Electron Scattering and Bragg's law

[jasonchiang97]

Homework Statement

A beam of thermal neutrons (K = 0.025 eV) scatters from a crystal with interatomic spacing 0.45 nm. What is the φ angle of the first order Bragg peak? (as defined in figure 5.11, φ and the scattering angle add up to 180 degrees).

Homework Equations

nλ = 2dsinθ
= DsinΦ
d = distance between Bragg planes
D = intermolecular distance
2θ = scattering angle
2θ = π = Φ
K= 1/2mv²
p=mv=h/λ

The Attempt at a Solution

Since K=1/2mv² and p=mv we can solve K and say
K=p²/2m = (pc)²/2mc²
so pc = √(2Kmc²)
and since p=h/λ we have λ=h/p
if we multiply top and bottom by c we have

λ=hc/pc = hc/√(2Kmc²) = DsinΦ since n= 1 for first order.

Thus sinΦ = (hc/D)(1/√(2Kmc²)
however when I plug these numbers in I get that
Φ = sin^-1 (17.239) which isn't possible. To me, this makes no sense because my units cancel out properly and I can't see what I did wrong. Thanks!

 

[jasonchiang97]

Never mind I think I solved it. I was putting in the mass of the electron instead of neutron. Can someone check for me that all my steps still make sense?