b
As we know that,

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

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.

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

\(=0.01 \times 10^{-10}\)

\(=10^{-12} sec\)