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For a molecule of an ideal gas, the numb...

For a molecule of an ideal gas, the number density is `2sqrt(2)xx10^(8) cm^(-3)` and the mean free path is `(10^(-2))/(pi) cm`. The diameter of the gas molecule is

A

`5xx10^(-4) cm`

B

`0.5xx10^(-4) cm`

C

`2.5xx10^(-4) cm`

D

`4xx10^(-4) cm`

Text Solution

Verified by Experts

The correct Answer is:
A
Mean free path,
`lamda =(1)/(sqrt(2) pi n d^(2))`
`rArr d^(2) =(1)/(sqrt(2) pi n lamda)=(1xxpi)/(sqrt(2) xx pi xx 2sqrt(2)xx10^(8)xx10^(-2))`
`rArr d^(2) =(1)/(4xx10^(6)`
`rArr d=(1)/(2)xx10^(-3) cm`
`rArr d=5xx10^(-4) cm`
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