To determine which ion exhibits the highest magnetic moment, we will follow these steps:
### Step 1: Understand the concept of magnetic moment
The magnetic moment (\( \mu \)) of an ion can be calculated using the formula:
\[
\mu = \sqrt{n(n + 2)}
\]
where \( n \) is the number of unpaired electrons in the ion.
### Step 2: Identify the electron configurations of the given ions
We will analyze the electron configurations of the ions provided in the options:
1. **Ti³⁺**: Titanium has an atomic number of 22. The electron configuration is \( [Ar] 3d^2 4s^2 \). For Ti³⁺, we remove 3 electrons (2 from 4s and 1 from 3d), resulting in \( 3d^1 \) configuration. Thus, it has **1 unpaired electron**.
2. **Ni²⁺**: Nickel has an atomic number of 28. The electron configuration is \( [Ar] 3d^8 4s^2 \). For Ni²⁺, we remove 2 electrons (both from 4s), resulting in \( 3d^8 \) configuration. Thus, it has **2 unpaired electrons**.
3. **Cu²⁺**: Copper has an atomic number of 29. The electron configuration is \( [Ar] 3d^{10} 4s^1 \). For Cu²⁺, we remove 2 electrons (1 from 4s and 1 from 3d), resulting in \( 3d^9 \) configuration. Thus, it has **1 unpaired electron**.
4. **Mn²⁺**: Manganese has an atomic number of 25. The electron configuration is \( [Ar] 3d^5 4s^2 \). For Mn²⁺, we remove 2 electrons (both from 4s), resulting in \( 3d^5 \) configuration. Thus, it has **5 unpaired electrons**.
### Step 3: Calculate the magnetic moments for each ion
Now we will calculate the magnetic moment for each ion using the formula \( \mu = \sqrt{n(n + 2)} \):
1. **Ti³⁺**:
\[
n = 1 \implies \mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73 \, \mu_B
\]
2. **Ni²⁺**:
\[
n = 2 \implies \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \, \mu_B
\]
3. **Cu²⁺**:
\[
n = 1 \implies \mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73 \, \mu_B
\]
4. **Mn²⁺**:
\[
n = 5 \implies \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \mu_B
\]
### Step 4: Compare the magnetic moments
From the calculations:
- Ti³⁺: \( \approx 1.73 \, \mu_B \)
- Ni²⁺: \( 2.83 \, \mu_B \)
- Cu²⁺: \( \approx 1.73 \, \mu_B \)
- Mn²⁺: \( \approx 5.92 \, \mu_B \)
### Conclusion
The ion with the highest magnetic moment is **Mn²⁺** with approximately \( 5.92 \, \mu_B \).
### Final Answer
The ion that exhibits the highest magnetic moment is **Mn²⁺**.
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