Homework Help: Electron Scattering and Bragg's law

1. Feb 25, 2017

jasonchiang97

1. The problem statement, all variables and given/known data

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).

2. Relevant 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
3. 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!

2. Feb 25, 2017

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?