Question

Which of the following states of matter exhibits the greatest mean free path?

Answer 1

Plasma

Answer 2

The mean free path ($\lambda$) is the average distance traveled by a particle between successive collisions. It is inversely proportional to the number density ($n$) of particles and the collision cross-section. The general formula for mean free path is:

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

where $d$ is the diameter of the particles and $n$ is the number density.

Let's analyze the mean free path for each state of matter:

1. Solids: Particles are tightly packed in fixed positions with very high number density. They primarily vibrate around their equilibrium positions, leading to extremely frequent "collisions" or interactions. Therefore, the mean free path in solids is negligible or extremely small.

2. Liquids: Particles are closely packed but are free to move past each other. The number density is high, though slightly less than solids. Particles collide frequently. The mean free path in liquids is small, but larger than in solids.

3. Gases: Particles are far apart from each other, and the number density is significantly lower than in liquids and solids. Particles move randomly and freely, resulting in much less frequent collisions. Consequently, gases have a much larger mean free path compared to liquids and solids.

4. Plasma: Plasma is an ionized gas, consisting of ions, electrons, and neutral atoms. Like gases, the particles in plasma are generally far apart. In many natural and laboratory plasmas (e.g., interstellar medium, fusion plasmas), the particle density can be extremely low, even lower than that of typical gases at atmospheric pressure. This low density leads to very infrequent collisions and, therefore, an exceptionally large mean free path. For instance, in the interstellar medium, the mean free path can be light-years.

Comparing the four states, the particle density decreases in the order: Solids > Liquids > Gases. Plasma can have a wide range of densities, but to achieve the "greatest" mean free path, we consider low-density plasmas. In such conditions, the mean free path in plasma is significantly larger than in gases, liquids, or solids.

Therefore, plasma exhibits the greatest mean free path.