Assertion `(A):` 1 Faraday of electricity deposits `1 g` equivalent of `Ag , Cu` or `Al`.
Reason `(R)`: 1 mole of electrons are required to reduce `1 mol e of Ag^(o+)` or `(1)/(2) mol e of Cu^(2+)` or `(1)/(3) `mole of `Al^(3+)` ions.

Options

A. If both `(A)` and `(R)` are correct, and `(R)` is the correct explanation of `(A)`.
B. If both `(A)` and `(R)` are correct, but `(R)` is not the correct explanation of `(A)`.
C. If `(A)` is correct, but `(R)` is incorrect.
D. If `(A)` is incorrect, `(R)` is correct.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "1 Faraday of electricity deposits 1 gram equivalent of Ag, Cu, or Al."
- To understand this, we need to recall that 1 Faraday (F) is equivalent to the charge of 1 mole of electrons (approximately 96485 coulombs).
- The gram equivalent of a substance is defined as the mass of the substance that will combine with or displace 1 mole of hydrogen atoms (or 1 mole of electrons in redox reactions).

2. **Analyzing the Reduction Reactions**:
- For Silver (Ag):
\[ \text{Ag}^+ + e^- \rightarrow \text{Ag} \]
- 1 mole of Ag^+ requires 1 mole of electrons to reduce to 1 mole of Ag. Thus, 1 Faraday deposits 1 gram equivalent of Ag.

- For Copper (Cu):
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]
- 1 mole of Cu^2+ requires 2 moles of electrons to reduce to 1 mole of Cu. Therefore, 1 Faraday will deposit 0.5 gram equivalent of Cu (since 1 Faraday can provide only 1 mole of electrons).

- For Aluminum (Al):
\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \]
- 1 mole of Al^3+ requires 3 moles of electrons to reduce to 1 mole of Al. Thus, 1 Faraday will deposit approximately 0.33 gram equivalent of Al.

3. **Conclusion on Assertion**:
- The assertion is not entirely correct because 1 Faraday does not deposit 1 gram equivalent of Cu or Al; it only deposits 1 gram equivalent of Ag. Therefore, the assertion is **incorrect**.

4. **Understanding the Reason (R)**:
- The reason states that "1 mole of electrons are required to reduce 1 mol of Ag^+, (1/2) mol of Cu^2+, or (1/3) mole of Al^3+ ions."
- This statement is accurate:
- 1 mole of Ag^+ requires 1 mole of electrons.
- 1 mole of Cu^2+ requires 2 moles of electrons, so 1 mole of electrons reduces 0.5 mole of Cu^2+.
- 1 mole of Al^3+ requires 3 moles of electrons, so 1 mole of electrons reduces 1/3 mole of Al^3+.

5. **Conclusion on Reason**:
- The reason is **correct**.

6. **Final Evaluation**:
- The assertion is incorrect, while the reason is correct. Therefore, the correct answer is that the assertion is false, and the reason is true, but the reason does not explain the assertion.

### Final Answer:
Assertion (A) is incorrect, and Reason (R) is correct.