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(D) According to the kinetic theory of gases:$(I)$ The energy of a molecule at absolute zero $(T = 0 \ K)$ is not zero due to zero-point energy (quant

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None of these

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(D) According to the kinetic theory of gases:$(I)$ The energy of a molecule at absolute zero $(T = 0 \ K)$ is not zero due to zero-point energy (quantum effects) or simply because the kinetic energy is $\frac{3}{2} k_B T$,which is zero at $T=0$,but the statement is generally considered incorrect in the context of classical kinetic theory as it ignores internal degrees of freedom.$(II)$ The $r.m.s.$ speed is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$. Since $M$ (molar mass) varies for different gases,$v_{rms}$ is not the same for different gases at the same temperature.$(III)$ Kinetic energy for $1 \ g$ of gas is $K = \frac{n f R T}{2} = \frac{m}{M} \frac{f R T}{2}$. Since $M$ and $f$ (degrees of freedom) differ for different gases,the kinetic energy is not the same.$(IV)$ The mean kinetic energy of one mole of an ideal gas is $U = \frac{f}{2} RT$. Since $f$ depends on the atomicity of the gas (e.g.,$f=3$ for monoatomic,$f=5$ for diatomic),the mean kinetic energy is not the same for all gases at the same temperature.Therefore,none of the statements are correct.

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