First slide

Matter waves (DC Broglie waves)

Question

The de-Broglie wavelength of neutrons in thermal equilibrium at temperature T is

Easy

A

$\frac{3.08}{\sqrt{T}} \overset{o}{A}$
B

$\frac{0.308}{\sqrt{T}} \overset{o}{A}$
C

$\frac{0.0308}{\sqrt{T}} \overset{o}{A}$
D

$\frac{30.8}{\sqrt{T}} \overset{o}{A}$

Solution

de Broglie wavelength of neutronsin thermalequilibrium at temperature T is
$λ = \frac{h}{\sqrt{2 m k_{B} T}}$
where $m$ is the mass of the neutron
$k_{B}$ is the Boltzmann constant
h is the Planck's constant
$Here, m = 1.67 \times 10^{- 27} kg k_{B} = 1.38 \times 10^{- 23} J K^{- 1} h = 6.63 \times 10^{- 34} J s ∴ λ = \frac{6.63 \times 10^{- 34}}{\sqrt{2 \times 1.67 \times 10^{- 27} \times 1.38 \times 10^{- 23} \times T}} = \frac{3.08 \times 10^{- 34} \times 10^{25}}{\sqrt{T}} m = \frac{30.8 \times 10^{- 10}}{\sqrt{T}} = \frac{30.8}{\sqrt{T}} \overset{o}{A}$

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