Q 11-12-098JEE MainJEE Main 2021 (27 Jul, Shift 1)Medium
The number of molecules in one litre of an ideal gas at $300$ K and $2$ atmospheric pressure with mean kinetic energy $2\times10^{-9}$ J per molecule is:
Answer: (C) $1.5\times10^{11}$
Kinetic theory: $PV = \dfrac23 N\bar{E}$, where $\bar E$ is the mean kinetic energy per molecule.
$$N = \frac{3PV}{2\bar E} = \frac{3\times(2\times10^5)\times10^{-3}}{2\times2\times10^{-9}} = \frac{600}{4\times10^{-9}} = 1.5\times10^{11}$$
(taking $1$ atm $\approx 10^5$ Pa).
Solution by Sreeraj P, M.Sc Physics