Question
On what parameter does the $\lambda ($mean free path$)$ depends?
✓
Answer
We know that :$\lambda=\frac{\text{kT}}{\sqrt{2}\pi\text{d}^2\rho}=\frac{\text{m}}{\sqrt{2}\pi\text{d}^2\rho}=\frac{1}{\sqrt{2}\pi\text{n}\text{d}^2}$
$\therefore\lambda$ depends upon:
$\therefore\lambda$ depends upon:
- Diameter $(d)$ of the molecule, smaller the $'d\ '$, larger is the mean free path $\lambda.$
- $\lambda\propto\text{T}$ i.e., higher the temperature larger is the $\lambda.$
- $\lambda\propto\frac{1}{\text{P}}$ i.e., smaller the pressure larger is the $\lambda.$
- $\lambda\propto\frac{1}{\text{P}}$ i.e., smaller the density $(\rho)$ larger will be the $\lambda.$
- $\lambda\propto\frac{1}{\text{P}}$ i.e., smaller the number of molecules per unit volume of the gas, larger is the $\lambda.$
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