Assertion :- Bromide ion is serving as a reducing agent in the reaction
`2MnO_(4)^(-)(aq.)+Br^(-)(aq.)+H_(2)Orarr2MnO_(2)(aq.)+BrO_(3)^(-)(aq.)+2OH^(-)(aq.)`
Reason :- Oxidation number of Br increases from `-1` to `+5`

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False.

Answer

To analyze the assertion and reason provided in the question, we will break down the redox reaction step by step.

### Step-by-Step Solution:

1. **Identify the Reaction**: The given reaction is:
\[ 2MnO_4^-(aq) + Br^-(aq) + H_2O \rightarrow 2MnO_2(aq) + BrO_3^-(aq) + 2OH^-(aq) \]

2. **Determine Oxidation States**:
- For the bromide ion \( Br^- \), the oxidation state is \(-1\).
- In the bromate ion \( BrO_3^- \), let the oxidation state of bromine be \( x \). The oxidation states of oxygen is \(-2\). The equation for the oxidation state can be set up as:
\[ x + 3(-2) = -1 \implies x - 6 = -1 \implies x = +5 \]
- Thus, the oxidation state of bromine in \( BrO_3^- \) is \( +5 \).

3. **Analyze the Change in Oxidation State**:
- The oxidation state of bromine changes from \(-1\) (in \( Br^- \)) to \( +5 \) (in \( BrO_3^- \)).
- This indicates that bromine is being oxidized, as its oxidation state is increasing.

4. **Identify the Role of Bromide Ion**:
- A reducing agent is a substance that donates electrons and gets oxidized in a chemical reaction. Since bromine goes from \(-1\) to \( +5\), it is losing electrons and thus acting as a reducing agent.

5. **Examine the Manganese Species**:
- In the reaction, manganese in \( MnO_4^- \) has an oxidation state of \( +7 \) and in \( MnO_2 \), it has an oxidation state of \( +4 \).
- This indicates that manganese is being reduced (gaining electrons) as its oxidation state decreases from \( +7 \) to \( +4 \).

6. **Conclusion**:
- Since bromide ion \( Br^- \) is being oxidized (its oxidation state increases from \(-1\) to \( +5\)), it is indeed serving as a reducing agent.
- Therefore, both the assertion and the reason are correct, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and reason are correct, and the reason is the correct explanation of the assertion.