A neutron beam of energy E scatters from atoms on a surface with a spacing d=0.1 nm. The first maximum of intensity in the reflected beam occurs at θ=30°. What is the kinetic energy E of the beam in eV?

Hint: The momentum of the particles depends on the wavelength of the beam.

Step 1: Find the wavelength of the beam.

Given, d=0.1 nm, θ=30° and n=1

Now, according to Bragg's law 

2dsinθ=2×0.1×sin30°=λλ=0.1 nm=1010 mStep 2: Find the momentum of the particles.Now,   λ=hmv=hpp=hλ=6.62×10341010=6.62×1024kgm/sStep 3: Find the kinetic energy of the particles.Now,  KE=12mv2=12m2v2m=12p2m=12×(6.62×1024)21.67×1027J=0.21 eV