Assertion`(A):` Whne acidified `ZnSO_(4)` solution is electrolyzed between `Zn` electrodes, it is `Zn` that is deposited at the cathode and `H_(2)(g)` is not evolved.
Reason `(R):` The electrode potential of `Zn` is more negative than hydrogen as the overpotential for hydrogen evolution in `Zn` is quite large.

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.

Answer

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

### Step-by-step Solution:

1. **Understanding the Electrolysis Process**:
- When an acidified solution of ZnSO4 is electrolyzed, we have Zn²⁺ ions and H⁺ ions present in the solution. The electrolysis occurs between two zinc electrodes.

2. **Identifying the Electrodes**:
- The cathode is the electrode where reduction occurs, and the anode is where oxidation occurs. In this case, both electrodes are zinc.

3. **Reduction Reactions at the Cathode**:
- At the cathode, two possible reduction reactions can occur:
- Reduction of Zn²⁺ ions:
\[ \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn (s)} \]
- Reduction of H⁺ ions:
\[ 2\text{H}^+ + 2e^- \rightarrow \text{H}_2(g) \]

4. **Comparing Standard Reduction Potentials**:
- The standard reduction potential for Zn²⁺/Zn is -0.76 V.
- The standard reduction potential for H⁺/H₂ is 0.00 V.
- Since the standard reduction potential for H⁺ is higher (less negative) than that for Zn²⁺, hydrogen ions are more likely to be reduced to hydrogen gas.

5. **Considering Overpotential**:
- The overpotential for hydrogen evolution on zinc is significant. This means that even though H⁺ ions have a higher reduction potential, the actual discharge of H⁺ may be hindered due to the overpotential, making Zn deposition more favorable under certain conditions.

6. **Conclusion**:
- The assertion states that Zn is deposited at the cathode and H₂ is not evolved, which is incorrect because, under standard conditions, H₂ gas would be evolved.
- The reason states that the electrode potential of Zn is more negative than that of hydrogen and that the overpotential for hydrogen evolution is quite large, which is true.

### Final Answer:
- The assertion (A) is **false** and the reason (R) is **true**. Therefore, the correct conclusion is that the assertion is incorrect while the reason is correct.