Kinetic energy of a recoiling nucleus

[roughtenator]

A Fe nucleus at rest emits a 14.0-keV photon. Use conservation of energy and momentum to deduce the kinetic energy of the recoiling nucleus in electron volts. (Use Mc² = 8.60E-9 J for the final state of the Fe nucleus.)
what I have so far is...

E = pc because E >> photon rest energy , which = 0 eV

P = E/C = 7.476 E-24

P₁ = P₂

I'm not sure what to do next.

Thanks in advance for the help!

 

[malawi_glenn]

what is the relation between Energy and kinetic energy in special relativity? And what is the relation between energy, momentum and mass in special relativity?

 

[roughtenator]

Relation between kinetic energy and total energy in special relativity is...
E = K + mc²
Relationship between mass, energy and momentum is...
E² = P²C² + (mc²)²

 

[malawi_glenn]

great, then can you find, from these two, a relation between momentum, mass and kinetic energy?

 

[roughtenator]

is this valid?

(K+MC²) = P²C² + (MC²)²

then isolate K?

 

[malawi_glenn]

you forgot to square the left-hand side ...