Physics · · 5 marks
An electron and a positron, both effectively at rest, annihilate. (a) Explain why two photons are produced rather than one. [2] (b) Calculate the frequency of each photon. [3] rest energy of an electron = 0.511 MeV · h = 6.63 × 10⁻³⁴ J s · e = 1.60 × 10⁻¹⁹ C
Mark scheme
- (a) Total momentum before annihilation is zero
- (a) A single photon would carry momentum, so momentum could not be conserved
- (b) Energy of each photon = 0.511 MeV = 0.511 × 10⁶ × 1.60 × 10⁻¹⁹ = 8.18 × 10⁻¹⁴ J
- (b) f = E/h = 8.18 × 10⁻¹⁴ / 6.63 × 10⁻³⁴
- (b) f = 1.23 × 10²⁰ Hz
The commonest loss is using the total 1.022 MeV for one photon. The energy is shared equally, so each photon carries the rest energy of one particle.