Question

Consider the four gases hydrogen, oxygen, nitrogen and helium at the same temperature. Arrange them in the increasing order of the de Broglie wavelengths 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

de Broglie wavelength of a gas molecule $\lambda =\frac{h}{\sqrt{3m{k}_{B}T}}$
where, T = Absolute temperature
kg = Boltzmann's constant
m = Mass of gas molecule
For the same temperature $\lambda \propto \frac{1}{\sqrt{m}}$

As $M_0>M_N>M_{He}>M_{H2}$

$\therefore {\lambda }_O<{\lambda }_N<{\lambda }_{He}<{\lambda }_{H2}$