Question

Number of molecules in a volume of $4 \,cm ^{3}$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2\, cm$ of mercury is close to ? (Given, mean kinetic energy of a molecule (at $T$ ) is $4 \times 10^{-14}$ erg, $g =980 cm / s ^{2},$ density of mercury $\left.=13.6\, g / cm ^{3}\right)$

• A. $5.8 \times 10^{18}$
• B. $5.8 \times 10^{16}$
• C. $4.0 \times 10^{18}$
• D. $4.0 \times 10^{16}$

Answer 1

Answer: (C)

$n =\frac{ PV }{ RT }, \frac{3}{2} kT =4 \times 10^{-14}$
$N =\frac{ PV }{ RT } \times Na$
$=\frac{2 \times 13.6 \times 980 \times 4}{\frac{8}{3} \times 10^{-14}}=3.99 \times 10^{18}$