Read the passage given below and answer the question.
A galvanic cell consists of a metallic zinc plate immersed in 0.1 M `Zn(NO_(3))_(2)` solution and metallic plate of lean in 0.02 M Pb`(NO_(3))_(2)` solution.
Q. What product is obtained at cathode ?

Options

A. Zn
B. `Pb`
C. `Zn^(2+)`
D. `Pb^(2+)`

Explanation

To determine the product obtained at the cathode in the given galvanic cell setup, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components of the Galvanic Cell**:
- The galvanic cell consists of a zinc plate in a 0.1 M `Zn(NO₃)₂` solution and a lead plate in a 0.02 M `Pb(NO₃)₂` solution.

2. **Understand the Role of the Anode and Cathode**:
- In a galvanic cell, the anode is where oxidation occurs (loss of electrons), and the cathode is where reduction occurs (gain of electrons).
- The cathode is negatively charged, and the anode is positively charged.

3. **Determine the Half-Reactions**:
- For zinc:
\[ \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \quad (\text{Reduction at cathode}) \]
- For lead:
\[ \text{Pb}^{2+} + 2e^- \rightarrow \text{Pb} \quad (\text{Reduction at cathode}) \]

4. **Consult Standard Reduction Potentials**:
- The standard reduction potential for zinc (Zn) is approximately -0.76 V.
- The standard reduction potential for lead (Pb) is approximately -0.13 V.

5. **Compare the Reduction Potentials**:
- A higher (less negative) reduction potential indicates a greater tendency to be reduced.
- Since -0.13 V (for Pb) is greater than -0.76 V (for Zn), lead has a higher tendency to be reduced compared to zinc.

6. **Identify the Product at the Cathode**:
- Since lead ions (`Pb^{2+}`) will be reduced at the cathode, the product formed will be solid lead (Pb).
- The reaction at the cathode can be summarized as:
\[ \text{Pb}^{2+} + 2e^- \rightarrow \text{Pb (s)} \]

### Conclusion:
The product obtained at the cathode is solid lead (Pb).

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