Is the nonbonding orbital of `"NH"_3` a `p` orbital?

MOSTLY true. The lone pair is in a molecular orbital that is similar to a `p` orbital because it has significant `p` orbital characteristics, but it is not in a pure `p` atomic orbital.

Consider this orbital diagram of `"NH"_3`:

http://www.chemtube3d.com/

In a sense, I suppose the lone pair is in a `p`-like orbital... How we label it depends on how we treat the atomic orbitals.

• In a hybridized treatment, one would place the nitrogen lone pair in an `sp^3` orbital, as seen in the above diagram. In this case, all four orbitals nitrogen uses for bonding are identical, with `75%` `p` character and `25%` `s` character.
• In an unhybridized treatment, one would place the nitrogen lone pair in a molecular orbital with significant `p` characteristics, and the molecular orbital would primarily belong to the nitrogen.

http://www.ch.ic.ac.uk/

And in the above molecular orbital diagram, I would be referring to the molecular orbital labeled `2a_1`, which you can see involves interactions between more than one orbital.

Therefore, it is not a pure, nonbonding atomic orbital.

Either approach leads to the conclusion that the orbital contains significant `bbp` orbital characteristics, but it is not in a pure `p` orbital because it is not a purely nonbonding orbital.