for the formula for the spin-only magnetic moment mu.

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The question asks for the formula for the spin-only magnetic moment $\mu$ .

Recall the standard formula for spin-only magnetic moment.
The spin-only magnetic moment ( $\mu$ ) is calculated based on the number of unpaired electrons ( $n$ ) in a metal ion. The formula is:
$\mu = \sqrt{n(n+2)}$
where $\mu$ is in Bohr magnetons (BM).
Compare this formula with the given options.
- A. $\sqrt{n(n+1)}$
- B. $2n+1$
- C. $n^2$
- D. $\sqrt{n(n+2)}$
The correct formula is option D.

The final answer is $\boxed{\text{D. }\sqrt{n(n+2)}}$

For the formula for the spin-only magnetic moment mu.