How Does Particle Decay Relate to the Speed of Resulting Particles?

[fredrick08]

Homework Statement

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))

The Attempt at a Solution

this one i don't 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)?

 

[fredrick08]

lol that doesn't even make sense...

 

[fredrick08]

no one has any ideaS?

 

[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?

 

[Astronuc]

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