Although fluorine is much more electronegative than hydrogen yet the dipole moment of `NF_(3)` (0.24 D) is much lower than that of `NH_(3)` (1.46 D). Explain.

Explanation

The dipole moment of molecules having lone pairs and polar bonds is the vector sum of the following two moments.
(i) Dipole moment of the lone pair/s
(ii) Resultant of the dipole moments of polar bonds.
Now both `NH_(3) and NF_(3)` have pyramidal structures with FNF and HNH bond angles of `102.4^(@) and 107.8^(@)` respectively. The direction of the dipole moment of the lone pair is in the same direction, i.e., away from the N atom as indicated in the Figure

Sine, N is more electronegative the H, therefore, the direction of the N-H bond moments is from H to N. The resultant of these three bonds adds to the moment of lone pair and hence the net dipole moment of `NH_(3)` is 1.46 D.
In contrast, F is more electronegative than N and hence the direction of the N-F bond moments is from N to F/ Tje resultant of the dipole moments of the three N-H bonds in `NH_(3)`. In other words, the only difference is that in cas of `NH_(3)`, the dipole moments of three N-H bonds adds to the dipole moment of lone pair but in case of `NF_(3)`, it opposes the dipole moment of the lone pair. Consequently, `NF_(3)` has a much lower dipole moment (0.24 D) than that if `NH_(3)` (1.46 D).