Question

(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. (mn= 1.675 × 10⁻²⁷ kg)

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

Answer 1

It is given in the previous problem that the inter-atomic spacing of a crystal is about 1 Å, i.e., 10⁻¹⁰ m. Hence, the inter-atomic spacing is about a hundred times greater. Hence, a neutron beam of energy 150 eV is not suitable for diffraction experiments.

This wavelength is comparable to the inter atomic spacing of a crystal. Hence, the high energy neutron beam should first be thermalised, before using it for diffraction.