Determine total number of unpaired electrons in following ions
`Ti^(3+),V^(3+),Cr^(3+),Mn^(3+),Mn^(2+),Fe^(3+),Fe^(2+),Co^(2+),Ni^(2+),Cu^(2+)`.

Answer

To determine the total number of unpaired electrons in the given ions, we will analyze each ion's electronic configuration based on their atomic number and the number of electrons removed due to ionization.

### Step-by-Step Solution:

1. **Titanium (Ti³⁺)**:
- Atomic number: 22
- Electronic configuration: [Ar] 3d² 4s²
- For Ti³⁺, we remove 3 electrons (2 from 4s and 1 from 3d).
- Resulting configuration: [Ar] 3d¹
- Unpaired electrons: **1**

2. **Vanadium (V³⁺)**:
- Atomic number: 23
- Electronic configuration: [Ar] 3d³ 4s²
- For V³⁺, we remove 3 electrons (2 from 4s and 1 from 3d).
- Resulting configuration: [Ar] 3d²
- Unpaired electrons: **2**

3. **Chromium (Cr³⁺)**:
- Atomic number: 24
- Electronic configuration: [Ar] 3d⁵ 4s²
- For Cr³⁺, we remove 3 electrons (2 from 4s and 1 from 3d).
- Resulting configuration: [Ar] 3d³
- Unpaired electrons: **3**

4. **Manganese (Mn²⁺)**:
- Atomic number: 25
- Electronic configuration: [Ar] 3d⁵ 4s²
- For Mn²⁺, we remove 2 electrons (2 from 4s).
- Resulting configuration: [Ar] 3d⁵
- Unpaired electrons: **5**

5. **Manganese (Mn³⁺)**:
- For Mn³⁺, we remove 3 electrons (2 from 4s and 1 from 3d).
- Resulting configuration: [Ar] 3d⁴
- Unpaired electrons: **4**

6. **Iron (Fe²⁺)**:
- Atomic number: 26
- Electronic configuration: [Ar] 3d⁶ 4s²
- For Fe²⁺, we remove 2 electrons (2 from 4s).
- Resulting configuration: [Ar] 3d⁶
- Unpaired electrons: **4**

7. **Iron (Fe³⁺)**:
- For Fe³⁺, we remove 3 electrons (2 from 4s and 1 from 3d).
- Resulting configuration: [Ar] 3d⁵
- Unpaired electrons: **5**

8. **Cobalt (Co²⁺)**:
- Atomic number: 27
- Electronic configuration: [Ar] 3d⁷ 4s²
- For Co²⁺, we remove 2 electrons (2 from 4s).
- Resulting configuration: [Ar] 3d⁷
- Unpaired electrons: **3**

9. **Nickel (Ni²⁺)**:
- Atomic number: 28
- Electronic configuration: [Ar] 3d⁸ 4s²
- For Ni²⁺, we remove 2 electrons (2 from 4s).
- Resulting configuration: [Ar] 3d⁸
- Unpaired electrons: **2**

10. **Copper (Cu²⁺)**:
- Atomic number: 29
- Electronic configuration: [Ar] 3d¹⁰ 4s¹
- For Cu²⁺, we remove 2 electrons (1 from 4s and 1 from 3d).
- Resulting configuration: [Ar] 3d⁹
- Unpaired electrons: **1**

### Summary of Unpaired Electrons:
- Ti³⁺: 1
- V³⁺: 2
- Cr³⁺: 3
- Mn²⁺: 5
- Mn³⁺: 4
- Fe²⁺: 4
- Fe³⁺: 5
- Co²⁺: 3
- Ni²⁺: 2
- Cu²⁺: 1