How Do You Calculate Recoil Shift in Atomic Emissions?

[atomicpedals]

Homework Statement

b) Calculate the recoil shift for the most energetic lyman line from a free H atom.

c) Calculate the recoil shift for the emission of a 14.4keV gamma from a free atom of Fe-57.

Homework Equations

E = hc / $\lambda$ = h $\nu$

$\Delta$ E = E^2 / 2mc^2

The Attempt at a Solution

I'm still not sure I'm going about this correctly...

b) start by finding the most energetic lyman line E = hc / $\lambda$ = (1.981E-16)/(912A) = 2.17E-19 (this is where I think my error is). Then find the recoil shift
$\Delta$ E = E^2 / 2mc^2 = (4.72E-38)/(0.003) = 1.57E-35.

c) calculate the recoil shift directly using the mass for Fe-57
$\Delta$ E = E^2 / 2mc^2 = (207.36)/(1.89E-22)(2.99E8)^2 = 12.27MeV ...again this answer just feels wrong, how can a keV scale emission result in an MeV scale recoil?

Quite clearly I've made some horrible mistake in here, I need some help to find what I did wrong.

 

[atomicpedals]

Ok, I've been able to answer part c:

((14.4keV)^2)/2(53.02GeV) = 0.002eV

(sorry for not using tex with the equation, I've been spending way too much time with C++ lately)

Still working on part b though.