An electron and a positron, both effectively at rest, annihilate each other.
(a) Explain why two photons are produced, rather than one. [1]
(b) Calculate the wavelength of each photon. [3]
- (a) total momentum before is zero, so two photons moving in opposite directions are needed to conserve momentum(1)
- (b) energy of each photon = rest energy of an electron = 0.511 MeV $= 0.511\times10^{6}\times1.60\times10^{-19} = 8.2\times10^{-14}$ J (allow $m_ec^2 = 9.11\times10^{-31}\times(3.00\times10^{8})^2$)(1)
- (b) $\lambda = \dfrac{hc}{E} = \dfrac{6.63\times10^{-34}\times3.00\times10^{8}}{8.2\times10^{-14}}$(1)
- (b) $2.4 \times 10^{-12}$ m(1)
- Answer: (a) to conserve momentum (b) $2.4\times10^{-12}$ m
- Examiner tip: Each photon carries the rest energy of ONE particle (0.511 MeV) — using the total 1.02 MeV for a single photon halves the wavelength.