Assertion `(A):` When an aqueous solution of `KNO_(3)` is electrolyzed, potassium is liberated at the cathode.
Reason `(R): K^(+)` ions are discharged at cathode and `NO_(3)^(-)` at anode.

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 will analyze the assertion and reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that when an aqueous solution of KNO₃ is electrolyzed, potassium (K) is liberated at the cathode.
- In electrolysis, cations are attracted to the cathode where reduction occurs.

2. **Identifying the Ions in Solution**:
- In an aqueous solution of KNO₃, the ions present are K⁺ (potassium ions) and NO₃⁻ (nitrate ions).
- During electrolysis, K⁺ ions would typically migrate towards the cathode.

3. **Analyzing the Reduction Potential**:
- However, we need to consider the reduction potentials of the ions involved.
- The reduction potential for K⁺ to K is quite low (more negative) compared to that of H⁺ to H₂ (which is 0 V).
- This means that H⁺ ions (from water) are more readily reduced than K⁺ ions.

4. **Conclusion on the Assertion**:
- Since H⁺ ions will be reduced at the cathode to produce hydrogen gas instead of K⁺ ions being reduced to potassium metal, the assertion is **incorrect**.

5. **Understanding the Reason (R)**:
- The reason states that K⁺ ions are discharged at the cathode and NO₃⁻ ions at the anode.
- While it is true that K⁺ ions are cations and will migrate to the cathode, they do not get discharged as potassium metal due to the higher reduction potential of H⁺.
- NO₃⁻ ions, being anions, will migrate to the anode where oxidation occurs.

6. **Conclusion on the Reason**:
- The statement about the movement of ions is correct; however, the specific discharge of K⁺ at the cathode is incorrect. Therefore, the reason is **partially correct** but does not support the assertion.

### Final Evaluation:
- The assertion is **incorrect**.
- The reason is **correct in terms of ion movement but incorrect regarding the discharge of K⁺**.

### Answer:
- The correct option is that the assertion is wrong and the reason is correct.