The reaction which is taking place in nickel cadmium battery can be represented by which of the following equations?

Options

A. `Cd+NiO_2 + 2H_2O to Cd(OH)_2 + Ni(OH)_2`
B. `Cd+ NiO_2 + 2OH^(-) to Ni + Cd(OH)_2`
C. `Ni+ Cd(OH)_2 to Cd to Ni(OH)_2`
D. `Ni(OH)_2 + Cd(OH)_2 to Ni + Cd + 2H_2O`

Explanation

To determine the reaction taking place in a nickel-cadmium battery, we need to analyze the components involved in the battery's electrochemical processes. The nickel-cadmium (NiCd) battery consists of cadmium as the anode and nickel oxide as the cathode, with potassium hydroxide serving as the electrolyte.

### Step-by-Step Solution:

1. **Identify the Anode and Cathode:**
- **Anode:** Cadmium (Cd)
- **Cathode:** Nickel oxide (NiO2)

2. **Determine the Electrolyte:**
- The electrolyte used in a nickel-cadmium battery is potassium hydroxide (KOH), which provides hydroxide ions (OH⁻).

3. **Write the Half-Reaction at the Anode:**
- At the anode, oxidation occurs. Cadmium loses electrons:
\[ \text{Cd (s)} + 2 \text{OH}^- \rightarrow \text{Cd(OH)}_2 (s) + 2 \text{e}^- \]
- Here, solid cadmium reacts with hydroxide ions to form cadmium hydroxide and releases 2 electrons.

4. **Write the Half-Reaction at the Cathode:**
- At the cathode, reduction occurs. Nickel oxide gains electrons:
\[ \text{NiO}_2 (s) + 2 \text{H}_2\text{O} + 2 \text{e}^- \rightarrow \text{Ni(OH)}_2 (s) + 2 \text{OH}^- \]
- Nickel oxide reacts with water and gains 2 electrons to form nickel hydroxide and hydroxide ions.

5. **Combine the Half-Reactions for Overall Reaction:**
- The overall reaction can be obtained by combining the two half-reactions:
\[ \text{Cd (s)} + \text{NiO}_2 (s) + 2 \text{H}_2\text{O} \rightarrow \text{Cd(OH)}_2 (s) + \text{Ni(OH)}_2 (s) \]

6. **Final Equation:**
- Therefore, the reaction that takes place in a nickel-cadmium battery can be represented by the equation:
\[ \text{Cd (s)} + \text{NiO}_2 (s) + 2 \text{H}_2\text{O} \rightarrow \text{Cd(OH)}_2 (s) + \text{Ni(OH)}_2 (s) \]

### Conclusion:
The correct representation of the reaction occurring in a nickel-cadmium battery is:
\[ \text{Cd} + \text{NiO}_2 + 2 \text{H}_2\text{O} \rightarrow \text{Cd(OH)}_2 + \text{Ni(OH)}_2 \]