Question

A gas at absolute temperature $300K$ has pressure $=4\times {10}^{-10}N/m^2$
Boltzman constant $=k=1.38\times {10}^{-23}J/K$. The number of molecules per ${cm}^3$ is of the order of

• A. $100$
• B. ${10}^5$
• C. ${10}^8$
• D. ${10}^{11}$

Answer 1

The correct option is B ${10}^5$

$\text{Given}:$ T = 300 K, P = $4\times {10}^{-10}N/m^2$, k = $1.38\times {10}^{-23}J/K$

$\text{Solution}:$

From $PV=nRT=nN\left(\frac{R}{N}\right)T=nNkT$

Also,

$\frac{nN}{V}=\frac{P}{kT}=numberofmolecules/m^3$

$\therefore Numberofmolecules/m^3=\frac{P}{kT}\times {10}^{-6}=\frac{4\times {10}^{-10}\times {10}^{-6}}{1.38\times {10}^{-23}\times 300}\cong {10}^5$

$\text{Hence B is the correct option}$