\(\text{The spin-only magnetic moment is calculated using the formula:} \\ \mu = \sqrt{n(n + 2)} \, \text{BM} \\ \text{where } n \text{ is the number of unpaired electrons. For } \text{Mn}^{2+}, \, n = 5, \text{ so:} \\ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \text{BM}\)