Step 1: Understanding the Concept:
Magnetic properties in transition metals arise primarily from the spin of unpaired electrons.
A substance with unpaired electrons is paramagnetic and is attracted into a magnetic field.
The "magnetic moment" (\( \mu \)) quantifies the strength of this magnetism.
In the transition series, the magnetic moment can be estimated using the "spin-only" formula.
Step 2: Key Formula or Approach:
The spin-only magnetic moment formula is:
\[ \mu = \sqrt{n(n+2)} \text{ Bohr Magnetons (BM)} \]
where \( n \) is the number of unpaired electrons.
From this formula, it is clear that as the number of unpaired electrons (\( n \)) increases, the magnetic moment (\( \mu \)) also increases.
Therefore, to find the highest magnetic moment, we must find the electronic configuration that contains the maximum number of unpaired electrons.
Step 3: Detailed Explanation:
A d-subshell has 5 degenerate orbitals. According to Hund's Rule, these orbitals are filled singly before pairing begins.
Let's count the unpaired electrons for each option:
- (A) \( 3d^7 \): Five electrons fill the 5 orbitals singly, and the remaining 2 electrons must pair up. Number of unpaired electrons (\( n \)) = \( 5 - 2 = 3 \).
- (B) \( 3d^5 \): All five electrons occupy the 5 orbitals singly. Number of unpaired electrons (\( n \)) = 5. This is the maximum possible number of unpaired electrons for a d-subshell.
- (C) \( 3d^8 \): Five electrons occupy orbitals singly, and 3 must pair up. Number of unpaired electrons (\( n \)) = \( 5 - 3 = 2 \).
- (D) \( 3d^2 \): Only two electrons are present, occupying 2 orbitals singly. Number of unpaired electrons (\( n \)) = 2.
Comparing the results:
- \( n=5 \) gives \( \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM} \).
- \( n=3 \) gives \( \mu = \sqrt{15} \approx 3.87 \text{ BM} \).
- \( n=2 \) gives \( \mu = \sqrt{8} \approx 2.83 \text{ BM} \).
Since \( 3d^5 \) has the highest number of unpaired electrons, it has the highest magnetic moment.
Step 4: Final Answer:
The configuration with five unpaired electrons (\( d^5 \)) yields the greatest magnetic moment among the choices given.
Therefore, the correct answer is (B).