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Date	November 2018	Marks available	2	Reference code	18N.3.HL.TZ0.6
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Explain	Question number	6	Adapted from	N/A

Question

An electron with total energy 1.50 MeV collides with a positron at rest. As a result two photons are produced. One photon moves in the same direction as the electron and the other in the opposite direction.

The momenta of the photons produced have magnitudes p₁ and p₂. A student writes the following correct equations.

p₁ – p₂ = 1.41 MeV c^–1

p₁ + p₂ = 2.01 MeV c^–1

Show that the momentum of the electron is 1.41 MeV c^–1.

[1]

a.

Explain the origin of each equation.

[2]

b.i.

Calculate, in MeV c^–1, p₁ and p₂.

[2]

b.ii.

Markscheme

$pc = \sqrt {{E^2} - {{\left( {m{c^2}} \right)}^2}} = \sqrt {{{150}^2} - {{0.511}^2}}$ «= 1.410 MeV» ✔

a.

first equation is due to momentum conservation ✔

second equation is due to total energy conservation ✔

b.i.

adding 2p₁ = 3.42 MeV c^–1 ⇒ p₁ = 1.17 MeV c^–1 ✔

p₂ = 0.30 MeV c^–1 ✔

b.ii.

Examiners report

[N/A]

a.

[N/A]

b.i.

[N/A]

b.ii.

Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.4 – Relativistic mechanics (HL only)

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18N.3.HL.TZ0.6a:
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18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
16N.3.HL.TZ0.8a: Explain, in terms of a conservation law, why two photons need to be created.
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16N.3.HL.TZ0.8c:
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18M.3.HL.TZ2.6b.i:
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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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17N.3.HL.TZ0.7a:
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19N.3.HL.TZ0.5b:
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18M.3.HL.TZ1.6a.ii:
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19M.3.HL.TZ2.8biii:
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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