Question

The calculated magnetic moment of a divalent ion of an atom with atomic number 24 in aqueous solution is

• A. 4.90 BM
• B. 5.92 BM
• C. 3.87 BM
• D. 2.84 BM
• E. 1.73 BM

Hint:

A useful shortcut: the magnetic moment value always starts with the number of unpaired electrons. If $n=4$, the answer must be $4.something$. This helps you eliminate options B, C, D, and E instantly!

Answer 1

The Correct Option is A

Concept: The magnetic moment of transition metal ions is primarily determined by the number of unpaired electrons in their $d$-orbitals, calculated using the "spin-only" formula.
• Atomic Configuration: For an atom with atomic number $Z=24$ (Chromium, Cr), the ground state configuration is $[Ar] 3d^5 4s^1$.
• Ion Formation: A "divalent ion" means the atom has lost two electrons to form a $+2$ charge ($Cr^{2+}$).
• Spin-only Formula: $\mu = \sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons and BM stands for Bohr Magneton.

Step 1: Determine the electron configuration and unpaired electrons. For $Cr (Z=24)$: $[Ar] 3d^5 4s^1$. To form $Cr^{2+}$, electrons are removed first from the $4s$ orbital and then from the $3d$ orbital: Configuration of $Cr^{2+}$: $[Ar] 3d^4$. The 4 electrons in the $3d$ subshell remain unpaired according to Hund's rule. Thus, $n = 4$.

Step 2: Calculate the magnetic moment. Using the formula $\mu = \sqrt{n(n+2)}$: \[ \mu = \sqrt{4(4+2)} = \sqrt{4 \times 6} = \sqrt{24} \] \[ \mu \approx 4.8989 \dots \approx 4.90 \text{ BM} \]