Which of the following ion has highest magnetic moment?

Question

Accepted Answer

The question asks which ion has the highest magnetic moment among the given options. The correct answer is Option 3: $Mn^{2+}$. Let's explore why this is the case and why the other options are incorrect.

### Explanation for $Mn^{2+}$ (Option 3):

1. **Electronic Configuration**: The $Mn^{2+}$ ion is derived from manganese, which has an atomic number of 25. The electronic configuration of neutral manganese is [Ar] 3d$^5$ 4s$^2$. When it loses two electrons to form $Mn^{2+}$, the configuration becomes [Ar] 3d$^5$.

2. **Unpaired Electrons**: In the 3d subshell, $Mn^{2+}$ has five unpaired electrons. The magnetic moment is directly related to the number of unpaired electrons, as it is calculated using the formula:
   $$
   \mu = \sqrt{n(n+2)}
   $$
   where $ \mu $ is the magnetic moment and $ n $ is the number of unpaired electrons. For $Mn^{2+}$, $ n = 5 $, so:
   $$
   \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \mu_B
   $$
   This is the highest magnetic moment among the given options.

### Explanation for Other Options:

1. **$Fe^{2+}$ (Option 1)**:
   - **Electronic Configuration**: [Ar] 3d$^6$
   - **Unpaired Electrons**: 4 unpaired electrons.
   - **Magnetic Moment**: $\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90 \mu_B$

2. **$Cr^{2+}$ (Option 2)**:
   - **Electronic Configuration**: [Ar] 3d$^4$
   - **Unpaired Electrons**: 4 unpaired electrons.
   - **Magnetic Moment**: $\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90 \mu_B$

3. **$Co^{2+}$ (Option 4)**:
   - **Electronic Configuration**: [Ar] 3d$^7$
   - **Unpaired Electrons**: 3 unpaired electrons.
   - **Magnetic Moment**: $\mu = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \mu_B$

### Conclusion:

The $Mn^{2+}$ ion has the highest magnetic moment because it has the maximum number of unpaired electrons (five) among the given options. This results in a larger magnetic moment compared to $Fe^{2+}$, $Cr^{2+}$, and $Co^{2+}$, which have fewer unpaired electrons. Therefore, Option 3 is indeed the correct answer.