If $n$ is the number density and $d$ is the diameter of the molecule,then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

What is the effect of a decrease in the number of molecules per unit volume on the mean free path?

In the adjoining figure,various isothermals are shown for a real gas. Then

We have $0.5 \, g$ of hydrogen gas in a cubic chamber of size $3 \, cm$ kept at $NTP$. The gas in the chamber is compressed keeping the temperature constant until a final pressure of $100 \, atm$ is reached. Is one justified in assuming the ideal gas law in the final state? (Hydrogen molecules can be considered as spheres of radius $1 \, \mathring{A}$).

Given below are two statements:
Statement $(I)$: The mean free path of gas molecules is inversely proportional to the square of the molecular diameter.
Statement $(II)$: The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.
In the light of the above statements,choose the correct answer from the options given below:

If the radius of an $O_{2}$ molecule is $40 \; \mathring{A}$,$T = 27^{\circ}C$,and $P = 1 \; \text{atm}$,find the relaxation time.