Step 1: Understanding the Question:
The spin-only magnetic moment ($\mu$) depends on the number of unpaired electrons ($n$) in the d-subshell of the metal ion. Step 2: Key Formula or Approach:
1. Write the electronic configuration of the ion.
2. Identify the number of unpaired electrons ($n$).
3. Use the formula:
\[ \mu = \sqrt{n(n+2)} \text{ BM} \] Step 3: Detailed Explanation:
Atomic number of Copper (Cu) is 29.
Ground state electronic configuration: $[\text{Ar}] 3d^{10} 4s^1$
$\text{Cu}^{2+}$ configuration: $[\text{Ar}] 3d^9$ (electrons are lost from 4s then 3d).
In $3d^9$, there are 4 pairs and 1 unpaired electron.
So, $n = 1$.
Calculation:
\[ \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.732 \text{ BM} \] Step 4: Final Answer:
The spin-only magnetic moment for $\text{Cu}^{2+}$ is 1.73 BM.