Which of the following ions show higher spin only magnetic moment value?

Options

A. `Ti^(3+)`
B. `Mn^(2+)`
C. `Fe^(2+)`
D. `Co^(3+)`

Explanation

To determine which of the given ions show a higher spin-only magnetic moment value, we will analyze each ion's electron configuration and the number of unpaired electrons. The ions we need to consider are Ti³⁺, Mn²⁺, Fe²⁺, and Co³⁺.

### Step-by-Step Solution:

1. **Determine the Electron Configuration of Each Ion:**
- **Ti³⁺ (Titanium):**
- Atomic number of Titanium (Ti) = 22
- Ground state configuration: [Ar] 4s² 3d²
- For Ti³⁺, it loses 3 electrons (2 from 4s and 1 from 3d):
- Configuration: 3d¹
- Number of unpaired electrons = 1

- **Mn²⁺ (Manganese):**
- Atomic number of Manganese (Mn) = 25
- Ground state configuration: [Ar] 4s² 3d⁵
- For Mn²⁺, it loses 2 electrons (both from 4s):
- Configuration: 3d⁵
- Number of unpaired electrons = 5

- **Fe²⁺ (Iron):**
- Atomic number of Iron (Fe) = 26
- Ground state configuration: [Ar] 4s² 3d⁶
- For Fe²⁺, it loses 2 electrons (both from 4s):
- Configuration: 3d⁶
- Number of unpaired electrons = 4 (in a high-spin state)

- **Co³⁺ (Cobalt):**
- Atomic number of Cobalt (Co) = 27
- Ground state configuration: [Ar] 4s² 3d⁷
- For Co³⁺, it loses 3 electrons (2 from 4s and 1 from 3d):
- Configuration: 3d⁶
- Number of unpaired electrons = 0 (in a low-spin state due to high crystal field splitting)

2. **Calculate the Spin-Only Magnetic Moment:**
The formula for calculating the spin-only magnetic moment (μ) is:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

- **Ti³⁺:**
- \( n = 1 \)
- \( \mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73 \, \mu_B \)

- **Mn²⁺:**
- \( n = 5 \)
- \( \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \mu_B \)

- **Fe²⁺:**
- \( n = 4 \)
- \( \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.90 \, \mu_B \)

- **Co³⁺:**
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = 0 \, \mu_B \)

3. **Compare the Magnetic Moment Values:**
- Ti³⁺: \( \approx 1.73 \, \mu_B \)
- Mn²⁺: \( \approx 5.92 \, \mu_B \)
- Fe²⁺: \( \approx 4.90 \, \mu_B \)
- Co³⁺: \( 0 \, \mu_B \)

### Conclusion:
The ions with the higher spin-only magnetic moment values are Mn²⁺ and Fe²⁺, with values of approximately 5.92 µB and 4.90 µB, respectively.

### Final Answer:
**Mn²⁺ and Fe²⁺ show higher spin-only magnetic moment values.**