Question

The wavelength of the de-Broglie wave associated with a thermal neutron of mass $m$ at absolute temperature $T$ is given by (Here, $k$ is the Boltzmann constant)

• A. $\frac{h}{\sqrt{2 m k T}}$
• B. $\frac{h}{\sqrt{m k T}}$
• C. $\frac{h}{\sqrt{3 k m T}}$
• D. $\frac{h}{2 \sqrt{m k T}}$

Answer 1

Answer: (C)

KE of thermal neutron, $\frac{1}{2}mv^{2}=\frac{3}{2}kT$
or $mv=\sqrt{3 k m T}$ ; So, $\lambda =\frac{h}{p}=\frac{h}{\sqrt{3 k m T}}$