Question

Some species are given: \( \text{Ni}^{2+}, \text{Fe}^{2+}, \text{Co}^{2+}, \text{V}^{3+}, \text{Ti}^{2+} \) How many species have a magnetic moment (spin only) less than 3 BM?

Hint:

For transition metal ions, the number of unpaired electrons in the d-orbital determines the magnetic moment. If the ion has fewer unpaired electrons, the magnetic moment tends to be lower.

Answer 1

Correct Answer: 2

Step 1: Formula for magnetic moment.
The magnetic moment \( \mu_{\text{sp}} \) for a transition metal ion can be calculated using the formula: \[ \mu_{\text{sp}} = \sqrt{n(n+2)} \, \text{BM} \] where \( n \) is the number of unpaired electrons.
Step 2: Determine the number of unpaired electrons for each species. 1. \( \text{Ni}^{2+} \): \( \text{Ni} \) has an atomic number of 28, and its electron configuration is \( [Ar] 3d^8 4s^2 \). For \( \text{Ni}^{2+} \), the electron configuration becomes \( [Ar] 3d^8 \), which has 2 unpaired electrons. \[ \mu_{\text{sp}} = \sqrt{2(2+2)} = \sqrt{8} = 2.83 \, \text{BM} \] This is less than 3 BM. 2. \( \text{Fe}^{2+} \): \( \text{Fe} \) has an atomic number of 26, and its electron configuration is \( [Ar] 3d^6 4s^2 \). For \( \text{Fe}^{2+} \), the electron configuration becomes \( [Ar] 3d^6 \), which has 4 unpaired electrons. \[ \mu_{\text{sp}} = \sqrt{4(4+2)} = \sqrt{24} = 4.9 \, \text{BM} \] This is greater than 3 BM. 3. \( \text{Co}^{2+} \): \( \text{Co} \) has an atomic number of 27, and its electron configuration is \( [Ar] 3d^7 4s^2 \). For \( \text{Co}^{2+} \), the electron configuration becomes \( [Ar] 3d^7 \), which has 3 unpaired electrons. \[ \mu_{\text{sp}} = \sqrt{3(3+2)} = \sqrt{15} = 3.87 \, \text{BM} \] This is greater than 3 BM. 4. \( \text{V}^{3+} \): \( \text{V} \) has an atomic number of 23, and its electron configuration is \( [Ar] 3d^3 4s^2 \). For \( \text{V}^{3+} \), the electron configuration becomes \( [Ar] 3d^3 \), which has 3 unpaired electrons. \[ \mu_{\text{sp}} = \sqrt{3(3+2)} = \sqrt{15} = 3.87 \, \text{BM} \] This is greater than 3 BM. 5. \( \text{Ti}^{2+} \): \( \text{Ti} \) has an atomic number of 22, and its electron configuration is \( [Ar] 3d^2 4s^2 \). For \( \text{Ti}^{2+} \), the electron configuration becomes \( [Ar] 3d^2 \), which has 2 unpaired electrons. \[ \mu_{\text{sp}} = \sqrt{2(2+2)} = \sqrt{8} = 2.83 \, \text{BM} \] This is less than 3 BM.
Step 3: Conclusion.
The species that have a magnetic moment less than 3 BM are: - \( \text{Ni}^{2+} \) (2.83 BM) - \( \text{Ti}^{2+} \) (2.83 BM) Thus, 2 species have a magnetic moment less than 3 BM.