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, heliuin
C. Oxygen, nitrogen, helium, hydrogen
D. Nitrogen, oxygen, helium, hydrogen

Answer

C

Explanation

de Broglie wavelength of a gas molecule
`lamda = h/(sqrt(3mk_(B)T)`
where, T = Absolute temperature
`k_B` = Boltzmann.z constant
m = Mass of gas molecule
For the same temperature
`lamda prop 1/sqrtm`
As `m_(O_2) gt m_(N_2) gt m_(He) gt m_(H_2)`
`:. lamda_(O_(2))lt lamda_(N_(2) ) lt lamda_(He) lt lamda_(H_2)`