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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)

$\frac{h}{\sqrt{m k T}}$
$\frac{h}{\sqrt{2 m k T}}$
$\frac{h}{\sqrt{3 m k T}}$
$\frac{h}{2 \sqrt{m k T}}$

A

\frac{h}{\sqrt{m k T}}

B

\frac{h}{\sqrt{3 m k T}}

C

\frac{h}{\sqrt{2 m k T}}

D

\frac{h}{2 \sqrt{m k T}}

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Solution

Verified by Toppr

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

$\frac{m v^{2}}{2} = k T$

$\Rightarrow p = m v = \sqrt{2 m k T}$

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

$λ = h / p = \frac{h}{\sqrt{2 m k T}}$ .

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