Question

The ratio of number of collisions per second at the walls of containers by he and 0 gas molecules kept at same volume and temperature is normal incident on walls

Answer 1

First, we will define Collision Frequency, it is defined as the number of collisions which take place in 1 second among the molecules present in $1cc$ of the gas.

Also, collision number $\left(Nc\right)$ is the number of collisions which a single molecule undergoes with other molecules in 1 second.

So $Nc=2\pi vo2n$

Where $v$ = average speed

$O$ = molecular diameter

$N$ = number of molecules

Collisions among molecules will be $Nc\ast n$

Each collision requires $2$ molecules, collision frequency

$Z=(Nc\ast n)/2=\left(½\right)\ast \pi vo2n2$Average speed $\left(v\right)=sqrt\left(8RT/\right(\pi M\left)\right)$ where M is the molecular mass

Hence, $Z=2o2n2sqrt\left(\pi RTM\right)$

This is the required formula for this question

We know that $M$ for $02$ molecule is $32u$ and for Helium molecule is $4u$

Hence $z1/z2$ = ratio of He to that of Oxygen = $\left(const/sqrt4\right)\ast \left(sqrt32/const\right)$

= $sqrt\left(8/1\right)$

$=22:1$