| Date | May 2018 | Marks available | 2 | Reference code | 18M.3.HL.TZ1.6 |
| Level | Higher level | Paper | Paper 3 | Time zone | 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.
show that the energy of the pion is about 140 MeV.
State the rest mass of the pion with an appropriate unit.
Markscheme
«–»29.8 «MeVc–1»
[1 mark]
Eπ = \(\sqrt {p_\mu ^2{c^2} + m_\mu ^2{c^4}} \) + pvc OR Eμ = 109.8 «MeV»
Eπ = «\(\sqrt {{{29.8}^2} + {{105.7}^2}} \) + 29.8 =» 139.6 «MeV»
Final value to at least 3 sig figs required for mark.
[2 marks]
139.6 MeVc–2
Units required.
Accept 140 MeVc–2.
[1 mark]
