Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27°C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Question

Philoid · Accepted Answer

De- Broglie wavelength, λ = 1.447 × 10^-10 m

Room temperature, T = 300K

The average KE of neutron is given as,

KE = 3/2 KT …(3)

Where,

K = Boltzmann constant = 1.38 × 10^-23 Jmol^-1K^-1

From equation 2,

Using equation (3) we can write,

By putting values in above equation we get,

λ = 1.447 × 10^-10 m

Now, the wavelength has come into comparable range with the inter-atomic spaces, it is now suitable for diffraction. Hence a beam should be thermalized before using for diffraction.