If the root mean square velocity of the particles in a gas is $450 \mathrm{~m} / \mathrm{s}$, and a particle collides with another particle every $2.0 \times 10^{-9}$ seconds on average, then the mean free path is
A) $9.0 \times 10^{-7} \mathrm{~m}$.
B) $6.0 \times 10^{-7} \mathrm{~m}$.
C) $6.9 \times 10^{-7} \mathrm{~m}$.
D) $85 \times 10^{-7} \mathrm{~m}$.
E) $7.5 \times 10^{-7} \mathrm{~m}$.

Question

Quizplus · Accepted Answer

The mean free path can be calculated using the formula $\lambda = v \times \tau$, where $v$ is the root mean square velocity and $\tau$ is the average time between collisions. Substituting the given values, $450 \, \mathrm{m/s} \times 2.0 \times 10^{-9} \, \mathrm{s} = 9.0 \times 10^{-7} \, \mathrm{m}$.

If the Root Mean Square Velocity of the Particles in a Gas