Question

Which of the following is correct?

(a) Total collision rate $\propto$ mean speed $\propto$ absolute temperature

(b) Total collision rate $\propto \frac{1}{\text { mean speed }} \propto$ $\frac{1}{\text { absolute temperature }}$

(c) Total collision rate $\propto$ mean speed $\propto$ (absolute temperature) $)^{1 / 2}$

(d) Total collision rate $\propto(\text { mean speed })^2 \propto$ (absolute temperature) $^3$

Answer 1

Correct Option : (c)

Explanation—

Collision rate $(z)=N_a N_b \sigma_{a b} \sqrt{\frac{8 k_B T}{\pi \mu_{a b}}}$ 

where, $\sqrt{\frac{8 k_B T}{\pi \mu_{a b}}}=$ mean speed

$N_a$ and $N_b$ are number of molecules of ' $a$ ' and ' $b$ '.