Recoil speed of an atomic nucleus

[Qnslaught]

Homework Statement

An atomic nucleus is in an excited state. It decays to its ground state with the emission of a gamma ray having energy, Egamma = 24.0 keV. The nucleus has a mass of 9.53e-26 kg. What is the recoil speed of the nucleus? (Note: This may be an inelastic collision)

Homework Equations

1 eV = 1.6e-19 J

The Attempt at a Solution

I tried setting the final kinetic equal to the rest energy, and I tried setting it equal to the energy of the gamma ray, and I can't get the answer. The answer key lists the correct answer as 134 m/s, and I have no idea how to get to that.

 

[Delphi51]

Why not use conservation of momentum?
Use the special formula for the momentum of a photon, using its energy to calculate its momentum.

 

[Qnslaught]

Thank you, I got it now :)