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Date	November 2016	Marks available	2	Reference code	16N.3.HL.TZ0.8
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
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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19M.3.HL.TZ1.6a:
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19N.3.HL.TZ0.5a(i):
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19N.3.HL.TZ0.5a(ii):
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17M.3.HL.TZ1.5b:
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Option A: Relativity » Option A: Relativity (Additional higher level option topics)

Option A: Relativity