1. For a gas at temperature $T$, the root mean square speed is

$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

where $M$ is the molar mass of the gas.

2. Since all three gases are at the same temperature, and $3RT$ is the same for all, we have

$v_{\text{rms}} \propto \frac{1}{\sqrt{M}}$

So, smaller molar mass means greater rms speed.

3. Molar masses:

• Hydrogen $H_2$: $M_H = 2$
• Oxygen $O_2$: $M_O = 32$
• Carbon dioxide $CO_2$: $M_C = 44$

4. Compare speeds using inverse square root dependence:

$v_H \propto \frac{1}{\sqrt{2}}, \quad v_O \propto \frac{1}{\sqrt{32}}, \quad v_C \propto \frac{1}{\sqrt{44}}$

Since

$2 < 32 < 44$

therefore

$\frac{1}{\sqrt{2}} > \frac{1}{\sqrt{32}} > \frac{1}{\sqrt{44}}$

Hence,

$V_H > V_O > V_C$

5. Option check:

• A: $V_H > V_O > V_C$ ✅
• B: $V_C > V_O > V_H$ ❌
• C: $V_H = V_O > V_C$ ❌
• D: $V_H = V_O = V_C$ ❌

Therefore, the correct option is A.