Assertion : In the species, `S_(4)O_(6)^(2-)` each of the two extreme sulphurs exhibits oxidation state of +5 and the two middle sulphurs as zero.
Reason : The average of four oxidation numbers of sulphurs of the `S_(4)O_(6)^(2-)` is 2.5.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question regarding the assertion and reason for the species \( S_4O_6^{2-} \), we will follow a systematic approach.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that in \( S_4O_6^{2-} \), the two extreme sulfur atoms have an oxidation state of +5, while the two middle sulfur atoms have an oxidation state of 0.
- To verify this, we need to analyze the structure of \( S_4O_6^{2-} \).

2. **Drawing the Structure**:
- The structure of \( S_4O_6^{2-} \) can be represented as:
\[ O=S=O \]
\[ S \]
\[ S \]
\[ O=S=O \]
- In this structure, the two sulfur atoms at the ends are bonded to oxygen atoms with double bonds, while the two middle sulfur atoms are bonded to each other.

3. **Assigning Oxidation States**:
- For the extreme sulfur atoms (the ones at the ends), they are bonded to oxygen with double bonds. Each of these sulfur atoms can be assigned an oxidation state of +5.
- The two middle sulfur atoms are bonded to each other and do not have any electronegative atoms around them, leading to an oxidation state of 0 for both.

4. **Conclusion for the Assertion**:
- Based on the structure and the assigned oxidation states, the assertion is correct: the extreme sulfur atoms have an oxidation state of +5, and the middle sulfur atoms have an oxidation state of 0.

5. **Understanding the Reason**:
- The reason states that the average oxidation number of the four sulfur atoms in \( S_4O_6^{2-} \) is 2.5.
- To find the average oxidation state, we can use the formula:
\[ \text{Average oxidation state} = \frac{\text{Total oxidation state}}{\text{Number of atoms}} \]

6. **Calculating the Total Oxidation State**:
- Let \( x \) be the average oxidation state of the four sulfur atoms.
- The equation can be set up as follows:
\[ 4x + 6(-2) = -2 \]
(where -2 is the overall charge of the ion and -2 is the oxidation state of each oxygen atom).
- Simplifying the equation:
\[ 4x - 12 = -2 \]
\[ 4x = 10 \]
\[ x = 2.5 \]

7. **Conclusion for the Reason**:
- The average oxidation state of the four sulfur atoms is indeed 2.5, making the reason correct.

8. **Final Evaluation**:
- Both the assertion and reason are true, but the reason does not correctly explain the assertion because the average oxidation state does not directly validate the specific oxidation states assigned to the extreme and middle sulfur atoms.

### Final Answer:
- The correct option is (B): Both assertion and reason are true, but the reason is not the correct explanation of the assertion.