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 .

Explanation

`T = t+273 = 27 +273 = 300 K, K = 1.38 xx 10^(-23)` J /mol/K
` E = 3/2 KT rArr lambda = h/(2"mE") = h/(sqrt(2mxx3/2 KT)) = h/(3"mKT")`
` (6.63 xx10^(-34))/(sqrt(3 xx 1.675 xx10^(-27) xx 1.38 xx10^(-23) xx 300 )) = 1.45 xx10^(-10)` m
This wavelength is order of interatomic spacing So, the neutron beam first thermalised and then used for diffraction .