Find number of basic radicals among the following cations, which can form soluble complex on adding excess of `NH_(4) ` solution.
`Cd^(2+)(aq.),Pb^(2+)(aq.),Ni^(2+)(aq.),Mn^(2+)(aq.),Zn^(2+)(aq.),Ag^(+)(aq.),Hg^(2+)(aq.),Fe^(3+)(aq.),Mg^(2+)(aq.)`

Explanation

To solve the question of how many basic radicals among the given cations can form soluble complexes upon the addition of excess NH4 solution, we will analyze each cation step by step.

### Step-by-Step Solution:

1. **Cadmium (Cd²⁺)**:
- When excess NH₄OH is added, it first forms Cd(OH)₂.
- On further addition of NH₄OH, it forms a soluble complex: [Cd(NH₃)₂]²⁺.
- **Conclusion**: Cd²⁺ forms a soluble complex.

2. **Lead (Pb²⁺)**:
- Pb²⁺ initially forms Pb(OH)₂ upon adding NH₄OH.
- However, it does not form any further soluble complex with excess NH₄OH.
- **Conclusion**: Pb²⁺ does not form a soluble complex.

3. **Nickel (Ni²⁺)**:
- Ni²⁺ forms Ni(OH)₂ when NH₄OH is added.
- With further addition of NH₄OH, it forms a soluble complex: [Ni(NH₃)₆]²⁺.
- **Conclusion**: Ni²⁺ forms a soluble complex.

4. **Manganese (Mn²⁺)**:
- Mn²⁺ forms Mn(OH)₂ upon the addition of NH₄OH.
- It does not form any further soluble complex.
- **Conclusion**: Mn²⁺ does not form a soluble complex.

5. **Zinc (Zn²⁺)**:
- Zn²⁺ forms Zn(OH)₂ when NH₄OH is added.
- On further addition, it forms a soluble complex: [Zn(NH₃)₄]²⁺.
- **Conclusion**: Zn²⁺ forms a soluble complex.

6. **Silver (Ag⁺)**:
- Ag⁺ forms a complex with ammonia: [Ag(NH₃)₂]⁺ upon the addition of excess NH₄OH.
- **Conclusion**: Ag⁺ forms a soluble complex.

7. **Mercury (Hg²⁺)**:
- Hg²⁺ forms Hg(NH₂)Cl upon adding NH₄OH.
- It does not form any further soluble complex.
- **Conclusion**: Hg²⁺ does not form a soluble complex.

8. **Iron (Fe³⁺)**:
- Fe³⁺ forms Fe(OH)₃ when NH₄OH is added.
- It does not form any further soluble complex.
- **Conclusion**: Fe³⁺ does not form a soluble complex.

9. **Magnesium (Mg²⁺)**:
- Mg²⁺ forms Mg(OH)₂ upon addition of NH₄OH.
- It does not form any further soluble complex.
- **Conclusion**: Mg²⁺ does not form a soluble complex.

### Summary of Findings:
- The cations that form soluble complexes upon the addition of excess NH₄OH are:
- Cd²⁺
- Ni²⁺
- Zn²⁺
- Ag⁺

### Total Count:
- Total number of basic radicals that form soluble complexes = **4**.

### Final Answer:
The number of basic radicals that can form soluble complexes on adding excess NH₄ solution is **4**.

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