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Number of molecules in a volume of 4\; cm^{3} of a perfect monoatomic gas at some temperature T and at 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=980cm/s^{2}, density of mercury =13.6\; g/cm^{3})
Option: 1 4.0\times 10^{18}  
Option: 2 4.0\times 10^{16}
Option: 3 5.8\times 10^{16}
Option: 4 5.8\times 10^{18}

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\begin{array}{l} \mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}}, \frac{3}{2} \mathrm{kT}=4 \times 10^{-14} \\ \\ \mathrm{~N}=\frac{\mathrm{PV}}{\mathrm{RT}} \times \mathrm{Na} \\\\ =\frac{2 \times 13.6 \times 980 \times 4}{\frac{8}{3} \times 10^{-14}}=3.99 \times 10^{18} \approx 4 \times 10^{18} \end{array}

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Deependra Verma

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