Degrees of freedom of hydrogen and ozone gases will be respectively

Options

A. 3 and 5
B. 5 and 6
C. 6 and 5
D. 5 and 3

Answer

To determine the degrees of freedom for hydrogen and ozone gases, we need to analyze their molecular structures and apply the formula for calculating degrees of freedom.

### Step-by-Step Solution:

1. **Identify the Type of Molecules**:
- Hydrogen (H₂) is a diatomic molecule.
- Ozone (O₃) is a triatomic molecule and is non-linear.

2. **Degrees of Freedom for Diatomic Molecules (Hydrogen)**:
- **Translational Degrees of Freedom**: A diatomic molecule can move in three dimensions (x, y, z), contributing 3 degrees of freedom.
- **Rotational Degrees of Freedom**: A diatomic molecule can rotate about two axes perpendicular to the bond axis. The rotation about the bond axis does not contribute to the degree of freedom because the moment of inertia about this axis is negligible. Therefore, it contributes 2 degrees of freedom.
- **Total Degrees of Freedom for Hydrogen**:
\[ \text{Total} = \text{Translational} + \text{Rotational} = 3 + 2 = 5 \]

3. **Degrees of Freedom for Triatomic Non-linear Molecules (Ozone)**:
- **Translational Degrees of Freedom**: Similar to hydrogen, ozone can also move in three dimensions (x, y, z), contributing 3 degrees of freedom.
- **Rotational Degrees of Freedom**: A non-linear triatomic molecule can rotate about three axes. Therefore, it contributes 3 degrees of freedom.
- **Total Degrees of Freedom for Ozone**:
\[ \text{Total} = \text{Translational} + \text{Rotational} = 3 + 3 = 6 \]

4. **Final Result**:
- The degrees of freedom for hydrogen and ozone gases are respectively 5 and 6.

### Conclusion:
The degrees of freedom of hydrogen and ozone gases are respectively **5 and 6**.

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