Question:
Number of molecules in a volume of $4 \mathrm{~cm}^{3}$ of a perfect monoatomic gas at some temperature $\mathrm{T}$ and at a pressure of $2 \mathrm{~cm}$ of mercury is close to ? (Given, mean kinetic energy of a molecule (at T) is $4 \times 10^{-14} \mathrm{erg}, \mathrm{g}=980 \mathrm{~cm} / \mathrm{s}^{2}$, density of mercury $=13.6 \mathrm{~g} / \mathrm{cm}^{3}$ )
Correct Option: , 3
Solution:
$\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}}, \frac{3}{2} \mathrm{kT}=4 \times 10^{-14}$
$N=\frac{P V}{R T} \times N a$
$=\frac{2 \times 13.6 \times 980 \times 4}{\frac{8}{3} \times 10^{-14}}=3.99 \times 10^{18}$