How much mass does an atom lose when it emits a photon?

[aurora14421]

Homework Statement

An atom initially at rest emits a photon with frequency f. Explain why the mass of the atom decreases, and by an amount greater than hf/c^2.

Homework Equations

E= mc^2
E = hf

The Attempt at a Solution

So I know that the atom must lose mass when the photon is emitted because in order for it to emit energy it must lose mass (by E = mc^2), but I don't understand why it should be more than hf/c^2, since from these 2 equations:

E = mc^2 = hf

therefore m = hf/c^2

Why is this wrong?

Thanks.

 

[Avodyne]

The atom is initially at rest. Is it at rest after it emits the photon?

 

[aurora14421]

Ok, I see. So the atom recoils with the opposite momentum of the photon (-hf/c), since momentum is conserved. Thanks, I was just thinking about energy conservation.