First slide

Matter waves (DC Broglie waves)

Question

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass m, is

Moderate

A

$\frac{h}{\sqrt{3 mkT}}$
B

$\frac{2 h}{\sqrt{3 mkT}}$
C

$\frac{2 h}{\sqrt{mkT}}$
D

$\frac{h}{\sqrt{mkT}}$

Solution

Kinetic energy of a neutron in thermal equilibrium with heavy water at a temperature T is given as
$K = \frac{3}{2} kT . . . . . (i)$
$Also momentum (p) is, p = \sqrt{2 mK}$
From eqn. (i)
$p = \sqrt{2 m \cdot \frac{3}{2} kT} = \sqrt{3 mkT}$
Required de-Broglie wavelength is given as
$λ = \frac{h}{p} = \frac{h}{\sqrt{3 mkT}}$

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