Question

The mean free path of a gas molecule at 270C is 2 cm. If the rms velocity of the gas at that temperature is 10 m/s. What is the time interval between two successive collisions ?

1) 1/5 s      2) 1/50 s     3) 1/500 s      4) 1/250 s


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Answer 1

Mean free path of a particle is the average distance travelled by the particle between two successive collisions.

So the time interval between two successive collisions should be equal to the mean free path divided by its speed.

In case of gas molecules, root mean square (rms) speed is considered since each particle has different speed.

Hence,

$\longrightarrow\sf{Time\ interval=\dfrac{Mean\ free\ path}{Rms\ speed}}$

Here,

$\longrightarrow\sf{Mean\ free\ path=0.02\ m}$

$\longrightarrow\sf{Rms\ speed=10\ m\,s^{-1}}$

Then,

$\longrightarrow\sf{Time\ interval=\dfrac{0.02}{10}}$

$\longrightarrow\underline{\underline{\sf{Time\ interval=\dfrac{1}{500}\ s}}}$

Hence (3) is the answer.