Basic radical(s) which can not be identified by borax bead test:

Options

A. `Mg^(2+)`
B. `Pb^(2+)`
C. `Fe^(3+)`
D. `Ag^(+)`

Explanation

To determine the basic radicals that cannot be identified by the borax bead test, we need to analyze the electronic configurations of the given cations and check for the presence of unpaired electrons. The borax bead test is effective for identifying cations that have unpaired electrons in their outermost shell.

### Step-by-Step Solution:

1. **Understand the Borax Bead Test**:
- The borax bead test involves heating borax (Na2B4O7), which decomposes into boric anhydride (B2O3) and sodium metaborate (NaBO2).
- Cations with unpaired electrons can react with boric anhydride to form colored metaborates, which can be observed.

2. **Identify the Cations Given**:
- The cations in question are:
- Mg²⁺ (Magnesium)
- Pb²⁺ (Lead)
- Fe³⁺ (Iron)
- Ag⁺ (Silver)

3. **Analyze Each Cation**:
- **Mg²⁺**:
- Electronic configuration: 1s² 2s² 2p⁶ (outermost shell is completely filled).
- Conclusion: No unpaired electrons → Cannot be identified by the borax bead test.

- **Pb²⁺**:
- Electronic configuration: [Xe] 6s² 4f¹⁴ 5d¹⁰ (outermost shell is completely filled).
- Conclusion: No unpaired electrons → Cannot be identified by the borax bead test.

- **Fe³⁺**:
- Electronic configuration: [Ar] 3d⁵ (5 unpaired electrons in the d-orbital).
- Conclusion: Has unpaired electrons → Can be identified by the borax bead test.

- **Ag⁺**:
- Electronic configuration: [Kr] 4d¹⁰ (outermost shell is completely filled).
- Conclusion: No unpaired electrons → Cannot be identified by the borax bead test.

4. **Final Conclusion**:
- The basic radicals that cannot be identified by the borax bead test are:
- Mg²⁺, Pb²⁺, and Ag⁺.

### Answer:
The basic radicals which cannot be identified by the borax bead test are Mg²⁺, Pb²⁺, and Ag⁺.