# Atom decay to ground state

1. Oct 8, 2012

### Guidenable

1. The problem statement, all variables and given/known data
An atom of mass M decays from an excited state to the ground state with a change in mass of ΔM<<M. In the decay process, the atom releases a photon. Use the laws of energy and momentum to determine the energy of the photon, assuming the atom decays from rest.

2. Relevant equations
The 4-momenta of the atom before the emission:

P=(Mc2,0,0,0)

After the emission:

P=(M-ΔM)c2, -pxc,0,0)

And the photon:

E=(M-ΔM)c2

p = hf

My main concern here is that this seems too straightforward. The book labels this problem as a challenging one. I think I'm missing a subtlety in the problem.

2. Oct 8, 2012

### Guidenable

Found it. The energy of the photon isn't delta(m)c^2 as the atom is moving. So in the atom's frame, the photon is redshifted. The energy of the photon (which is hf in a rest frame) is now hf', where f' is the shifted frequency due to the transverse relativistic doppler effect.