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Boron trifluoride $(B{F_3})$ is a nonpolar, whereas ammonia $(N{H_3})$ is a polar molecule. The difference in polarities is related to the fact that:
(A) $B{F_3}$ has no hydrogen bonding and $N{H_3}$ does
(B) $B{F_3}$ triangular planar and $N{H_3}$ is pyramidal
(C) $B{F_3}$ is lewis base and $N{H_3}$ is a lewis acid
(D) The \[B - F\] bond is less polar than the \[N - H\] bond
(E) Boron is more electronegative than nitrogen

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Answer
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Hint:
Polar molecules result from an unequal / unsymmetrical sharing of valence electrons. While there may be unequal sharing of electrons in the individual bonds, in a nonpolar molecule, these bonds are evenly distributed and cancel out. There is no net dipole.

Complete step by step answer:
Well $B{F_3}$ as most of the people know here is triangular planar in shape and is confined only in one place. $F$ has an electronegativity of $4.0$ on the pauling scale which is very high as compared to that of boron which is around $2.4$.
This means that the dipole moment vector for one $C - F$ bond will point towards.
The knowledge of dipole moment is important for the following reasons.
1. Helps to clearly distinguish between a polar molecule and nonpolar molecule.
2. Helps to accurately determine the shape of the various molecules
3. Helps to determine the degree of polarity in a diatomic molecule.
Also, we have,
A. In $B{F_3}$, there is no lone pair of electrons on the boron atom and the individual dipole moment of every bond is directed from $B$ to $F$.
B. $B{F_3}$ is trigonal planar and shows the individual dipole moment of every bond from boron to $F$.
If the structure of $N{H_3}$ was planar, then the center of negative and positive charge would coincide and the molecule would be non-polar. In reality the $N{H_3}$ molecule looks more like a tetraeder. The three $H$ -atoms forming the base with the $N$ -atom rear the center of the tetraeder. The top of the tetraeder is the lone electron pair.

And hence option B is the correct answer.

Note: Nonpolar molecules are symmetric with no unshared electrons; polar molecules are asymmetrical, either containing lone pairs of electrons on a central atom or having atoms with different electronegativities bonds.