ParticlesAQA A-Level Physics: Topic test

1. 1
   Hydrogen has three isotopes: protium $^{1}_{1}\mathrm{H}$, deuterium $^{2}_{1}\mathrm{H}$ and tritium $^{3}_{1}\mathrm{H}$. Use e = 1.60×10⁻¹⁹ C and take the mass of a proton or a neutron to be 1.67×10⁻²⁷ kg, ignoring the mass of an electron.

   (a)

   How many neutrons are there in a nucleus of tritium?

   [1 mark]

   • A0
   • B1
   • C3
   • D2

   (b)

   Which statement correctly compares the ions $^{2}_{1}\mathrm{H}^{+}$ and $^{3}_{1}\mathrm{H}^{+}$?

   [1 mark]

   • AThey have the same charge and the same specific charge.
   • BThey have the same charge, and $^{2}_{1}\mathrm{H}^{+}$ has the greater specific charge.
   • CThey have the same charge, and $^{3}_{1}\mathrm{H}^{+}$ has the greater specific charge.
   • DThey have different charges because they have different numbers of neutrons.

   (c)

   Calculate the specific charge of the $^{3}_{1}\mathrm{H}^{+}$ ion.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a detector, a neutron and an antineutron, each with negligible kinetic energy, annihilate and the energy is released as two photons. The rest energy of a neutron is 939.6 MeV. Use h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹ and e = 1.60×10⁻¹⁹ C.

   (a)

   What is the total energy of the two photons?

   [1 mark]

   • A1.88×10³ MeV
   • B9.40×10² MeV
   • C3.76×10³ MeV
   • D0.511 MeV

   (b)

   Which statement about the antineutron is correct?

   [1 mark]

   • AIt has the same rest energy as the neutron and the opposite charge.
   • BIt has a smaller rest energy than the neutron and zero charge.
   • CIt has the same rest energy and charge as the neutron, but the opposite baryon number.
   • DIt has the same rest energy, charge and baryon number as the neutron.

   (c)

   Calculate the wavelength of each photon, assuming that the energy is shared equally between them.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a high-energy collision experiment an electron is fired at a stationary proton and the following reaction occurs: $\mathrm{e}^{-} + \mathrm{p} \rightarrow \mathrm{n} + \nu_{\mathrm{e}}$, where $\nu_{\mathrm{e}}$ is an electron neutrino.

   (a)

   Describe how this reaction takes place in terms of the exchange particle and the particles involved.

   [3 marks]

   (b)

   Show that charge, baryon number and electron lepton number are all conserved in this reaction. Explain why the strong interaction cannot be responsible for it.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The lambda particle, $\Lambda^{0}$, is a neutral baryon with strangeness −1. It can be produced in the strong interaction $\mathrm{K}^{-} + \mathrm{p} \rightarrow \Lambda^{0} + \pi^{0}$, and it decays through the reaction $\Lambda^{0} \rightarrow \mathrm{p} + \pi^{-}$ with a mean lifetime of about 10⁻¹⁰ s. The kaon $\mathrm{K}^{-}$ has strangeness −1 and the pions have strangeness 0. The $\Lambda^{0}$ is made of one up, one down and one strange quark.

   (a)

   Use conservation laws to show that the production reaction can occur through the strong interaction but the decay can occur only through the weak interaction.

   [6 marks]

   (b)

   Explain, in terms of quarks, why the $\Lambda^{0}$ has baryon number +1, zero charge and strangeness −1, and describe how the decay $\Lambda^{0} \rightarrow \mathrm{p} + \pi^{-}$ happens at the quark level.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   A positively charged pion, $\pi^{+}$, decays into an antimuon, $\mu^{+}$, and a muon neutrino, $\nu_{\mu}$.

   (a)

   Which of the following correctly classifies the $\pi^{+}$ and the $\mu^{+}$?

   [1 mark]

   • ABoth are hadrons.
   • BThe $\pi^{+}$ is a lepton and the $\mu^{+}$ is a hadron.
   • CThe $\pi^{+}$ is a meson, which is a hadron, and the $\mu^{+}$ is a lepton.
   • DThe $\pi^{+}$ is a baryon and the $\mu^{+}$ is a meson.

   (b)

   Muon lepton number is conserved in this decay. What is the muon lepton number of the $\nu_{\mu}$?

   [1 mark]

   • A+1
   • B0
   • C−1
   • D+2

   (c)

   A student suggests that the $\pi^{+}$ could instead decay by $\pi^{+} \rightarrow \mathrm{e}^{+} + \nu_{\mu}$. Use lepton numbers to explain why this decay does not happen.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   The sigma-plus particle, $\Sigma^{+}$, is a baryon with charge +1 and strangeness −1. It is produced in the strong interaction $\pi^{+} + \mathrm{p} \rightarrow \Sigma^{+} + \mathrm{K}^{+}$, and later it decays in the weak interaction $\Sigma^{+} \rightarrow \mathrm{n} + \pi^{+}$.

   (a)

   Use conservation of strangeness to deduce the strangeness of the $\mathrm{K}^{+}$.

   [1 mark]

   • A−1
   • B+1
   • C0
   • D+2

   (b)

   Which statement about strange particles is correct?

   [1 mark]

   • AThey are produced by the weak interaction and decay by the strong interaction.
   • BStrangeness is conserved in every interaction.
   • CStrangeness can change by ±2 in a weak interaction.
   • DThey are produced in pairs by the strong interaction and decay by the weak interaction.

   (c)

   Deduce the change in strangeness in the decay of the $\Sigma^{+}$ and explain what this shows about the interaction responsible.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A smoke detector contains a small sample of americium-241, $^{241}_{95}\mathrm{Am}$, which decays by alpha emission to an isotope of neptunium (Np). The alpha particles ionise the air in a small chamber.

   (a)

   Write the nuclear equation for this decay and state the number of neutrons in the neptunium nucleus formed.

   [3 marks]

   (b)

   The americium nucleus contains 95 protons. Explain why the nucleus can exist at all, and why such a large nucleus is unstable.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   In a collision experiment an electron and a positron, each with kinetic energy 5.00 MeV, travel towards each other along the same straight line and annihilate to produce photons. The rest energy of an electron or a positron is 0.511 MeV. Use h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹ and e = 1.60×10⁻¹⁹ C.

   (a)

   Calculate the energy in joules and the wavelength of each photon, assuming that two photons of equal energy are produced. Explain why at least two photons must be produced.

   [6 marks]

   (b)

   Explain why the annihilation of the electron and positron into two photons obeys the conservation laws for charge, baryon number and lepton number, and explain why it is an electromagnetic interaction and not a strong or weak interaction.

   [6 marks]

   Total for question 8: 12 marks

End of questions