The transition metal having highest 3rd ionisation enthalpy is:

We need to identify the transition metal with the highest 3rd ionisation enthalpy among Cr, Mn, V, and Fe.

After removal of two electrons (to form $$M^{2+}$$):

$$V^{2+}$$: $$[Ar]3d^3$$

$$Cr^{2+}$$: $$[Ar]3d^4$$

$$Mn^{2+}$$: $$[Ar]3d^5$$ (half-filled, extra stable)

$$Fe^{2+}$$: $$[Ar]3d^6$$

The 3rd IE involves removing an electron from the $$M^{2+}$$ configuration. The $$Mn^{2+}$$ ion has a half-filled $$3d^5$$ configuration, which is exceptionally stable due to maximum exchange energy. Removing an electron from this half-filled configuration requires the most energy.

$$Mn^{2+}$$ ($$3d^5$$) has the highest 3rd IE because disrupting the half-filled d-subshell requires extra energy.

The correct answer is Option B) Mn.