This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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The question asks for the formula for the spin-only magnetic moment .
Step 1: Recall the standard formula for spin-only magnetic moment. The spin-only magnetic moment () is calculated based on the number of unpaired electrons () in a metal ion. The formula is: where is in Bohr magnetons (BM).
Step 2: Compare this formula with the given options.
The correct formula is option D.
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This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.