| Date | November 2016 | Marks available | 2 | Reference code | 16N.3.HL.TZ0.8 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Calculate | Question number | 8 | Adapted from | N/A |
Question
An electron and a positron have identical speeds but are travelling in opposite directions. Their collision results in the annihilation of both particles and the production of two photons of identical energy. The initial kinetic energy of the electron is 2.00 MeV.
Explain, in terms of a conservation law, why two photons need to be created.
[1]
a.
Determine the speed of the incoming electron.
[3]
b.
Calculate the energy and the momentum for each photon after the collision.
[2]
c.
Markscheme
as the total initial momentum is zero, it must be zero after the collision
a.
2 = (\(\gamma \)–1)m0c2 = (\(\gamma \)–1) 0.511
\(\gamma \) = 4.91
v = 0.978c
b.
«2 + 2 + 2 × 0.511 = 5.02 MeV» so each photon is 2.51«MeV»
\(p = \frac{E}{c} = 2.51\) «MeVc–1»
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
Syllabus sections
Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.4 – Relativistic mechanics (HL only)
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