(a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in Exercise 11.31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. `(m_(n) = 1.675 xx 10^(-27) kg)`
(b) 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

`lambda=(h)/(p)=(h)/(sqrt(2mK))`.Thus, for some K, `lambda` decreases with m as `(1//sqrtm)`. Now `(m_(n)//m_(e))=1838.6`, therefore for the same energy, (150 ev) as in Ex. 11.31 wavelength of neutron `=(1//sqrt(1838.6))xx10^(-10)m=2.33xx10^(-12)m`.
The interatomic spacing is about a hundred times greater. A neutron beam of 150 ev energy is therefore not suitable for diffraction experiments.
(b) `lambda=1.45xx10^(-10)m[" Use "lambda=(h//sqrt(3mkT))]` which is comparable to interatomic spacing in a crystal.
Clearly, from (a) and (b) above, thermal neutrons are a suitable probe for diffraction experiments, so a high energy neutron beam should be first thermalised before using it for diffraction.