Which one of the following molecules has maximum dipole moment ?

The correct option is NH₃.

To determine which molecule has the maximum dipole moment, let's analyze the molecular geometry and individual bond dipoles of each option:

1. CH₄ (Methane):
CH₄ has a symmetrical tetrahedral geometry with sp³ hybridization. The individual C-H bond dipoles point towards carbon (as carbon is slightly more electronegative than hydrogen). Due to the perfect tetrahedral symmetry, the vector sum of all four C-H bond dipoles cancels out completely, resulting in a net dipole moment of zero ($\mu =0$).

2. PF₅ (Phosphorus Pentafluoride):
PF₅ has a symmetrical trigonal bipyramidal geometry (sp³d hybridization). The three equatorial P-F bonds are arranged at 120-degree angles to each other and their dipoles cancel each other out in the equatorial plane. The two axial P-F bonds point in opposite directions along the vertical axis and cancel each other out. Thus, the net dipole moment is zero ($\mu =0$).

3. NH₃ (Ammonia) vs NF₃ (Nitrogen Trifluoride):
Both NH₃ and NF₃ have a pyramidal geometry due to the presence of three bond pairs and one lone pair on the central nitrogen atom (sp³ hybridized).
In NH₃, nitrogen is more electronegative than hydrogen. Therefore, the N-H bond dipoles are directed towards nitrogen. The dipole moment of the lone pair also points upwards, away from the nitrogen atom. Consequently, the orbital dipole of the lone pair and the vector sum of the N-H bond dipoles act in the same direction, reinforcing each other. This results in a relatively high net dipole moment ($\mu \approx 1.47\text{D}$).
In NF₃, fluorine is much more electronegative than nitrogen. The N-F bond dipoles are directed away from nitrogen (towards fluorine). The orbital dipole of the lone pair points upwards, in the opposite direction of the vector sum of the N-F bond dipoles. As a result, the lone pair dipole partially cancels the N-F bond dipoles, resulting in a very low net dipole moment ($\mu \approx 0.23\text{D}$).

Comparing all the given molecules, NH₃ has the maximum dipole moment.