Question

What is spin only magnetic moment of an element having one unpaired electron?

• A. 0.34 BM
• B. 1.0 BM
• C. 1.73 BM
• D. 3.1 BM

Hint:

You can instantly estimate the spin-only magnetic moment by looking at $n$. The value of $\mu$ is always equal to $n$ point something! For example: $n=1 \rightarrow 1.73 \text{ BM}$, $n=2 \rightarrow 2.83 \text{ BM}$, $n=3 \rightarrow 3.87 \text{ BM}$.

Answer 1

The Correct Option is C

Step 1: Write the spin only formula.
$$\mu = \sqrt{n(n+2)}\ \text{BM}$$ where $n$ is the number of unpaired electrons.

Step 2: Put in the value.
Here $n = 1$, so $\mu = \sqrt{1(1+2)} = \sqrt{3}$.

Step 3: Take the root.
$\sqrt{3}$ is about $1.73$.
\[ \boxed{1.73\ \text{BM}} \]