Question 232: Thermodynamics & KTG

Question

If $$\mathrm{n}$$ is the number density and $$\mathrm{d}$$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

Accepted Answer

The mean free path $$\lambda$$ is the average distance covered by a molecule between two successive collisions. It is given by the formula:
$$\lambda = \frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}$$
Where:
$$n$$ is the number density of the molecules, i.e., the number of molecules per unit volume,
$$d$$ is the diameter of the molecules, and
$$\sqrt{2}$$ arises from considering the relative motion of a pair of particles in a gas, taking into account that either particle can be moving towards the other, which effectively doubles the cross-sectional area through which they can collide.
This formula shows that the mean free path is inversely proportional to the number density $$n$$ of the molecules and the square of the diameter $$d$$ of the molecules. It also takes into account that collisions are more likely as the cross-sectional area of the molecules increases, or as the density of the molecules increases.
Therefore, the correct answer is:
Option A: $$\frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}$$

Answer

$$\frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}$$

Answer

$$\frac{1}{\sqrt{2} n^2 \pi^2 d^2}$$

Answer

$$\frac{1}{\sqrt{2 n \pi d^2}}$$

Answer

$$\sqrt{2} \mathrm{n} \pi \mathrm{d}^2$$

Thermodynamics & KTG

If $\mathrm{n} is the number density and \mathrm{d}$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

Choose the correct answer: