Physics · Kinetic Theory · NEET
It is the average straight-line distance a single gas molecule covers between one collision and the next collision. Molecules move fast but keep hitting each other, so the path is a zig-zag. The mean free path is the average length of each zig-zag segment. In air at room conditions it is very small, about 10^-7 m, roughly 1500 times the molecular diameter.
lambda is the mean free path. d is the diameter of a molecule (treated as a hard sphere). n is the number density, meaning the number of molecules per unit volume (not the number of moles). pi d^2 is the effective collision cross-section area. The root 2 comes from the fact that all molecules move, not just the one we track.
If we assumed only one molecule moved and the rest were fixed, we would get lambda = 1/(pi d^2 n). But every molecule is moving. When we use the relative speed between molecules instead of the speed of one molecule, the average relative speed is root 2 times larger. A faster relative approach means more collisions, so the path shrinks by root 2. That is why root 2 sits in the denominator.
Yes, through n. Using n = P/(kB T), the formula becomes lambda = kB T/(root2 pi d^2 P). So at fixed pressure, higher temperature gives a longer mean free path. At fixed temperature, higher pressure gives a shorter mean free path. If both P and T change together such that density stays fixed, lambda stays fixed.
No. The molecular diameter d is the size of one molecule (about 10^-10 m). The mean free path is the gap a molecule travels between collisions (about 10^-7 m in air), which is around 1000 times larger than d. Do not confuse the size of the molecule with the distance it travels freely.
Mean free path is a length, so its SI unit is the metre (m) and its dimensional formula is [L]. You can check this from the formula: d^2 has units m^2 and n has units m^-3, so d^2 x n has units m^-1, and its reciprocal is m.
The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If the number densities of gases A and B are nA and nB respectively, the correct option is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is the average distance a gas molecule travels between two successive collisions, given by lambda = 1/(root2 pi d^2 n).
For air at normal room temperature and pressure it is about 10^-7 m (around 0.1 micrometre), which is roughly 1500 times the diameter of a molecule.
In a highly evacuated tube the number density n is very small, so the mean free path becomes very large and can even equal the length of the tube, letting molecules cross without colliding.
At constant temperature it is inversely proportional to pressure, because higher pressure packs more molecules per volume (larger n), causing more frequent collisions and a shorter free path.
Not directly. Mean free path depends on molecular diameter and number density, not mass. A heavier molecule may or may not be bigger, so you must compare d and n, not the mass.
