A lambda $\Lambda$⁰ particle at rest decays into a proton p and a pion ${\pi ^ - }$ according to the reaction

$\Lambda$⁰ → p + $\pi$^–

where the rest energy of p = 938 MeV and the rest energy of $\pi$^– = 140 MeV.

The speed of the pion after the decay is 0.579c. For this speed $\gamma$ = 1.2265. Calculate the speed of the proton.

pion momentum is $\gamma mv = 1.2265 \times 140 \times 0.579 = 99.4$ «MeV$\,$c^–1»

use of momentum conservation to realize that produced particles have equal and opposite momenta

so for proton $\gamma v = \frac{{99.4}}{{938}} = 0.106c$

solving to get v = 0.105c

Accept pion momentum calculation using E ² = p ²c ² +m ²c ⁴.

Award [2 max] for a non-relativistic answer of v = 0.0864c

[4 marks]