Calculate the kinetic energy of the recoiling particle.

[Gavins]

Homework Statement

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.

Homework Equations

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

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.

 

[vela]

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.

Try solving the problem that way and ask your instructor for clarification about the wording.

 

[Gavins]

Hm.. That's pretty bad since I found this on an final exam paper a few years back. Thanks anyway. I'm glad that it wasn't me who was wrong.