Question

The wavelength of the de-Broglie wave associated with a thermal neutron of mass $m$ at absolute temperature $T$ is given by:

($k$ is the Boltzmann constant)

• A. $\frac{h}{\sqrt{mkT}}$
• B. $\frac{h}{\sqrt{2mkT}}$
• C. $\frac{h}{\sqrt{3mkT}}$
• D. $\frac{h}{2\sqrt{mkT}}$

Answer 1

The correct option is B $\frac{h}{\sqrt{2mkT}}$

The kinetic energy of the thermal neutron of mass m at absolute temperature T is given by

$\frac{m{v}^2}{2}=kT$

$\Rightarrow p=mv=\sqrt{2mkT}$

The wavelength of the deBroglie wave associated with the thermal neutron is

$\lambda =h/p=\frac{h}{\sqrt{2mkT}}$.