Question

If N is the number of collisions per unit area per second which the molecules may make with the wall of the vessel. Find $x$ such that $x=\frac{N}{{10}^{26}}$.

Answer 1

The RMS velocity of particles will be

$v_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\left(8.314\right)300}{28X{10}^{-3}}}=517m/s$

Thus, momentum change per unit area per second will be

$\frac{\Delta p}{A\Delta t}=P$

Assuming collision to be elastic, the molecules will return with the same speed. Hence,

$\frac{N2m{v}_{rms}}{A\Delta t}=P$

$\frac{N}{A\Delta t}=\frac{P}{2m{v}_{rms}}$

$\frac{N}{A\Delta t}=\frac{2X{10}^5\left(6.022X{10}^{23}\right)}{2\left(28X{10}^{-3}\right)\left(517\right)}=4.2X{10}^{27}$

Answer is $4.2X{10}^{27}$