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.

Options

A. hydrogen, helium, nitrogen, oxygen
B. oxygen, nitrogen, hydrogen, helium
C. oxygen, nitrogen, helium, hydrogen
D. nitrogen, oxygen, helium, hydrogen

Answer

C

Explanation

de Broglie wavelength of a gas molecule
`lambda = (h)/(sqrt(3 mk_BT))`
For the same temperature `lambda prop (1)/(sqrt(m))`
As `mO_(2) gt mN_2 gt mHe gt mH_2`
`therefore lambda _(O_2)) lt lambdaN_(2) lt lambda_(He) lt lambdaH_(2)`