Which of the following reaction does not take place at cathode ?

Options

A. `Ag^(+)rarr Ag-e^(-)`
B. `Fe^(2+)rarr Fe^(3+)+e^(-)`
C. `Cu^(2+)+2e^(-) rarr Cu`
D. `Al^(3+) rarr Al-3e^(-)`

Explanation

To determine which reaction does not take place at the cathode, we need to understand the processes occurring at the cathode and anode in an electrochemical cell.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Oxidation**: Loss of electrons.
- **Reduction**: Gain of electrons.
- At the **anode**, oxidation occurs.
- At the **cathode**, reduction occurs.

2. **Identify the Reactions**:
We need to analyze the reactions provided in the options to determine which one involves oxidation (loss of electrons).

3. **Examine Each Reaction**:
- **Reaction 1**: \( \text{Ag}^+ + e^- \rightarrow \text{Ag} \)
- Here, \( \text{Ag}^+ \) gains an electron to form \( \text{Ag} \). This is a reduction reaction.
- **Reaction 2**: \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^- \)
- In this case, \( \text{Fe}^{2+} \) loses an electron to become \( \text{Fe}^{3+} \). This is an oxidation reaction.
- **Reaction 3**: \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \)
- Here, \( \text{Cu}^{2+} \) gains electrons to form \( \text{Cu} \). This is a reduction reaction.
- **Reaction 4**: \( \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \)
- In this reaction, \( \text{Al}^{3+} \) gains electrons to form \( \text{Al} \). This is a reduction reaction.

4. **Identify the Reaction that Does Not Occur at Cathode**:
- From our analysis, **Reaction 2** involves oxidation (loss of electrons) and therefore does not occur at the cathode.

5. **Conclusion**:
The reaction that does not take place at the cathode is **Reaction 2**: \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^- \).

### Final Answer:
**Option B: \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^- \)** does not take place at the cathode.