Transition metals and many of their compounds show paramagnetic behaviour where there are unpaired electron or electrons. The magnetic moment arises from the spin and orbital motions in ions or molecule. Magnetic moment of n unpaired electrons is given as
`mu=sqrt(n(n+2))` Bohr magneton
Magnetic moment increases as the number of unpaired electrons increases.
Q. Which among the following ions has maximum value of magnetic moment

Options

A. `Cu^(2+)`
B. `Mn^(2+)`
C. `Cr^(2+)`
D. `Ti^(2+)`

Explanation

To determine which ion among the given options has the maximum value of magnetic moment, we will calculate the magnetic moment for each ion based on the number of unpaired electrons using the formula:

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

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

### Step 1: Identify the electronic configurations and number of unpaired electrons for each ion.

1. **Cu²⁺ (Copper ion)**
- Atomic number of Copper (Cu) = 29
- Electronic configuration of Cu = [Ar] 3d¹⁰ 4s²
- For Cu²⁺, the configuration becomes [Ar] 3d⁹ (losing 2 electrons from 4s and 1 from 3d)
- Number of unpaired electrons = 1 (3d⁹ has 1 unpaired electron)

2. **Mn²⁺ (Manganese ion)**
- Atomic number of Manganese (Mn) = 25
- Electronic configuration of Mn = [Ar] 3d⁵ 4s²
- For Mn²⁺, the configuration becomes [Ar] 3d⁵ (losing 2 electrons from 4s)
- Number of unpaired electrons = 5 (3d⁵ has 5 unpaired electrons)

3. **Cr²⁺ (Chromium ion)**
- Atomic number of Chromium (Cr) = 24
- Electronic configuration of Cr = [Ar] 3d⁵ 4s¹
- For Cr²⁺, the configuration becomes [Ar] 3d⁴ (losing 1 electron from 4s and 1 from 3d)
- Number of unpaired electrons = 4 (3d⁴ has 4 unpaired electrons)

4. **Ti²⁺ (Titanium ion)**
- Atomic number of Titanium (Ti) = 22
- Electronic configuration of Ti = [Ar] 3d² 4s²
- For Ti²⁺, the configuration becomes [Ar] 3d² (losing 2 electrons from 4s)
- Number of unpaired electrons = 2 (3d² has 2 unpaired electrons)

### Step 2: Calculate the magnetic moment for each ion.

1. **For Cu²⁺:**
\[ \mu = \sqrt{1(1+2)} = \sqrt{3} \text{ Bohr magneton} \]

2. **For Mn²⁺:**
\[ \mu = \sqrt{5(5+2)} = \sqrt{35} \text{ Bohr magneton} \]

3. **For Cr²⁺:**
\[ \mu = \sqrt{4(4+2)} = \sqrt{24} \text{ Bohr magneton} \]

4. **For Ti²⁺:**
\[ \mu = \sqrt{2(2+2)} = \sqrt{8} \text{ Bohr magneton} \]

### Step 3: Compare the magnetic moments.

- Cu²⁺: \(\sqrt{3}\) Bohr magneton
- Mn²⁺: \(\sqrt{35}\) Bohr magneton
- Cr²⁺: \(\sqrt{24}\) Bohr magneton
- Ti²⁺: \(\sqrt{8}\) Bohr magneton

### Conclusion:
The ion with the maximum value of magnetic moment is **Mn²⁺** with a magnetic moment of \(\sqrt{35}\) Bohr magneton.