Calculating Particle Speed in a Relativistic Decay Scenario

[faen]

Homework Statement

A particle with mass M decays into 2 particles of equal mass m.

1: Calculate the speed of the decay particles

2: Concider the case ρ->$$\Pi\Pi$$: M = 770 MeV and m$$\Pi$$= 140 MeV

Homework Equations

m = $$\gamma$$m(restmass) ?

The Attempt at a Solution

I suppose M/2 is restmass and found an expression for the speed. However since the mass increase when the speed approaches the speed of light, this would imply that m is a larger number than M/2. But in task 2, it says M/2 is larger than m$$\Pi$$, which implies I've done something wrong.

Please help me solve this task or find out what i did wrong.

 

[nrqed]

Homework Statement

A particle with mass M decays into 2 particles of equal mass m.

1: Calculate the speed of the decay particles

2: Concider the case ρ->$$\Pi\Pi$$: M = 770 MeV and m$$\Pi$$= 140 MeV

Homework Equations

m = $$\gamma$$m(restmass) ?

The Attempt at a Solution

I suppose M/2 is restmass and found an expression for the speed. However since the mass increase when the speed approaches the speed of light, this would imply that m is a larger number than M/2. But in task 2, it says M/2 is larger than m$$\Pi$$, which implies I've done something wrong.

Please help me solve this task or find out what i did wrong.

The question is ambiguous since you don't say in what frame the calculation is done. I assume in the rest frame of the decaying particle? Then the eenrgy of each produced particle is M/2 and this is equal to $$\gamma m c^2$$ where m is the mass of each produced particle.

 

[faen]

The question is ambiguous since you don't say in what frame the calculation is done. I assume in the rest frame of the decaying particle? Then the eenrgy of each produced particle is M/2 and this is equal to $$\gamma m c^2$$ where m is the mass of each produced particle.

Ok now i understand it, thank you for the answer. :)