Question

Spin only magnetic moement given not correct is

• A. Ni\(^{2+}\) (4.73)
• B. Fe\(^{2+}\) (4.90)
• C. Ti\(^{2+}\) (2.84)
• D. CO\(^{2+}\) (3.89)
• E. Mg\(^{2+}\) (5.92)

Hint:

To quickly estimate the spin-only magnetic moment, note that the value is always slightly greater than the number of unpaired electrons (e.g., \( n=2 \) gives \( \sim 2.8 \), \( n=3 \) gives \( \sim 3.9 \)).
Since \( 4.73 \) starts with a 4, it corresponds to an ion with 4 unpaired electrons, not 2.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The spin-only magnetic moment (\( \mu \)) is dependent on the number of unpaired electrons (\( n \)) present in the outermost d-orbitals of the transition metal ion.
Step 2: Key Formula or Approach:
The formula for spin-only magnetic moment is:
\[ \mu = \sqrt{n(n+2)} \text{ B.M.} \] Step 3: Detailed Explanation:
Let's evaluate the number of unpaired electrons and the theoretical magnetic moment for each given ion.
For option (A), \( \text{Ni}^{2+} \):
The electronic configuration of Ni is \( [Ar] 4s^2 3d^8 \).
The \( \text{Ni}^{2+} \) ion has an outer configuration of \( 3d^8 \).
According to Hund's rule, filling 8 electrons in 5 d-orbitals leaves 2 unpaired electrons (\( n = 2 \)).
\[ \mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 \text{ B.M.} \] The value given in the option is 4.73, which is drastically incorrect.
For option (B), \( \text{Fe}^{2+} \):
Configuration is \( 3d^6 \), which has 4 unpaired electrons (\( n = 4 \)).
\[ \mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90 \text{ B.M.} \] (This is correct).
For option (C), \( \text{Ti}^{2+} \):
Configuration is \( 3d^2 \), which has 2 unpaired electrons (\( n = 2 \)).
\[ \mu = \sqrt{2(4)} = \sqrt{8} \approx 2.83 \text{ B.M.} \] (This is correct).
For option (D), \( \text{CO}^{2+} \) (Cobalt ion \( \text{Co}^{2+} \)):
Configuration is \( 3d^7 \), which has 3 unpaired electrons (\( n = 3 \)).
\[ \mu = \sqrt{3(5)} = \sqrt{15} \approx 3.87 \text{ B.M.} \] (This is approximately 3.89, so it is considered correct).
For option (E), the text says \( \text{Mg}^{2+} \) (5.92). This is a clear typographical error in the paper for \( \text{Mn}^{2+} \) (Manganese).
\( \text{Mn}^{2+} \) has a \( 3d^5 \) configuration with 5 unpaired electrons (\( n = 5 \)).
\[ \mu = \sqrt{5(7)} = \sqrt{35} \approx 5.92 \text{ B.M.} \] Assuming the intended ion was \( \text{Mn}^{2+} \), this value is correct.
Thus, the unequivocally incorrect value matched to the wrong ion is in option (A).
Step 4: Final Answer:
The given magnetic moment for \( \text{Ni}^{2+} \) is not correct.