The value of `gamma` of linear, arragement of triatomic gas molecules is

Options

A. `9/7`
B. `7/5`
C. `5/3`
D. `8/6`

Explanation

To find the value of gamma (γ) for a linear arrangement of triatomic gas molecules, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Degrees of Freedom**:
For a triatomic gas with a linear arrangement, the number of degrees of freedom (f) is given as 7. This is because a linear triatomic molecule can move in three translational directions and has rotational motion about two axes (it cannot rotate about the axis along its length).

2. **Use the Formula for Gamma**:
The relationship between gamma (γ) and the degrees of freedom (f) is given by the formula:
\[ \gamma = 1 + \frac{2}{f} \]

3. **Substitute the Value of f**:
Now, we substitute the value of f (which is 7) into the formula:
\[ \gamma = 1 + \frac{2}{7} \]

4. **Calculate the Value**:
To calculate this, we first find \(\frac{2}{7}\):
\[ \frac{2}{7} \approx 0.2857 \]
Adding this to 1 gives:
\[ \gamma = 1 + 0.2857 = 1.2857 \]
To express this as a fraction, we can convert it:
\[ \gamma = \frac{9}{7} \]

5. **Conclusion**:
Therefore, the value of gamma (γ) for a linear arrangement of triatomic gas molecules is:
\[ \gamma = \frac{9}{7} \]

### Final Answer:
The correct option is **A) \(\frac{9}{7}\)**.

---