The correct order of spin multiplicity of various ions of manganese including its neutral state is 

Options

A. `Mn^(7+) gt Mn^(6+) gt  Mn^(4+) gt Mn^(2+) gt  Mn`
B. `Mn gt Mn^(2+) gt Mn^(4+) gt Mn^(6+) gt Mn^(7+)`
C. `Mn^(7+) lt Mn^(6+) lt Mn^(4+) lt Mn^(2+) = Mn`
D. All have equal spin multiplicity

Answer

To determine the correct order of spin multiplicity for various ions of manganese (Mn) including its neutral state, we will follow the steps outlined below:

### Step-by-Step Solution:

1. **Identify the Ground State Electronic Configuration of Manganese (Mn)**:
- The atomic number of manganese is 25. Therefore, its ground state electronic configuration is:
\[ \text{Mn: } [Ar] 3d^5 4s^2 \]

2. **Determine the Electronic Configurations for Various Ions**:
- **Mn²⁺**: Loses 2 electrons (from 4s orbital):
\[ \text{Mn}^{2+}: [Ar] 3d^5 \]
- **Mn⁴⁺**: Loses 4 electrons (2 from 4s and 2 from 3d):
\[ \text{Mn}^{4+}: [Ar] 3d^3 \]
- **Mn⁶⁺**: Loses 6 electrons (2 from 4s and 4 from 3d):
\[ \text{Mn}^{6+}: [Ar] 3d^1 \]
- **Mn⁷⁺**: Loses 7 electrons (2 from 4s and 5 from 3d):
\[ \text{Mn}^{7+}: [Ar] 3d^0 \]

3. **Count the Number of Unpaired Electrons**:
- For **Mn**: 5 unpaired electrons (in 3d).
- For **Mn²⁺**: 5 unpaired electrons (in 3d).
- For **Mn⁴⁺**: 3 unpaired electrons (in 3d).
- For **Mn⁶⁺**: 1 unpaired electron (in 3d).
- For **Mn⁷⁺**: 0 unpaired electrons (in 3d).

4. **Calculate Spin Multiplicity Using the Formula**:
- Spin multiplicity is calculated using the formula:
\[ \text{Spin Multiplicity} = 2s + 1 \]
- Where \( s \) is the number of unpaired electrons.
- **For Mn**: \( s = 5 \) → \( 2(5) + 1 = 11 \)
- **For Mn²⁺**: \( s = 5 \) → \( 2(5) + 1 = 11 \)
- **For Mn⁴⁺**: \( s = 3 \) → \( 2(3) + 1 = 7 \)
- **For Mn⁶⁺**: \( s = 1 \) → \( 2(1) + 1 = 3 \)
- **For Mn⁷⁺**: \( s = 0 \) → \( 2(0) + 1 = 1 \)

5. **Order the Spin Multiplicities**:
- Based on the calculated spin multiplicities:
- Mn: 11
- Mn²⁺: 11
- Mn⁴⁺: 7
- Mn⁶⁺: 3
- Mn⁷⁺: 1
- The correct order of spin multiplicity from highest to lowest is:
\[ \text{Mn} = \text{Mn}^{2+} > \text{Mn}^{4+} > \text{Mn}^{6+} > \text{Mn}^{7+} \]

### Final Answer:
The correct order of spin multiplicity is:
\[ \text{Mn} = \text{Mn}^{2+} > \text{Mn}^{4+} > \text{Mn}^{6+} > \text{Mn}^{7+} \]