# Homework Help: Derivation qn, decay process

1. Jun 20, 2009

### fredrick08

1. The problem statement, all variables and given/known data
A particle at rest with mass M, decays into n identical smaller particles with equal mass, m. Show that speed of the particles is given by

u=c*root(1-(((n^2)(m^2))/M^2))

3. The attempt at a solution
this one i dont really know where to start, M has a rest energy... m's have Et=Eo+Ek so,

Mc^2=(n*mc^2)+(n*(1/2)mv^2)???

2. Jun 20, 2009

### fredrick08

lol that doesnt even make sense...

3. Jun 20, 2009

### fredrick08

no one has any ideaS?

4. Jun 21, 2009

### fredrick08

is it Mc^2=ynmc^2=>y=M/nm=>1/root(1-B^2)=M/nm=>B=root(1-(nm)^2/M^2)=v/c=>v=c*root(1-(nm)^2/M^2) this works out but can someone tell me why there is no kinetic energy part in the equation?? does ymc^2= total energy, because i thought it was just relativistic rest mass?

5. Jun 21, 2009

### Astronuc

Staff Emeritus
Well M would be the rest mass of the initial particle, m is the rest mass of the smaller particles, and M > nm. The total energy is conserved, and so is momentum.

It should be straightforward for two particles (colinear) and three particles (coplanar). Four or more starts getting complicated because momentum is in three dimensions.

Try with 2 particles (products), then 3.

Since the products are identical (m), there is some symmetry which is the key.

Has one considered E2 = p2c2 + m2c4

Last edited: Jun 21, 2009