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To solve the problem of determining the ratio of the mean kinetic energy of an oxygen molecule to a hydrogen molecule at the same temperature, we can refer to the concept of kinetic energy in ideal gases.

The mean kinetic energy \( E \) of a molecule in an ideal gas is given by the equation:

\[
E = \frac{3}{2} k_B T
\]

Where:
- \( k_B \) is the Boltzmann constant.
- \( T \) is the absolute temperature.

According to this equation, the mean kinetic energy depends only on the temperature \( T \). This means that at the same temperature, **all gases have the same mean kinetic energy**, regardless of their molecular mass.

Thus, the ratio of the mean kinetic energy of oxygen (\( O_2 \)) to hydrogen (\( H_2 \)) at the same temperature is:

\[
\text{Ratio} = \frac{E_{\text{O}_2}}{E_{\text{H}_2}} = 1:1
\]

Hence, the correct answer is **(A) 1:1**.

Would you like more details on this topic or have any questions?

Here are 5 related questions for further understanding:
1. How does the molecular mass of a gas affect its velocity at a given temperature?
2. What is the relationship between temperature and kinetic energy in an ideal gas?
3. How would the velocities of hydrogen and oxygen molecules compare at the same temperature?
4. How is the root mean square velocity of gas molecules related to their mass?
5. What assumptions are made about gas molecules in the kinetic theory of gases?

**Tip:** Remember, in kinetic theory, temperature is a measure of the average kinetic energy of gas molecules, not their individual speeds or masses.

If an oxygen molecule and a hydrogen molecule are at the same temperature, then what is the ratio of their mean kinetic energy?

Explore the ratio of mean kinetic energy between oxygen and hydrogen molecules at the same temperature, explained using the kinetic theory of gases. This problem discusses the core concepts of kinetic energy in ideal gases and provides a clear solution with formulas. Suitable for students in Grades 11-12.

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