Relativistic Momentum of a photon

[jacksonb62]

1.
An elementary particle of mass M completely absorbs a photon, after which its mass is 1.01M. (a) What was the energy of the incoming photon? (b) Why is that energy greater than 0.01Mc2?

Homework Equations

p (photon) = E/c
p (particle) = γmv
p(i) = p(f)
Ek = γmc^2 -mc^2

The Attempt at a Solution

I really have no idea where to start without having knowledge of the velocity of the particle after the collision

 

[mfb]

Just use v as velocity. Momentum conservation will give you that velocity during the calculations.

 

[vela]

Homework Statement

An elementary particle of mass M completely absorbs a photon, after which its mass is 1.01M. (a) What was the energy of the incoming photon? (b) Why is that energy greater than 0.01Mc2?

Homework Equations

p (photon) = E/c
p (particle) = γmv
p(i) = p(f)
Ek = γmc^2 -mc^2

The Attempt at a Solution

I really have no idea where to start without having knowledge of the velocity of the particle after the collision

Was that the complete problem statement? I don't think the situation described is physically possible.

 

[mfb]

It is possible, it is the reverse process of a gamma decay.

 

[vela]

But that's with a nucleus, which has a substructure. I guess it seems a little odd to me to say that an elementary particle changes its mass by absorbing a photon unless it's referring to its relativistic mass.

 

[mfb]

It becomes a different elementary particle. There are no suitable elementary particles for that process (and it would probably need weak higher-order processes), but I don't think we have to worry about that.
"Mass" has to be rest mass, otherwise the second question does not make sense.
Elementary just guarantees we don't have to worry about rotations and so on.