Concept of Mean Free Path

The mean free path $\left(\mathrm{\lambda }\right)$ of a gas sample is given by:

If the temperature and pressure of a gas is doubled the mean free path of the gas molecules

For a molecule of an ideal gas, the number density is $2\sqrt{2}\times {10}^8 {\mathrm{cm}}^{-3}$ and the mean free path is $\frac{{10}^{-2}}{\pi } \mathrm{cm}$. The diameter of the gas molecule is

The mean free path of molecules of a gas (radius $\text{'}r\text{'}$) is inversely proportional to

If temperature of a gas in closed container is doubled, then mean free path of gas molecules will be

Select the correct relation between mean free path ( $\mathrm{\lambda }$ ) and pressure $\left(\mathrm{P}\right)$for an ideal gas at constant temperature

Assume temperature to be constant, then the mean free path of the gas molecules varies with pressure as:
 

Which of the following represents the mean free path for a gas ? (where $n$ is number of gas molecules per unit volume, $d$ is diameter of gas molecules)
 

In the following a statement of Assertion is followed by a statement of Reason.

Assertion: Mean free path of a gas molecule is inversely proportional to the density of gas.

Reason: Path of a gas molecule between two adjacent collision is straight line.

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^q$ , where $V$ is the volume of the gas. The value of $q$ is $\left(\mathrm{\gamma }=\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$

Which of the following is/are correct regarding mean free path ?

Which of the following is/are correct regarding mean free path ?

Air becomes conducting when the pressure ranges between

If the mean free path for a gas is $l$ at $1atm$ pressure then its value at $5atm$ pressure will be-

The mean free path of the molecule of a certain gas at $300 \mathrm{K}$ is $2.6\times {10}^{-5} \mathrm{m}$. The collision diameter of the molecule is $0.26 \mathrm{nm}$. After calculating pressure of the gas. The number of molecules per unit volume of the gas  is $x\times 10^{20}$. The value of $x$ will be