Question

Consider the four gases hydrogen. Oxygen , nitrogen and helium at the same temperature. Arrange them in the increasing order of the de Broglie wavelength of their molecules.

• A. Hydrogen, helium, nitrogen, oxygen
• B. Oxygen, nitrogen, hydrogen, helium,
• C. Oxygen, nitrogen, helium, hydrogen
• D. Nitrogen, oxygen , helium, hydrogen

Answer 1

Answer: (C)

Oxygen, nitrogen, helium, hydrogen

Answer 2

: de Broglie wavelength of a gas molecule

$\lambda = \frac{h}{\sqrt{3mk_{B}T}}$

Where, T =Absolute temperature

$K^{B} =$Boltzmann’s constant

m= Mass of gas molecule

for the same temperature

$\lambda \propto \frac{1}{\sqrt{m}}$

As $m_{o_{2}} > m_{N_{2}} > m_{He} > m_{H_{2}}$$$\therefore\lambda_{O_{2}} < \lambda_{N_{2}} < \lambda_{He} < \lambda_{H_{2}}$$