1. Identify the metal ion from borax bead test

   In the borax bead test, the colour in the hot flame helps identify the metal ion.

   Common hot bead colours:

   • $\mathrm{Cu^{2+}}$ : blue-green
   • $\mathrm{Ni^{2+}}$ : brown
   • $\mathrm{Fe^{3+}}$ : yellow to brown
   • $\mathrm{Mn^{2+}}$ : amethyst/violet in oxidising flame, but green bead under hot/reducing condition due to manganate-type species

   Since the bead is stated to be green under hot condition, the metal is identified as manganese.

2. Determine the relevant electronic configuration

   Atomic number of Mn is $25$.

   Neutral Mn: $\mathrm{Mn} : [Ar] \, 3d^5 4s^2$

   The common salt involved in such tests is typically taken as $\mathrm{Mn^{2+}}$: $\mathrm{Mn^{2+}} : [Ar] \, 3d^5$

3. Count the number of unpaired electrons

   For $3d^5$, all five $d$-orbitals are singly occupied: $n = 5$

4. Calculate spin-only magnetic moment

   Spin-only magnetic moment is: $\mu = \sqrt{n(n+2)} \text{ BM}$

   Substituting $n=5$: $\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM}$

5. Nearest integer

   $5.92 \approx 6$

Therefore, the required magnetic moment is $6$ BM (nearest integer).