Final answer:
The hybridization of bromine in BrF5 is sp3d2, derived from one s orbital, three p orbitals, and two d orbitals to accommodate five Br-F bonds and one lone pair, resulting in a square pyramidal molecular geometry.
Step-by-step explanation:
The hybridization of the bromine atom in BrF5 is determined by considering its electron domains including both bonding pairs and lone pairs of electrons. Bromine has seven valence electrons, and in BrF5, it forms five Br-F bonds and has one lone pair. This accounts for six electron domains (five bonding pairs and one lone pair).
According to the Valence Shell Electron Pair Repulsion (VSEPR) model, these six electron domains will arrange themselves into an octahedral geometry for the minimum repulsion. However, since one of the vertices is occupied by a lone pair, the actual molecular geometry is square pyramidal. The hybridization that accommodates this arrangement involves one s orbital, three p orbitals, and two d orbitals, resulting in sp3d2 hybridization.