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When you draw the Lewis structure, the molecule is shown to have two lone pairs on Br in addition to the three bonds Br forms with the three F. Because each lone pair represents another region of electron density, five hybridized orbitals are needed and there are five sp3d orbitals.
When we find the lewis dot structure for BrF3 we realize that it is T-shaped. It is bonded to 3 atoms and has 2 lone pairs. The electron density or electron arrangement is 5. The atomic orbitals has to match the number of hybrid orbitals. In sp^3d: there are 5 hybrid orbitals.
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