Question -
Answer -
(a) DeBroglie wavelength =
; neutron is not suitable for thediffraction experiment
Kinetic energy of the neutron, K =150 eV
= 150 × 1.6 × 10−19
= 2.4 × 10−17 J
Mass of a neutron, mn =1.675 × 10−27 kg
The kinetic energy of theneutron is given by the relation:
Where,
v = Velocity of the neutron
mnv = Momentum of the neutron
De-Broglie wavelength ofthe neutron is given as:
It is given in the previous problem that theinter-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, aneutron beam of energy 150 eV is not suitable for diffraction experiments.
(b) De Broglie wavelength = 
Room temperature, T = 27°C= 27 + 273 = 300 K
The average kinetic energyof the neutron is given as:
Where,
k = Boltzmann constant = 1.38 × 10−23 Jmol−1 K−1
The wavelength of theneutron is given as:
Thiswavelength is comparable to the inter-atomic spacing of a crystal. Hence, thehigh-energy neutron beam should first be thermalised, before using it fordiffraction.