Number of molecules in a volume of $4 \mathrm{~cm}^{3}$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2 \mathrm{~cm}$ of mercury is close to? (Given, mean kinetic energy of a molecule (at $T$ ) is $4 \times 10^{-14} \mathrm{erg}, g=980 \mathrm{~cm} /$ $\mathrm{s}^{2}$, density of mercury $=13.6 \mathrm{~g} / \mathrm{cm}^{3}$ )
Correct Option: , 3
(3) Given : K.E. $_{\text {mean }}=\frac{3}{2} k T=4 \times 10^{-14}$
$P=2 \mathrm{~cm}$ of $\mathrm{Hg}, V=4 \mathrm{~cm}^{3}$
$N=\frac{P V}{K T}=\frac{P \rho g V}{K T} \frac{2 \times 13.6 \times 980 \times 4}{\frac{8}{3} \times 10^{-14}} \simeq 4 \times 10^{18}$
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