the diameter of a molecule of argon gas is d .find the mean free path

1.	the diameter of a molecule of argon gas is d .find the mean free path of molecules of argon at 37°C temperature and 10^5 PA pressure.(KB = Boltzmann constant )
Answer» Given : Diameter of molecule = d Temperature = 37°C Pressure = 10⁵ Pa To FIND : Mean free path of ARGON molecules. Solution : ❖ The mean free path is the average distance travelled by a moving molecule between collisions. Formula : $\dag\:\underline{\boxed{\bf{\purple{\lambda=\dfrac{K_BT}{\sqrt2P\pi d^2}}}}}$ $\sf{K_B}$ denotes Boltzmann constant T denotes temperature P denotes pressure d denotes diameter By substituting the given values; $\sf:\implies\:\lambda=\dfrac{K_BT}{\sqrt2P\pi d^2}$ Temperature = 37°C = 310K $\sf:\implies\:\lambda=\dfrac{1.38\times 10^{-23}\times 310}{\sqrt2(10^5)(3.14)d^2}$ $\sf:\implies\:\lambda=\dfrac{96.62\times 10^{-23}}{(10^5)d^2}$ $:\implies\:\underline{\boxed{\bf{\orange{\lambda=\dfrac{9.66\times10^{-27}}{d^2}\:m}}}}$