Mean Free Path

Relating pressure to mean free path builds on the kinetic theory results in NCERT Class 11, Chapter 13 (Kinetic Theory). The mean free path is $\lambda =\frac{1}{\sqrt{2}n\pi d^2}$, and at constant temperature the number density is proportional to pressure through $P=n{k}_{B}T$, so $n=\frac{P}{k_{B}T}$. Substituting shows $\lambda =\frac{k_{B}T}{\sqrt{2}\pi d^{2}P}$, meaning the mean free path is inversely proportional to pressure when temperature is fixed. Reducing the pressure to one-tenth therefore increases the mean free path tenfold, because there are far fewer molecules to collide with. The option that it decreases to one-tenth reverses the inverse relationship. The option that it stays unchanged neglects the pressure dependence. The option involving the square root of ten wrongly borrows a speed-type dependence. This is precisely why high-vacuum equipment can allow particle beams to travel long distances without scattering, since lowering the pressure dramatically lengthens the mean free path. A sanity check aligns with intuition: pumping a chamber down to lower pressure thins out the gas, so molecules fly much farther between collisions, and a tenfold pressure drop giving a tenfold longer path is entirely consistent.