(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle with rest mass [tex]M_0[/tex] can decay at rest into a pair of particles each with rest

mass [tex]m_0[/tex]. Calculate the following in the rest inertial frame of the original particle

using [tex]M_0c^2=600[/tex]MeV and [tex]m_0c^2=150[/tex] MeV .

(i) The total energy of each particle produced in the decay.

(ii) The magnitude of the relativistic linear momentum of each particle produced in

the decay.

(iii) The speed of the particles produced in the decay.

2. Relevant equations

[tex]E^2=p^2c^2 + E_0^2[/tex] [1]

[tex]E=\gamma m_0c^2[/tex] [2]

3. The attempt at a solution

i)Ok, first I'm assuming that the new particles will have equal energy, so each E=300MeV

ii) I think I'm meant to use equation [1], where E=300 and E_{0}=150. This gives [tex]p=\frac{259.8}{c}=0.866[/tex]. This is the part I'm unsure on (and possibly the next one). If the method is correct, what are the units?

iii) I use the fact that [tex]E=\gamma m_0c^2[/tex], giving [tex]\gamma=2 \Rightarrow v=\frac{\sqrt{3}}{2}c[/tex]

Thanks very much for helping!!

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# Homework Help: Special Relativity and Particle Decay

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