Which of the following reactions occurs at the cathode?

Options

A. `2OH^(-) rarr H_(2)O + O + 2e^(-)`
B. `Zn rarr Zn^(2+) + 2e^(-)`
C. `Sn^(2+) rarr Sn^(4+) + 2e^(-)`
D. `Cu^(2+) + 2e^(-) rarr Cu`

Answer

To determine which of the given reactions occurs at the cathode, we need to understand the concepts of oxidation and reduction in electrochemistry.

### Step-by-Step Solution:

1. **Understanding Anode and Cathode**:
- The anode is where oxidation occurs (loss of electrons).
- The cathode is where reduction occurs (gain of electrons).

2. **Analyzing Each Option**:
- **Option 1**: \( 2 \text{OH}^- \rightarrow \text{H}_2\text{O} + \text{O}_2 + 2e^- \)
- In this reaction, hydroxide ions are losing electrons (oxidation). Therefore, this reaction occurs at the anode. **(Incorrect)**

- **Option 2**: \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \)
- Here, zinc is losing electrons (oxidation). Thus, this reaction also occurs at the anode. **(Incorrect)**

- **Option 3**: \( \text{Sn}^{2+} + 2e^- \rightarrow \text{Sn}^{4+} \)
- In this case, tin is gaining electrons (reduction). This reaction occurs at the cathode. **(Incorrect)**

- **Option 4**: \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \)
- Here, copper ions are gaining electrons (reduction). This reaction occurs at the cathode. **(Correct)**

3. **Conclusion**:
- The reaction that occurs at the cathode is **Option 4**: \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \).

### Final Answer:
The reaction that occurs at the cathode is **Option 4: \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \)**.