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Question

Physics Question on de broglie hypothesis

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

A

3.08TA˚\frac {3.08}{\sqrt T}\mathring{A}

B

0.308TA˚\frac {0.308}{\sqrt T}\mathring{A}

C

0.0308TA˚\frac {0.0308}{\sqrt T}\mathring{A}

D

30.8TA˚\frac {30.8}{\sqrt T}\mathring{A}

Answer

30.8TA˚\frac {30.8}{\sqrt T}\mathring{A}

Explanation

Solution

de Broglie wavelength of neutrons in thermal equilibrium at temperature T is ?=h2mkBT?= \frac {h}{\sqrt {2mk_BT}} where m is the mass of the neutron kBk_B is the Boltzmann constant h is the Planck's constant Here, m=1.67×10−27kg\times 10^{-27} kg     kB=1.38×10−23J K−1\, \, \, \, k_B=1.38 \times 10^{-23} J \, K^{-1} h=6.63×1034J sh=6.63 \times 10^{34} J \, s ∴?=6.63×10−342×1.67×10−27×1.38×10−23×T\therefore ?= \frac {6.63 \times 10^{-34}}{\sqrt {2 \times 1.67 \times 10^{-27} \times 1.38 \times 10^{-23} \times T}} =3.08×10−34×1025Tm= \frac {3.08 \times 10^{-34} \times 10^{25}}{\sqrt T}m =30.8×10−10T=30.8TA˚= \frac {30.8 \times 10^{-10} }{\sqrt T}=\frac {30.8}{\sqrt T} \mathring{A}