Number of molecules in a volume of

Question:

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

  1. $5.8 \times 10^{18}$

  2. $5.8 \times 10^{16}$

  3. $4.0 \times 10^{18}$

  4. $4.0 \times 10^{16}$


Correct Option: , 3

Solution:

$\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}}, \frac{3}{2} \mathrm{kT}=4 \times 10^{-14}$

$N=\frac{P V}{R T} \times N a$

$=\frac{2 \times 13.6 \times 980 \times 4}{\frac{8}{3} \times 10^{-14}}=3.99 \times 10^{18}$

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