Final answer:
Bromine in BrF3 uses sp3d hybrid orbitals due to its trigonal bipyramidal geometry, differing from boron's sp2 hybridization in BF3 which supports a trigonal planar structure.
Step-by-step explanation:
The valence bond theory is used to predict the types of hybrid orbitals atoms will use in covalent bonding. When looking at bromine in BrF3, we must consider both the electron configuration of bromine and the molecular geometry as predicted by VSEPR theory. Bromine has seven valence electrons and in BrF3, it forms three sigma bonds with fluorine atoms and has two lone pairs. This results in a sp3d hybridization in order to accommodate the five areas of electron density (three bonds and two lone pairs), thus fulfilling the requirements for its trigonal bipyramidal molecular geometry.
It is important to note that although the question references boron's sp2 hybridization in BF3 which facilitates a trigonal planar structure, bromine in BrF3 operates differently due to a larger number of valence electrons and a different molecular geometry. Boron (in BF3) only forms three bonds with no lone pairs leading to sp2 hybridization.