Question

Which elements have the same magnetic moment \( \mu \)?

• A. \( \text{Cr}^{3+}, \text{Mn}^{2+} \)
• B. \( \text{Fe}^{2+}, \text{Ni}^{2+} \)
• C. \( \text{Cu}^{2+}, \text{Zn}^{2+} \)
• D. \( \text{Mn}^{2+}, \text{Fe}^{3+} \)

Hint:

To calculate the magnetic moment of an ion, identify the number of unpaired electrons (\( n \)) from its electronic configuration and use the formula \( \mu = \sqrt{n(n+2)} \, \mu_B \). This formula is useful for understanding the magnetic properties of ions.

Answer 1

The Correct Option is D

The **magnetic moment** (\( \mu \)) of an ion is an important property that is directly related to the number of unpaired electrons in the ion. It is calculated using the formula: \[ \mu = \sqrt{n(n+2)} \, \mu_B, \] where: \( n \) is the number of unpaired electrons in the ion, \( \mu_B \) is the Bohr magneton, a physical constant used to express magnetic moments.
Step 1: Determine the Electronic Configuration and Unpaired Electrons. We will now determine the electronic configuration and the number of unpaired electrons for the given ions: \( \text{Mn}^{2+} \): Manganese (Mn) has an atomic number of 25. The neutral Mn configuration is \( [\text{Ar}] \, 3d^5 4s^2 \). When it loses two electrons to become \( \text{Mn}^{2+} \), the electron configuration becomes \( [\text{Ar}] \, 3d^5 \). Since all five electrons in the \( 3d \) orbital are unpaired, the number of unpaired electrons \( n = 5 \). \( \text{Fe}^{3+} \): Iron (Fe) has an atomic number of 26. The neutral Fe configuration is \( [\text{Ar}] \, 3d^6 4s^2 \). When it loses three electrons to become \( \text{Fe}^{3+} \), the configuration becomes \( [\text{Ar}] \, 3d^5 \). As with \( \text{Mn}^{2+} \), all five electrons in the \( 3d \) orbital are unpaired, so \( n = 5 \) for \( \text{Fe}^{3+} \) as well. Step 2: Calculate the Magnetic Moment. Using the formula for the magnetic moment and substituting \( n = 5 \): \[ \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \, \mu_B. \] Thus, both \( \text{Mn}^{2+} \) and \( \text{Fe}^{3+} \) have a magnetic moment of approximately \( 5.92 \, \mu_B \).
Step 3: Conclusion. The elements \( \text{Mn}^{2+} \) and \( \text{Fe}^{3+} \) have the same magnetic moment because they both have 5 unpaired electrons. Therefore, the correct answer is \( \mathbf{(4)} \).