[ramboacid]

Nitrogen atoms can have three substituents and a lone pair. If you consider the lone pair as a fourth unique substituent, then can't an sp3 hybridized nitrogen atom in an organic molecule can be a chiral stereocenter? I asked my teacher and she said that only carbon atoms can be chiral stereocenters, but she didn't have a good explanation for why.

[sjb]

Nitrogen atoms can have three substituents and a lone pair. If you consider the lone pair as a fourth unique substituent, then can't an sp3 hybridized nitrogen atom in an organic molecule can be a chiral stereocenter? I asked my teacher and she said that only carbon atoms can be chiral stereocenters, but she didn't have a good explanation for why.

If the structure is restricted in some way, then yes, the nitrogen can be an asymmetric centre, see for instance sparteine. However, in the cases of things like ethylmethylamine, the inversion is usually very rapid at room temperature due to quantum tunnelling and other effects, so optical activity is less. Indeed, look into things like the ammonia clock. Phosphines (the phosphorous equivalent of amines) are more configurationally stable.

[ramboacid]

Oh ok, I see your point about sparteine. And if the three substituents are unique but not attached to each other like in methylethylamine (but unlike in a ring) then the lone pair can switch sides as the molecule undergoes spontaneous inversion. However, if the nitrogen is in a simple ring structure (say something like a cyclohexane molecule with an NH replacing a CH2 in the ring), would that impose enough steric restriction on the lone pair so that the nitrogen can't invert and change configurations? Or does there need to be serious steric restriction like in sparteine?

[AWK]

In 1976 two oxaziridines with stereocenter at nitrogen was solved by X-ray.
It was published in Tetrahedron letters page 1025-1028 (my publication) and Chemical Communications page 60-61.

[Dan]

However, if the nitrogen is in a simple ring structure (say something like a cyclohexane molecule with an NH replacing a CH2 in the ring), would that impose enough steric restriction on the lone pair so that the nitrogen can't invert and change configurations? Or does there need to be serious steric restriction like in sparteine?

There has to be a serious steric restriction. In addition to aziridines, azetidines can also show slow inversion - the small ring size disfavours the trigonal planar transition state of the inversion.

I asked my teacher and she said that only carbon atoms can be chiral stereocenters, but she didn't have a good explanation for why.

Your teacher was bluffing (hence no explanation), complete rubbish. While amines can be chiral at N in some special cases as discussed here, quaternary ammonium salts can be chiral at N and do not invert. Sulfoxides and phosphines can be chiral at S and P respectively, and have a high barrier to inversion. Chiral sulfoxides are quite common in asymmetric catalysis as ligands or auxiliaries, and there are some phosphine ligands that are chiral at P (for example, QuinoxP). Transition metal complexes can be "chiral-at-metal" as well, for example Ru(bipy)₃²⁺ has a chiral centre at Ru and can be resolved.