Conservation laws and particle equationsEdexcel A-Level Physics: Subtopic test

1. 1
   In β⁻ decay a neutron in an unstable nucleus changes into a proton, and an electron and a third particle X are emitted. The neutron and proton are baryons with baryon number +1, and the neutron, proton and electron have lepton numbers 0, 0 and +1 respectively.

   (a)

   If the neutron decayed as n → p + e⁻ with no third particle, which quantity would not be conserved?

   [1 mark]

   • ALepton number
   • BCharge
   • CBaryon number
   • DCharge and baryon number

   (b)

   What is particle X?

   [1 mark]

   • AAn electron neutrino
   • BA positron
   • CAn electron antineutrino
   • DA photon

   (c)

   Write the particle equation for the decay and show that charge and lepton number are conserved.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A positive pion (π⁺) decays into a positive muon and a muon neutrino, π⁺ → μ⁺ + νμ. The pion is a meson with baryon number 0 and lepton number 0. Muons and neutrinos are leptons with lepton number +1, and their antiparticles have lepton number −1.

   (a)

   What is the total lepton number of the μ⁺ and the νμ produced?

   [1 mark]

   • A+2
   • B0
   • C−2
   • D+1

   (b)

   Which decay of the π⁺ conserves charge, baryon number and lepton number?

   [1 mark]

   • Aπ⁺ → μ⁺ + ν̄μ
   • Bπ⁺ → μ⁻ + νμ
   • Cπ⁺ → p + ν̄μ
   • Dπ⁺ → e⁺ + νe

   (c)

   The positive muon decays as μ⁺ → e⁺ + νe + ν̄μ. Show that charge and lepton number are conserved in this decay.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Particle physicists analyse the products of high-energy collisions between protons. Pions are mesons with baryon number 0 and lepton number 0; the π⁺, π⁻ and π⁰ have charges +1 e, −1 e and 0. An antiproton has charge −1 e and baryon number −1.

   (a)

   In one collision, p + p → p + n + X, where X is a single particle. Use conservation laws to identify X.

   [3 marks]

   (b)

   A proton and an antiproton collide and annihilate: p + p̄ → π⁺ + π⁻ + π⁰. Show that this is allowed by conservation of charge and baryon number, and explain why the same products cannot be made from two protons.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Nuclei with too many protons become more stable by emitting a positron (β⁺ decay) or by capturing an electron from the atom's inner shell. In each case a proton in the nucleus changes into a neutron and a neutrino is involved.

   (a)

   Explain, with the particle equation, how β⁺ decay conserves charge, baryon number and lepton number, and show how it changes a nucleus such as carbon-11.

   [6 marks]

   (b)

   Determine whether each of these processes is possible, justifying each answer with conservation laws: (i) p → e⁺ + π⁰; (ii) n → p + e⁻; (iii) p + e⁻ → n + νe.

   [6 marks]

   Total for question 4: 12 marks

End of questions