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Date	May 2018	Marks available	2	Reference code	18M.3.HL.TZ1.6
Level	Higher level	Paper	Paper 3	Time zone	1
Command term	Show that	Question number	6	Adapted from	N/A

Question

A positive pion decays into a positive muon and a neutrino.

${\pi ^ + } \to {\mu ^ + } + {v_\mu }$

The momentum of the muon is measured to be 29.8 MeV c^–1 in a laboratory reference frame in which the pion is at rest. The rest mass of the muon is 105.7 MeV c^–2 and the mass of the neutrino can be assumed to be zero.

For the laboratory reference frame

write down the momentum of the neutrino.

[1]

a.i.

show that the energy of the pion is about 140 MeV.

[2]

a.ii.

State the rest mass of the pion with an appropriate unit.

[1]

Markscheme

«–»29.8 «MeVc^–1»

[1 mark]

a.i.

E_π = $\sqrt {p_\mu ^2{c^2} + m_\mu ^2{c^4}}$ + p_vc OR E_μ = 109.8 «MeV»

E_π = « $\sqrt {{{29.8}^2} + {{105.7}^2}}$ + 29.8 =» 139.6 «MeV»

Final value to at least 3 sig figs required for mark.

[2 marks]

a.ii.

139.6 MeVc^–2

Units required.

Accept 140 MeVc^–².

[1 mark]

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

Syllabus sections

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

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Option A: Relativity » Option A: Relativity (Additional higher level option topics)

Option A: Relativity

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Examiners report

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