The root mean square speed of an ideal gas is given by: $u_{rms}=\sqrt{\frac{3RT}{M}}$  . Thus, we conclude that $u_{rms}$ speed of an ideal gas molecules is proportional to square root of the temperature and inversely proportional to the square root of the molar mass. The translational kinetic energy/mol can also be given as $\frac{1}{2}M{u}_{rms}^2$ . The mean free path $\left(\lambda \right)$   is the average of distances travelled by a molecules in between two successive collisions, whereas collision number $\left(z_1\right)$ is expressed as number of collisions taking place unit volume in unit time. The two terms $\lambda$   and $z_1$are related by  $\frac{z_1=u_{AV}}{\lambda }$