Among the following series of transition metal ions, how many metals ions have `d^(2)` electronic configuration
`Fe^(4+), V^(3+), Sn^(2+), Au^(3+)Ti^(2+), As^(3+), Cr^(3+), Mn^(5+)Co^(3+), Zr^(2+), Cd^(2+), Mo^(4+), La^(2+), Ta^(4+), Co^(6+), Ni^(4+)`

Answer

To determine how many transition metal ions have a `d^2` electronic configuration from the given list, we will analyze each ion's electronic configuration step by step.

1. **Fe^(4+)**:
- Atomic number of Fe = 26
- Electronic configuration: [Ar] 3d^6 4s^2
- For Fe^(4+), remove 4 electrons:
- 3d^6 → 3d^4
- **Result**: Not d^2.

2. **V^(3+)**:
- Atomic number of V = 23
- Electronic configuration: [Ar] 3d^3 4s^2
- For V^(3+), remove 3 electrons:
- 3d^3 → 3d^2
- **Result**: d^2.

3. **Sn^(2+)**:
- Atomic number of Sn = 50
- Electronic configuration: [Kr] 4d^10 5s^2 5p^2
- For Sn^(2+), remove 2 electrons:
- 4d^10 5s^2 → 4d^10 5p^2
- **Result**: Not d^2.

4. **Au^(3+)**:
- Atomic number of Au = 79
- Electronic configuration: [Xe] 4f^14 5d^10 6s^1
- For Au^(3+), remove 3 electrons:
- 5d^10 6s^1 → 5d^9
- **Result**: Not d^2.

5. **Ti^(2+)**:
- Atomic number of Ti = 22
- Electronic configuration: [Ar] 3d^2 4s^2
- For Ti^(2+), remove 2 electrons:
- 3d^2 4s^2 → 3d^2
- **Result**: d^2.

6. **As^(3+)**:
- Atomic number of As = 33
- Electronic configuration: [Ar] 3d^10 4s^2 4p^3
- For As^(3+), remove 3 electrons:
- 3d^10 4s^2 4p^3 → 3d^10 4p^2
- **Result**: Not d^2.

7. **Cr^(3+)**:
- Atomic number of Cr = 24
- Electronic configuration: [Ar] 3d^5 4s^1
- For Cr^(3+), remove 3 electrons:
- 3d^5 4s^1 → 3d^3
- **Result**: Not d^2.

8. **Mn^(5+)**:
- Atomic number of Mn = 25
- Electronic configuration: [Ar] 3d^5 4s^2
- For Mn^(5+), remove 5 electrons:
- 3d^5 4s^2 → 3d^2
- **Result**: d^2.

9. **Co^(3+)**:
- Atomic number of Co = 27
- Electronic configuration: [Ar] 3d^7 4s^2
- For Co^(3+), remove 3 electrons:
- 3d^7 4s^2 → 3d^6
- **Result**: Not d^2.

10. **Zr^(2+)**:
- Atomic number of Zr = 40
- Electronic configuration: [Kr] 4d^2 5s^2
- For Zr^(2+), remove 2 electrons:
- 4d^2 5s^2 → 4d^2
- **Result**: d^2.

11. **Cd^(2+)**:
- Atomic number of Cd = 48
- Electronic configuration: [Kr] 4d^10 5s^2
- For Cd^(2+), remove 2 electrons:
- 4d^10 5s^2 → 4d^10
- **Result**: Not d^2.

12. **Mo^(4+)**:
- Atomic number of Mo = 42
- Electronic configuration: [Kr] 4d^5 5s^1
- For Mo^(4+), remove 4 electrons:
- 4d^5 5s^1 → 4d^2
- **Result**: d^2.

13. **La^(2+)**:
- Atomic number of La = 57
- Electronic configuration: [Xe] 5d^1 6s^2
- For La^(2+), remove 2 electrons:
- 5d^1 6s^2 → 5d^1
- **Result**: Not d^2.

14. **Ta^(4+)**:
- Atomic number of Ta = 73
- Electronic configuration: [Xe] 4f^14 5d^3 6s^2
- For Ta^(4+), remove 4 electrons:
- 5d^3 6s^2 → 5d^1
- **Result**: Not d^2.

15. **Co^(6+)**:
- For Co^(6+), remove 6 electrons from [Ar] 3d^7 4s^2:
- 3d^7 4s^2 → 3d^1
- **Result**: Not d^2.

16. **Ni^(4+)**:
- Atomic number of Ni = 28
- Electronic configuration: [Ar] 3d^8 4s^2
- For Ni^(4+), remove 4 electrons:
- 3d^8 4s^2 → 3d^6
- **Result**: Not d^2.

**Final Count of d^2 Configurations**:
- V^(3+), Ti^(2+), Mn^(5+), Zr^(2+), Mo^(4+)

**Total d^2 configurations = 5.**