Read the given statements and decide which is/are correct on the basis of kinetic theory of gases (I) Energy of one molecule at absolute temperature is zero (II) rms speeds of different gases are same at same temperature (III)For one gram of all ideal gas kinetic energy is same at same temperature (IV)For one mole of all ideal gases mean kinetic energy is same at same temperature

The correct option is IV is correct.

Let us evaluate each statement step-by-step on the basis of the kinetic theory of gases:

Statement (I): Energy of one molecule at absolute temperature is zero.
According to the kinetic theory of gases, the average kinetic energy of a single molecule of an ideal gas at an absolute temperature $T$ is given by the formula:
$E=\frac{3}{2}{k}_{B}T$
where $k_B$ is the Boltzmann constant. This energy is zero only at absolute zero temperature ($T=0\text{K}$). At any other non-zero absolute temperature $T$, the energy is not zero. Therefore, statement (I) is incorrect.

Statement (II): rms speeds of different gases are same at same temperature.
The root-mean-square (rms) speed of gas molecules is represented by:
$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$
where $R$ is the universal gas constant and $M$ is the molar mass of the gas. Since different gases have different molar masses ($M$), their rms speeds will be different even if they are at the same temperature ($T$). Therefore, statement (II) is incorrect.

Statement (III): For one gram of all ideal gas kinetic energy is same at same temperature.
The kinetic energy of a mass $m$ of an ideal gas is given by:
$K=\frac{3}{2}nRT=\frac{3}{2}\left(\frac{m}{M}\right)RT$
For one gram of gas ($m=1\text{g}$), the kinetic energy becomes:
$K=\frac{3RT}{2M}$
Since the kinetic energy per gram depends on the molar mass $M$, it varies for different gases at the same temperature. Therefore, statement (III) is incorrect.

Statement (IV): For one mole of all ideal gases mean kinetic energy is same at same temperature.
The kinetic energy of one mole ($n=1$) of any ideal gas is given by:
$K=\frac{3}{2}RT$
This value depends solely on the universal gas constant $R$ and the absolute temperature $T$, and is completely independent of the identity or molar mass of the gas. Thus, for one mole of any ideal gas at the same temperature, the kinetic energy is identical. Therefore, statement (IV) is correct.