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: Understanding the Question:
We are asked to calculate the spin-only magnetic moment for an atom or ion that possesses exactly one unpaired electron.

Step 2: Key Formula or Approach:
The spin-only magnetic moment ($\mu$) is calculated using the following fundamental equation:
$$\mu = \sqrt{n(n + 2)} \text{ BM}$$
Where $n$ represents the total number of unpaired electrons, and BM stands for Bohr Magnetons (the unit of magnetic moment).

Step 3: Detailed Explanation:
The problem explicitly states that the number of unpaired electrons is one, so we substitute $n = 1$ into our formula.
$$\mu = \sqrt{1(1 + 2)}$$
$$\mu = \sqrt{1(3)}$$
$$\mu = \sqrt{3}$$
The square root of 3 is approximately 1.732.
$$\mu \approx 1.73 \text{ BM}$$

Step 4: Final Answer:
The calculated spin-only magnetic moment is 1.73 BM, which matches option (C).