Mean Free Path

Question

In a laboratory vacuum chamber the pressure of a gas is reduced to one-tenth of its initial value while the temperature is held fixed, so how does the mean free path respond?

RankGuru · Accepted Answer

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.

Mean Free Path

Select the correct option:

🔒 Solution Hidden from View

More kinetic theory of gases Practice Questions

How does the mean free path of molecules in a gas sample change if the number density of molecules i...

Air molecules of effective diameter 3 \times 10^{-10} m occupy a vessel at 300 K and 1.0 \times 10^5...

Mean free path increases if:

Which of the following assumptions is fundamental to the kinetic theory model of an ideal gas as des...

Equal volumes of two different ideal gases are compared at the same temperature and pressure, so wha...

A rigid insulated tank contains a mixture of 2 moles of a monatomic gas and 2 moles of a diatomic ga...

A weather balloon contains 2 moles of an ideal gas, so approximately how many gas molecules are pres...

As the temperature of a gas sample is increased, how does the shape of its Maxwell molecular speed d...

According to the law of equipartition of energy, what average energy is associated with each degree ...

When the absolute temperature of a fixed sample of ideal gas is raised from 300 K to 600 K, by what ...

Two containers hold helium and oxygen respectively at the same absolute temperature, so how do the a...

A rigid diatomic gas molecule at ordinary room temperature, ignoring vibrational modes, possesses ho...

About This Question

Solution