The mean free path of molecules in an ideal gas $A$ is half that of another ideal gas $B$. The diameter of the spherical molecules of gas $A$ is twice the diameter of the molecules of gas $B$. If number densities of the gases $A$ and $B$ are $n_A$ and $n_B$, respectively, then the correct option is :

The mean free path for a gas at temperature $300 \ K$ and pressure $600 \ \text{torr}$ is $10^{-7} \ m$. The mean free path of the gas at a temperature $400 \ K$ and pressure $200 \ \text{torr}$ will be

Ten small planes are flying at a speed of $150 \ km/h$ in total darkness in an air space that is $20 \times 20 \times 1.5 \ km^3$ in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average, about how long a time will elapse between near collisions with your plane? Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius $10 \ m$.

$Assertion:$ Mean free path of a gas molecule varies inversely as the density of the gas.
$Reason:$ Mean free path varies inversely as the pressure of the gas.

$A$ fixed amount of nitrogen gas ($1$ mole) is taken and subjected to pressure and temperature variations. The experiment is performed at high pressures and various temperatures. The results obtained are shown in the figure. The correct variation of $PV/RT$ with $P$ for nitrogen gas at high temperatures will be exhibited by:

The mean free path of molecules of a certain gas at $STP$ is $1500\,d$,where $d$ is the diameter of the gas molecules. While maintaining the standard pressure,the mean free path of the molecules at $373\,K$ is approximately $..........\,d$