(a) Obtain the de-Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in previous problem 31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. Given `m_(n)=1.675xx10^(-27)kg`.
(b) Obtain the de-Broglie wavelength associated with thermal neutrons at room temperature `(27^(@)C)`. Hence explain why a fast neutrons beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Explanation

Given , KE = 150 ev, `m_(n) = 1.675 xx10^(-27)` kg
`lambda = h/(sqrt(2m_(n)KE))= (6.63 xx10^(-34))/(2xx1.675 xx10^(-27) xx 150 xx 1.6 xx10^(-19)) = 2.33 xx10^(-12) ` m
The interatomic spacing is ` 10^(-10)` m , which is greater than this wavelength , So neutron beam of 150 eV is not suitable for diffraction experiment .