Nuclear and particle physicsEdexcel A-Level Physics: Topic test

1. 1
   A strontium nucleus is written ⁹⁰₃₈Sr. A strontium atom has a radius of about 2 × 10⁻¹⁰ m and its nucleus has a radius of about 5 × 10⁻¹⁵ m.

   (a)

   How many neutrons are there in this nucleus?

   [1 mark]

   • A38
   • B52
   • C90
   • D128

   (b)

   What fraction of the volume of the atom is occupied by the nucleus?

   [1 mark]

   • A2.5 × 10⁻⁵
   • B6.3 × 10⁻¹⁰
   • C4.0 × 10⁴
   • D1.6 × 10⁻¹⁴

   (c)

   Explain how the results of large-angle alpha particle scattering experiments show that the nucleus is much smaller than the atom.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Protons, initially at rest, are accelerated through a potential difference of 3.0 MV in an electrostatic accelerator. They then enter a region of uniform magnetic field of flux density 1.2 T, at right angles to the field. The mass of a proton is 1.67 × 10⁻²⁷ kg and the elementary charge is 1.60 × 10⁻¹⁹ C. Ignore relativistic effects.

   (a)

   What is the momentum of a proton as it enters the magnetic field?

   [1 mark]

   • A4.0 × 10⁻²⁰ kg m s⁻¹
   • B2.8 × 10⁻²⁰ kg m s⁻¹
   • C8.0 × 10⁻²⁰ kg m s⁻¹
   • D4.8 × 10⁻¹³ kg m s⁻¹

   (b)

   What is the radius of the circular path of a proton in the magnetic field?

   [1 mark]

   • A0.15 m
   • B0.42 m
   • C0.21 m
   • D3.3 × 10⁻²⁰ m

   (c)

   State the different roles of the electric field and the magnetic field in this arrangement.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A proton and an antiproton, both at rest, annihilate and are converted entirely into photons. The mass of a proton is 1.673 × 10⁻²⁷ kg, the speed of light is 3.00 × 10⁸ m s⁻¹ and the elementary charge is 1.60 × 10⁻¹⁹ C.

   (a)

   Calculate the total energy released in the annihilation, in joules and in GeV.

   [3 marks]

   (b)

   At least two photons are produced in this annihilation. Explain why a single photon cannot be produced, and state the energy of each photon when two are produced.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A neutral lambda particle Λ⁰ has the quark composition uds. It decays at rest into a proton and a negative pion: Λ⁰ → p + π⁻. The rest masses of the Λ⁰, the proton and the π⁻ are 1116 MeV/c², 938 MeV/c² and 140 MeV/c² respectively. An up quark has charge +⅔e, and down and strange quarks have charge −⅓e. The elementary charge is 1.60 × 10⁻¹⁹ C.

   (a)

   Use the quark composition to show that the Λ⁰ is a baryon with zero charge. Show that the decay conserves charge, baryon number and lepton number.

   [6 marks]

   (b)

   Calculate the energy released in the decay, in joules. Explain why the proton and the pion move off in opposite directions, and why the pion is expected to have more kinetic energy than the proton.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   The K⁺ meson (kaon) is made of an up quark and an anti-strange quark. An up quark has charge +⅔e and a strange quark has charge −⅓e.

   (a)

   What is the charge of the K⁺ meson?

   [1 mark]

   • A0
   • B+⅓e
   • C+1e
   • D−1e

   (b)

   What is the quark composition of the antiparticle of the K⁺ meson?

   [1 mark]

   • Aa strange quark and an anti-up quark
   • Ban anti-up quark and an anti-strange quark
   • Can up quark and a strange quark
   • Da down quark and an anti-strange quark

   (c)

   Explain why the K⁺ is classified as a hadron and as a meson.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   Antineutrinos from a nuclear reactor are detected through the interaction ν̄e + p → n + e⁺.

   (a)

   What is the total lepton number of the particles on the right-hand side of this interaction?

   [1 mark]

   • A+2
   • B+1
   • C0
   • D−1

   (b)

   Which of these interactions is also possible?

   [1 mark]

   • Aν̄e + n → p + e⁻
   • Bνe + n → p + e⁻
   • Cνe + p → n + e⁺
   • Dν̄e + p → n + e⁻

   (c)

   Show that charge and baryon number are both conserved in the interaction ν̄e + p → n + e⁺.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   Muons are created in the upper atmosphere, about 15 km above the ground, when cosmic rays collide with air molecules. A muon has a mean lifetime of 2.2 μs measured in its own rest frame. The muons travel towards the ground at 0.99c, where c = 3.0 × 10⁸ m s⁻¹.

   (a)

   Calculate the distance a muon would travel in 2.2 μs, and the time it takes a muon to travel 15 km to the ground.

   [3 marks]

   (b)

   Large numbers of these muons are detected at ground level. Explain why this is evidence for the relativistic increase in the lifetime of particles moving at speeds close to c.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   In a circular collider, beams of electrons and positrons travel in opposite directions around the same evacuated ring. Every particle has a momentum of 45 GeV/c. The ring lies in a uniform magnetic field of flux density 0.080 T, perpendicular to the plane of the ring. Use c = 3.00 × 10⁸ m s⁻¹ and e = 1.60 × 10⁻¹⁹ C.

   (a)

   Calculate the radius of the path of each particle. Explain why the same magnetic field can hold both beams on the same ring, and why electric fields are also needed to accelerate the particles.

   [6 marks]

   (b)

   An electron and a positron collide head-on and annihilate to produce a muon and an antimuon: e⁻ + e⁺ → μ⁻ + μ⁺. Show that charge and lepton number are conserved. Explain why head-on collisions of equal beams make the energy efficiently available for creating particles, and comment on whether this collision, with total energy 90 GeV, can produce a pair of muons, each of rest mass 105.7 MeV/c².

   [6 marks]

   Total for question 8: 12 marks

End of questions