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

Question

Philoid · Accepted Answer

From Bragg’s Law, we have

Here, n is the order, λ is the wavelength, d is the lattice spacing and ϴ is the angle of scattering.

Using the values given in the question to find , (note 1nm = 10^-9m)

Kinetic Energy of the beam can be given by

Here m is mass of the neutron.

Converting to eV by dividing by 1.6 X 10^-19