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 formula.
The spin-only magnetic moment is found from $\mu = \sqrt{n(n+2)}$ Bohr Magnetons, where $n$ is the number of unpaired electrons.
Step 2: Read the given data.
The element has exactly one unpaired electron, so $n = 1$.
Step 3: Put it in.
$\mu = \sqrt{1(1+2)}$.
Step 4: Simplify inside.
$1 \times 3 = 3$, so $\mu = \sqrt{3}$.
Step 5: Take the square root.
The square root of $3$ is about $1.73$. So $\mu \approx 1.73\ \text{BM}$.
Step 6: Final choice.
The magnetic moment is $1.73\ \text{BM}$, which is option 3.
\[ \boxed{1.73\ \text{BM}} \]