The ratio of number of collisions per second at the walls of containers by He and O₂​ gas molecules kept at same volume and temperature, is (assume normal incidence on walls)
​(1) 2 : 1
(2) 1 : 2
(3) $2\sqrt{2}$ : 1
(4) 1 : $2\sqrt{2}$

Dear Student,

Here we are required to find the ratio of the collision frequency(Z) between He and O₂molecules. Let us first begin with the definition of Collision Frequency.

It is defined as the number of collisions which take place in 1 second among the molecules present in 1 cc of the gas.

Also, Collision number (N_c)is the number of collisions which a single molecule undergoes with other molecules in 1 second.

Now, 

N_c= 2πvσ²n

Where v = average speed 

σ = molecular diameter

n = number of molecules

collisions among molecules will be = N_c * n

As each collision requires 2 molecules,collision frequency, Z = (N_c* n )/2 = (1/2) * πvσ²n²

Now Average speed (v) = sqrt(8RT/(πM)) where M is the molecular mass.

Hence,

Z = 2σ²n²sqrt(πRT/M) 

This is the required formula for this question.

We know that M for O₂molecule is 32u and for Helium molecule is 4u.

Hence Z₁/Z₂= ratio of He to that of Oxygen = (const/sqrt4) * (sqrt32/const)

= sqrt(8/1)….. ( here the constant is defined as 2σ²n²sqrt(πRT) )

= 2  $\sqrt{2}$ :1 which is the required answer.

Regards