Conservation laws in particle interactionsAQA A-Level Physics: Subtopic test

1. 1
   Caesium-137 in stored nuclear waste decays by beta-minus emission. Inside each decaying nucleus a neutron changes into a proton, and an electron is emitted at high speed together with one other, very weakly interacting, particle.

   (a)

   Which quark change takes place inside the nucleus in beta-minus decay?

   [1 mark]

   • Aup → down
   • Bup → strange
   • Cdown → up
   • Ddown → strange

   (b)

   Which particle is emitted with the electron?

   [1 mark]

   • Aelectron antineutrino
   • Belectron neutrino
   • Cpositron
   • Dmuon antineutrino

   (c)

   Show that charge and baryon number are both conserved in the decay n → p + e⁻ + $\bar{\nu}_e$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A positron emission tomography (PET) scanner uses a tracer containing fluorine-18. Each fluorine-18 nucleus decays by beta-plus emission: a proton in the nucleus changes into a neutron and a positron is emitted together with a neutrino.

   (a)

   Which quark change takes place inside the nucleus in beta-plus decay?

   [1 mark]

   • Adown → up
   • Bup → down
   • Cup → strange
   • Dstrange → up

   (b)

   Which statement about the decay p → n + e⁺ + $\nu_e$ is correct?

   [1 mark]

   • ABaryon number is not conserved because the proton disappears
   • BCharge is not conserved because the neutron is neutral
   • CThe neutrino has a strangeness of −1
   • DLepton number is conserved because the positron and neutrino have lepton numbers of −1 and +1

   (c)

   A free proton does not decay in this way, although a proton inside some nuclei can. Using conservation of energy, explain why.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   At a particle accelerator a beam of negative pions is fired into a target of liquid hydrogen, so that pions collide with protons. Data: a pion π⁻ has charge −1, baryon number 0 and strangeness 0; a proton has charge +1, baryon number +1 and strangeness 0. The Λ⁰ has charge 0, baryon number +1 and strangeness −1. The K⁰ has charge 0, baryon number 0 and strangeness +1. The K⁻ has charge −1, baryon number 0 and strangeness −1. The Σ⁺ has charge +1, baryon number +1 and strangeness −1. Strangeness is conserved in these collisions.

   (a)

   Show that the interaction π⁻ + p → K⁰ + Λ⁰ obeys the conservation of charge, baryon number and strangeness.

   [3 marks]

   (b)

   A second interaction is proposed: π⁻ + p → K⁻ + Σ⁺. Deduce whether this interaction can occur.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A university particle physics group analyses decays and collisions recorded in a detector. Leptons have lepton number +1 and antileptons −1, counted separately for the electron family and the muon family. A photon has zero charge, zero baryon number and zero lepton number, and the particles named have zero strangeness.

   (a)

   A neutron decays into a proton, an electron and an antineutrino. Discuss this decay in terms of the quark change, the conservation laws and the conservation of energy and momentum.

   [6 marks]

   (b)

   Three interactions are proposed: (i) p + p → p + n + π⁺, (ii) μ⁻ → e⁻ + γ, (iii) n + $\nu_e$ → p + e⁻. A π⁺ has charge +1 and baryon number 0. Deduce which of the interactions can occur, giving reasons.

   [6 marks]

   Total for question 4: 12 marks

End of questions