60 × 10⁻¹³ J
    • 1.60 × 10⁻¹⁰ J (the answer)
    • 1.60 × 10⁹ J

    10⁹ × 1.60 × 10⁻¹⁹.

  5. A fast-moving unstable particle is measured to live longer than the same particle at rest. Why?
    • It is moving at close to the speed of light. (the answer)
    • It has gained mass from the air.
    • It has less energy.
    • The detector is slow.

    This is the relativistic increase in lifetime.

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