Nuclear and Particle PhysicsEdexcel International A Level Physics: Topic test

1. 1
   Americium-241 (proton number 95) is a source of alpha particles used in smoke detectors. In a laboratory, alpha particles from such a source are directed at a very thin metal foil in an evacuated chamber.

   (a)

   How many neutrons are there in a nucleus of americium-241?

   [1 mark]

   • A95
   • B241
   • C146
   • D336

   (b)

   A nucleus of americium-241 emits an alpha particle. What are the nucleon number and proton number of the nucleus that remains?

   [1 mark]

   • Anucleon number 237, proton number 93
   • Bnucleon number 241, proton number 93
   • Cnucleon number 237, proton number 95
   • Dnucleon number 245, proton number 97

   (c)

   The experiment is first carried out with a gold foil (proton number 79) and then repeated with an aluminium foil (proton number 13) of the same thickness. State how the number of alpha particles scattered through large angles changes and explain why.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   An alpha particle of mass 6.64 × 10⁻²⁷ kg and charge +3.20 × 10⁻¹⁹ C travels at 1.5 × 10⁷ m s⁻¹ in a cloud chamber. It enters a region of uniform magnetic field of flux density 0.80 T, perpendicular to its velocity.

   (a)

   What is the momentum of the alpha particle?

   [1 mark]

   • A4.4 × 10⁻³⁴ kg m s⁻¹
   • B5.0 × 10⁻²⁰ kg m s⁻¹
   • C2.0 × 10⁻¹⁹ kg m s⁻¹
   • D1.0 × 10⁻¹⁹ kg m s⁻¹

   (b)

   What is the radius of the circular path of the alpha particle in the magnetic field?

   [1 mark]

   • A0.78 m
   • B0.39 m
   • C0.31 m
   • D0.19 m

   (c)

   A proton of mass 1.67 × 10⁻²⁷ kg and charge +1.60 × 10⁻¹⁹ C enters the same field at the same speed, perpendicular to the field. Calculate the radius of its circular path.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A neutral pion ($\pi^0$) of rest mass 135 MeV/$c^2$ decays at rest into two photons that travel away in opposite directions. Take 1 eV = 1.60 × 10⁻¹⁹ J and $c$ = 3.00 × 10⁸ m s⁻¹.

   (a)

   Explain why the two photons have equal energies, and calculate the energy of each photon in MeV.

   [3 marks]

   (b)

   Calculate the rest energy of the pion in joules and its mass in kg. Hence state how many times smaller the mass of the pion is than the mass of a proton, 1.67 × 10⁻²⁷ kg.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A positive pion ($\pi^+$, rest mass 139.6 MeV/$c^2$) at rest in a bubble chamber decays into a positive muon ($\mu^+$, rest mass 105.7 MeV/$c^2$) and a muon neutrino ($\nu_\mu$). The chamber is in a uniform magnetic field of flux density 1.0 T, perpendicular to the track of the muon.

   (a)

   Show that the decay $\pi^+ \rightarrow \mu^+ + \nu_\mu$ is consistent with the conservation laws and is energetically possible. In your answer refer to the quark structure of the pion, and the classes to which each particle belongs.

   [6 marks]

   (b)

   The muon is observed to have momentum 29.8 MeV/$c$. Calculate its momentum in kg m s⁻¹ and the radius of curvature of its track. State the momentum of the neutrino and explain why the neutrino leaves no track.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   In the standard quark model the up quark ($u$) has charge $+\frac{2}{3}e$ and the strange quark ($s$) has charge $-\frac{1}{3}e$. The $\mathrm{K}^+$ meson is made of an up quark and a strange antiquark ($\bar{s}$).

   (a)

   What is the charge of the $\mathrm{K}^+$ meson?

   [1 mark]

   • A$+\frac{1}{3}e$
   • B$+1e$
   • C$-1e$
   • D$-\frac{1}{3}e$

   (b)

   What is the baryon number of the $\mathrm{K}^+$ meson?

   [1 mark]

   • A+1
   • B$+\frac{2}{3}$
   • C$+\frac{1}{3}$
   • D0

   (c)

   State the quark composition, charge and baryon number of the antiparticle of the $\mathrm{K}^+$ meson.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   Fluorine-18, used in PET scanning, has a nucleon number of 18 and a proton number of 9. A nucleus of fluorine-18 decays by $\beta^+$ emission into a nucleus of oxygen, with the emission of a positron and a neutrino. In the decay a proton in the nucleus changes into a neutron.

   (a)

   What are the proton number and nucleon number of the oxygen nucleus formed?

   [1 mark]

   • Aproton number 8, nucleon number 18
   • Bproton number 10, nucleon number 18
   • Cproton number 8, nucleon number 17
   • Dproton number 9, nucleon number 17

   (b)

   Which statement describes the change that happens to the quarks in the nucleon that decays?

   [1 mark]

   • Aa down quark changes to an up quark
   • Ban up quark changes to a strange quark
   • Can up quark changes to a down quark
   • Da down quark changes to a strange quark

   (c)

   Explain why the particle emitted with the positron must be a neutrino and not an antineutrino.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   Muons are produced at a height of 15 km in the upper atmosphere when cosmic rays collide with air molecules. A typical muon travels vertically downwards at 0.998$c$, where $c$ = 3.00 × 10⁸ m s⁻¹ is the speed of light in a vacuum. A muon at rest has a mean lifetime of 2.2 × 10⁻⁶ s.

   (a)

   Calculate the distance that a muon would travel in one lifetime if there were no relativistic effect.

   [3 marks]

   (b)

   Many of these muons are detected at sea level. Explain why this observation cannot be accounted for without a relativistic increase in the lifetime of the muons.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   In a collision experiment, high-energy protons are fired at a stationary hydrogen target (protons) and the particles produced are identified. Physicists use conservation of charge, baryon number and lepton number to decide which reactions can occur.

   (a)

   The reaction $p + p \rightarrow p + n + \pi^+$ is observed, where the $\pi^+$ is a meson made of an up quark and an anti-down quark. Use conservation laws and the quark model to show that this reaction is possible, and explain where the energy for the mass of the pion comes from.

   [6 marks]

   (b)

   A student proposes three further reactions: (1) $p + p \rightarrow p + p + p + \bar{p}$; (2) $p + p \rightarrow p + p + n$; (3) $\pi^- \rightarrow e^- + \nu_e$. Evaluate which of these reactions can occur.

   [6 marks]

   Total for question 8: 12 marks

End of questions