12 . kinetic theory of gases — Physics STD 11 Science — Question

$\tau=\frac{\lambda}{V_{ rms }}=\frac{1}{\sqrt{2} \pi nd ^{2}} \frac{\sqrt{ m _{0}}}{\sqrt{3 RT }}$

Now,

$n =\frac{ N }{ V }=\frac{\mu N _{ a }}{ V }$

And,

$PV =\mu RT$

$\frac{\mu}{ V }=\frac{ P }{ RT }$

So,

$n =\frac{ P }{ RT } \times N _{ a }$

Therefore,

$\tau=\frac{\sqrt{ m _{0} RT }}{\sqrt{2} \pi PN _{ a } d ^{2} \sqrt{3 RT }}$

Substitute the values.

$\tau=\frac{\sqrt{(32)\left(3 \times 8.3 \times 10^{-1}\right)}}{\sqrt{2}(3.14)\left(10^{5}\right)\left(6.02 \times 10^{23}\right)\left(40 \times 10^{-10}\right)^{2}}$

$=0.01 \times 10^{-10}$

$=10^{-12} sec$