| Date | November 2017 | Marks available | 4 | Reference code | 17N.3.HL.TZ0.7 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Determine | Question number | 7 | Adapted from | N/A |
Question
The \({\Lambda ^0}\) (Lambda) particle decays spontaneously into a proton and a negatively charged pion of rest mass 140 MeV c–2. After the decay, the particles are moving in the same direction with a proton momentum of 630 MeV c–1 and a pion momentum of 270 MeV c–1.
Determine the rest mass of the \({\Lambda ^0}\) particle.
Determine, using your answer to (a), the initial speed of the \({\Lambda ^0}\) particle.
Markscheme
\(\Lambda \) momentum = 900
Eproton = «\(\sqrt {p{c^2} + {{\left( {m{c^2}} \right)}^2}} = \sqrt {{{630}^2} + {{938}^2}} = \)» 1130 «MeV»
Epion = «\(\sqrt {{{270}^2} + {{140}^2}} = \)» 304 «MeV»
so rest mass of \(\Lambda \) = «\(\sqrt {{{\left( {1130 + 304} \right)}^2} - {{900}^2}} = \)» 1116 «MeV c–2»
«E = \(\gamma \) mc2 so» \(\gamma \) = « \(\frac{{1434}}{{1116}}\) =» 1.28
to give 0.64c
