Two gases X (mol wt. `M_(X)`) and Y (mo. At. `M_(Y),M_(Y) gt M_(X)`) are at the same temperature, T in two different containers. Their root mean square velocities are `C_(X)` and `C_(Y)` respectively. If average kinetic energies per molecule of two gases X and Y are `E_(X) and E_(Y)` respectively, then which of the following relation(s) is (are) true-

Options

A. `E_(X) gt E_(Y)`
B. `C_(X) gt C_(Y)`
C. `E_(X)=E_(Y)=(3)/(2)RT`
D. `E_(X)=E_(Y)=(3)/(2)k_(B)T`

Answer

B, D

Explanation

When temperature is constant, higher the molar mass lower is the rms velocity of gas. Hence `C_(X) gt C_(Y)`. At TK temperature, average kinetic energy of a gas molecule =(3/2)KT. Average kinetic energy of a gas molecule does not deepnd on mass of the molecule, it depends only on absolute temperature of gas. At a given temperature, average kinetic energy of a ligher gas molecule is same as that of a heavier gas molecule. So, `E_(X)=E_(Y)=(3)/(2)KT`.