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The type of overlapping in Br-F bond in $ Br{{F}_{3}} $ molecule is:
(A) $ s{{p}^{3}}-p $
(B) $ s{{p}^{2}}-p $
(C) $ s{{p}^{3}}d-p $
(D) $ s{{p}^{3}}{{d}^{2}}-p $

Answer
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Hint: Hybridization is the concept of mixing of two atomic orbitals with the same energy levels to give a new type of degenerate orbitals. $ Br{{F}_{3}} $ has a Bent T shaped structure with Br as a central atom bonded with three F atoms (three bond pairs) and two lone pairs. So, the hybridization would be $ s {{p} ^ {3}} d $ .

Complete Step By Step Solution
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To determine the hybridization of bromine trifluoride we will first take the bromine atom which is the central atom and look at its electron configuration. It is represented as-
 $ 1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{2}}4{{p}^{5}} $ . But to form bonds with the fluorine atom some electrons in Bromine are shifted to 4d-orbitals. Also due to higher oxidative capacity of fluorine, it forces bromine atoms to promote electrons to the d- level. Now, d-orbitals are used for hybridization. $ Br{{F}_{3}} $ will consist of seven electrons in its outermost shell. After the bond formation, it will further have 2 lone pairs and 3 Br—F covalent bonds. As the hybridization value is equal to 5 it gives rise to $ s{{p}^{3}}d $ hybrid orbitals. A bond with p orbital of Fluorine is formed.

Hence, option-(C) is correct.
 $ Br{{F}_{3}} $ has T-shaped or Trigonal Bipyramidal molecular geometry with a bond angle of $ 86\cdot 2{}^\circ $ .

Additional Information
Types of hybridization: The sp hybridization is observed when one s and one p orbital in the same main shell of an atom mix to form two new equivalent orbitals. The new orbitals formed are called sp $ 180{} ^ \circ $ hybridized orbitals. It forms linear molecules with an angle of $ 180{} ^ \circ $ .
 $ s {{p} ^ {2}} $ hybridization is observed when one s and two p orbitals of the same shell of an atom mix to form 3 equivalent orbitals. The new orbitals formed are called $ s {{p} ^ {2}} $ hybrid orbitals. It is also called trigonal hybridization. Atomic orbitals with equal energies undergo hybridization.

Note
The central atom bromine uses the d-orbitals for hybridization. Lone pairs take part in hybridization. The electrons $ s{{p}^{3}} $ hybridized species are held farther from the nucleus than those in $ s{{p}^{2}} $ ( $ 33% $ s-character) and sp ( $ 50% $ s-character) hybridized species. The closer the electrons are to the nucleus, the more stable they are.