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Date November 2016 Marks available 1 Reference code 16N.3.HL.TZ0.8
Level Higher level Paper Paper 3 Time zone Time zone 0
Command term Explain 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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