Which of the following ion has the maximum magnetic moment?

Options

A. `Mn^(3+)`
B. ` Cu^(2+)`
C. ` Fe^(3+)`
D. ` V^(3+)`

Answer

To determine which of the given ions has the maximum magnetic moment, we need to analyze the electronic configurations and the number of unpaired electrons for each ion. The magnetic moment (μ) can be calculated using the formula:

\[ \mu = \sqrt{n(n + 2)} \]

where \(n\) is the number of unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Electronic Configuration of Each Ion:**
- **Mn³⁺:**
- Manganese (Mn) has an atomic number of 25. Its electronic configuration is:
\[ \text{Mn: } [Ar] 4s^2 3d^5 \]
- For Mn³⁺, two electrons are removed from the 4s and 3d orbitals:
\[ \text{Mn³⁺: } [Ar] 3d^4 \]
- In the 3d orbital, there are 4 electrons, all of which are unpaired.

2. **Calculate the Magnetic Moment for Mn³⁺:**
\[ n = 4 \quad \Rightarrow \quad \mu = \sqrt{4(4 + 2)} = \sqrt{24} \]

3. **Cu²⁺:**
- Copper (Cu) has an atomic number of 29. Its electronic configuration is:
\[ \text{Cu: } [Ar] 4s^2 3d^{10} \]
- For Cu²⁺, two electrons are removed from the 4s orbital:
\[ \text{Cu²⁺: } [Ar] 3d^9 \]
- In the 3d orbital, there are 9 electrons, with 1 unpaired electron.

4. **Calculate the Magnetic Moment for Cu²⁺:**
\[ n = 1 \quad \Rightarrow \quad \mu = \sqrt{1(1 + 2)} = \sqrt{3} \]

5. **Fe³⁺:**
- Iron (Fe) has an atomic number of 26. Its electronic configuration is:
\[ \text{Fe: } [Ar] 4s^2 3d^6 \]
- For Fe³⁺, three electrons are removed (2 from 4s and 1 from 3d):
\[ \text{Fe³⁺: } [Ar] 3d^5 \]
- In the 3d orbital, there are 5 electrons, all of which are unpaired.

6. **Calculate the Magnetic Moment for Fe³⁺:**
\[ n = 5 \quad \Rightarrow \quad \mu = \sqrt{5(5 + 2)} = \sqrt{35} \]

7. **V³⁺:**
- Vanadium (V) has an atomic number of 23. Its electronic configuration is:
\[ \text{V: } [Ar] 4s^2 3d^3 \]
- For V³⁺, three electrons are removed (2 from 4s and 1 from 3d):
\[ \text{V³⁺: } [Ar] 3d^2 \]
- In the 3d orbital, there are 2 electrons, both of which are unpaired.

8. **Calculate the Magnetic Moment for V³⁺:**
\[ n = 2 \quad \Rightarrow \quad \mu = \sqrt{2(2 + 2)} = \sqrt{8} \]

9. **Compare the Magnetic Moments:**
- Mn³⁺: \(\sqrt{24}\)
- Cu²⁺: \(\sqrt{3}\)
- Fe³⁺: \(\sqrt{35}\)
- V³⁺: \(\sqrt{8}\)

The maximum magnetic moment is for **Fe³⁺** with a value of \(\sqrt{35}\).

### Final Answer:
The ion with the maximum magnetic moment is **Fe³⁺**.