Total angular momentum of electrons For spin-1/2 particles (like electrons), is there a limit of their total angular momentum? Since J = L + S, (I'm imagining the vector model of the atom), if L is really large, could electrons have very large total angular momentum J? Thanks!!
 A: Angular momentum is defined as :

In three dimensions, the angular momentum for a point particle is a pseudovector $r × p$, the cross product of the particle's position vector r (relative to some origin) and its momentum vector;

So by definition, if momentum can be infinite so can angular momentum. Electrons, though quantum mechanical particles, when free in space can have as large an angular momentum as their momentum defines, for a given (x,y,z) in space.

Since J = L + S, (I'm imagining the vector model of the atom)

This is a quantum mechanical solutions of the electron in a potential well . The S is given by the electron, the L by the quantum level of the solution. Qualitatively the size of the potential will limit the number of energy levels which are occupied by electrons, but as all numbers entering the problem are limited by the number of charges of the nucleus, the total angular momentum J levels cannot have a very large L.
For example:

High-resolution grating and Fourier transform spectroscopy measurements, using hollow-cathode and electrodeless discharge lamp sources, have resulted in a list of 92 000 lines of U I and U II.

Many lines, L limited .
As the possibility of getting very heavy nuclei is limited by the forces that hold a nucleus stable, one can safely say that L at the atomic level is limited .
