Energy, mass and antimatterEdexcel A-Level Physics: Subtopic test

1. 1
   In a positron emission tomography (PET) scanner, a positron emitted by a radioactive tracer in a patient annihilates with an electron in the surrounding tissue. Both particles can be taken to be at rest when they annihilate. The rest mass of an electron is 0.511 MeV/c².

   (a)

   Which statement correctly compares a positron with an electron?

   [1 mark]

   • AIt has the same mass and the same charge as an electron, but moves in the opposite direction
   • BIt has the same mass as an electron but the opposite charge
   • CIt has a greater mass than an electron and the opposite charge
   • DIt has the same mass as an electron and no charge

   (b)

   The electron and positron annihilate to give two photons rather than one. Which statement gives the reason?

   [1 mark]

   • ACharge can only be conserved if two photons are produced
   • BEnergy cannot be conserved if only one photon is produced
   • CLepton number can only be conserved with two photons
   • DThe total momentum before annihilation is zero, so the photons must have equal and opposite momenta

   (c)

   Calculate the energy, in MeV, of each photon produced.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A gamma ray photon of energy 3.0 MeV, which leaves no track in a bubble chamber, converts into an electron and a positron close to an atomic nucleus. The chamber is in a uniform magnetic field and the two particles leave tracks that start at the same point. The rest mass of an electron is 0.511 MeV/c².

   (a)

   What is the minimum photon energy needed to create an electron–positron pair?

   [1 mark]

   • A1.02 MeV
   • B0.511 MeV
   • C2.04 MeV
   • D0.255 MeV

   (b)

   The two tracks curve in opposite senses. What is the best explanation?

   [1 mark]

   • AThe particles have opposite masses, so they are deflected in opposite directions
   • BThe photon carried a charge that was shared unequally between the particles
   • CThe particles have opposite charges, so the magnetic force on them acts in opposite directions
   • DThe particles were created with different speeds, so one is deflected more than the other

   (c)

   Calculate the total kinetic energy of the electron and the positron, in MeV, immediately after the pair is created. Assume the nucleus takes negligible energy.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Physicists fire a beam of electrons at liquid hydrogen to investigate the structure of the proton, which has a radius of about 1 × 10⁻¹⁵ m. At low beam energies the electrons scatter as if the proton were a single point. At very high beam energies some electrons are scattered through large angles, showing that the proton has internal structure.

   (a)

   Explain why electrons of very high energy are needed to investigate the internal structure of the proton.

   [3 marks]

   (b)

   The electrons have an energy of 5.0 GeV. At this energy the electron's momentum can be taken as p = E/c. Calculate the de Broglie wavelength of the electrons and comment on whether they can probe the structure of the proton.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Charged pions are unstable particles with a mean lifetime of 26 ns measured in their own rest frame. In an accelerator experiment a beam of pions travels at 0.999c along an evacuated pipe 50 m long. At this speed the mean lifetime measured in the laboratory is 22 times the rest-frame lifetime. Muons created high in the atmosphere also reach the ground in far greater numbers than a calculation without this effect predicts.

   (a)

   Use a calculation to explain why the survival of muons at ground level shows that relativistic effects are significant. Take the muon speed as 0.99c and its mean lifetime in its own rest frame as 2.2 μs.

   [6 marks]

   (b)

   Evaluate whether the relativistic increase in lifetime is significant for the pion beam, by finding how far the pions travel on average before decaying, with and without the increase.

   [6 marks]

   Total for question 4: 12 marks

End of questions