# Homework Help: Calculate the kinetic energy of the recoiling particle.

1. Apr 25, 2010

### Gavins

1. The problem statement, all variables and given/known data
A particle of rest mass 6x10^-30 kg is at rest. It then emits a gamma ray of 2 MeV (3.2x10^-13). Calculate the kinetic energy of the recoiling particle.

2. Relevant equations
$$KE = (\gamma - 1)m_{0}c^{2}$$
$$E^{2} - p^{2}c^{2} = m_{0}^{2}c^{4}$$

3. The attempt at a solution
I used the conservation of energy to find the energy of the recoiling particle.
(6x10^-30)c^2 = 3.2x10^-13 + E
E = 2.2x10^-13

Then I used the conservation of momentum.
p = -(3.2x10^-13)/c = 1.06x10^-21

But I'm stuck. I try to put this in the energy-momentum invariant but it doesn't work.

2. Apr 25, 2010

### vela

Staff Emeritus
Re: Relativity

One of your classmates posted this problem awhile back. Either the numbers don't work, meaning it's a physically impossible situation, or the wording is confusing or wrong. The way the problem is worded, it sounds like the particle has a rest mass of 6x10-30 kg=3.375 MeV/c2 before it emits the photon. If that's the case, however, it can't emit a 2 MeV photon. (At most, it can emit a photon of energy half the rest mass.) So the only interpretation that seems to make sense is that the particle is going from an excited state to its ground state, and its ground state rest mass is 6x10-30 kg.