Conservation laws, mass-energy and antimatterEdexcel International A Level Physics: Subtopic test

1. 1
   An electron and a positron, both moving very slowly, annihilate to produce two gamma-ray photons. The rest mass of an electron or of a positron is 0.511 MeV/c².

   (a)

   Why must at least two photons be produced when a slow-moving electron and positron annihilate?

   [1 mark]

   • ACharge would not be conserved if only one photon were produced
   • BEnergy would not be conserved with a single photon
   • COne photon would carry momentum, but the total initial momentum is almost zero
   • DEach particle must produce a photon of its own

   (b)

   The energy of each photon, in MeV, is about

   [1 mark]

   • A1.02
   • B0.511
   • C0.256
   • D938

   (c)

   Describe what happens to the mass of the electron and the positron in the annihilation and how energy is conserved.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A gamma-ray photon of energy 2.50 MeV passes close to a nucleus in a bubble chamber and produces an electron-positron pair. The chamber is in a uniform magnetic field. The recoil of the nucleus may be ignored.

   (a)

   The minimum photon energy needed to produce an electron-positron pair is

   [1 mark]

   • A1.02 MeV
   • B0.511 MeV
   • C2.04 MeV
   • D511 MeV

   (b)

   In the magnetic field the electron and positron tracks curve in opposite directions. This is because

   [1 mark]

   • Athe two particles have different masses
   • Bmomentum is not conserved in pair production
   • Cthe photon is deflected by the field
   • Dthe two particles have opposite charges

   (c)

   Calculate the total kinetic energy of the electron and positron.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Particle physicists quote the masses of particles in MeV/c² or GeV/c². A muon has a mass of 105.7 MeV/c². A proton and an antiproton each have a mass of 0.938 GeV/c². Use 1 eV = 1.60 × 10⁻¹⁹ J and c = 3.00 × 10⁸ m s⁻¹.

   (a)

   Calculate the mass of the muon in kg.

   [3 marks]

   (b)

   A proton and an antiproton, both at rest, annihilate. Calculate the total energy released in GeV and in joules, and explain why this is the least energy that can be released.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Physicists investigate the internal structure of the proton, which has a radius of about 1 × 10⁻¹⁵ m, by firing high-energy electrons at protons. Many of the unstable particles produced, such as muons, which have a lifetime of 2.2 µs when at rest, travel several kilometres along an evacuated beam line before decaying.

   (a)

   Explain why electrons of very high energy are needed to investigate the internal structure of the proton. Include a calculation of the minimum momentum of the electrons.

   [6 marks]

   (b)

   Muons produced in the experiment travel at 0.99c. Calculate the distance a muon would travel in one lifetime if there were no relativistic effects, and explain why muons in practice travel several kilometres before decaying.

   [6 marks]

   Total for question 4: 12 marks

End of questions