If hydrogen gas is heated to a very high temperature, then the fraction of energy possessed by gas molecules correspond to rotational motion :-

Options

A. `3/5`
B. `2/7`
C. `3/7`
D. `2/5`

Answer

To solve the problem regarding the fraction of energy possessed by hydrogen gas molecules corresponding to rotational motion when heated to a very high temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Degrees of Freedom**:
For a diatomic gas like hydrogen (H₂), the degrees of freedom can be categorized into translational, rotational, and vibrational motions.
- Translational degrees of freedom = 3 (movement in x, y, z directions)
- Rotational degrees of freedom = 2 (rotation about two axes perpendicular to the molecular axis)
- Vibrational degrees of freedom = 2 (one for stretching and one for bending)

2. **Calculate Total Degrees of Freedom**:
The total degrees of freedom (f) for hydrogen gas can be calculated as:
\[ f = \text{Translational} + \text{Rotational} + \text{Vibrational} = 3 + 2 + 2 = 7 \]

3. **Determine the Fraction of Energy Corresponding to Rotational Motion**:
The fraction of energy corresponding to rotational motion can be expressed as:
\[ \text{Fraction of energy for rotational motion} = \frac{\text{Rotational degrees of freedom}}{\text{Total degrees of freedom}} = \frac{2}{7} \]

4. **Conclusion**:
Therefore, the fraction of energy possessed by gas molecules corresponding to rotational motion when hydrogen gas is heated to a very high temperature is:
\[ \frac{2}{7} \]

### Final Answer:
The fraction of energy possessed by gas molecules corresponding to rotational motion is \(\frac{2}{7}\).

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