Question

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

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

Answer 1

The correct option is A $4.0\times {10}^{18}$

Given: $K.E{.}_{\text{mean}}=\frac{3}{2}kT=4\times {10}^{-14}$
$P=2\text{cm}$ of $Hg,$
$V=4{\text{cm}}^3$

No of molecules is

$N=\frac{PV}{KT}=\frac{\rho gHV}{KT}=\frac{2\times 13.6\times 980\times 4}{\frac{8}{3}\times {10}^{-14}}\simeq 4\times {10}^{18}$