Question

The mean free path of molecules of a gas is inversely proportional to

• A. $r^3$
• B. $r^2$
• C. $r$
• D. $\sqrt{r}$

Answer 1

The correct option is B

$r^2$

Step 1: Formula used

We know, mean free path, $\lambda =\frac{1}{\sqrt{2}n{d}^2}$

where,

$\lambda \to$Mean free path

$n\to$Number density (number of molecules per unit volume)

$d\to$diameter of the molecule

Step 2: From the equation, find the relation between $\lambda$ and $r$

$\lambda \propto \frac{1}{d^2}$

$\Rightarrow \lambda \propto \frac{1}{r^2}$

where $r$ is the radius of the molecule $(r=\frac{d}{2}\because r\propto d)$

The mean free path of molecules of a gas is inversely proportional to $r^2$.