# Electrons in atoms

1. Dec 23, 2004

### rgshankar76

Do the electrons revolving around the nucleus have a current associated with them?

2. Dec 23, 2004

### dextercioby

Yes of course.
The charge curent is
$$j^{\mu}(x^{\mu})=-e\bar{\Psi}_{\alpha}(x^{\mu})}(\gamma^{\mu})^{\alpha}\\_{\beta} \Psi^{\beta}(x^{\mu})$$
,where Psi bar and Psi are solutions of the Dirac equations for a Coulomb potential.Compute this 4 vector and compare to the one found for a free Dirac field.

Daniel.

PS.Chose the Dirac-Pauli representation of the Clifford algebra.

3. Dec 23, 2004

### DaveC426913

Except - of course - that electrons haven't "revolved" around the nucleus in almost a hundred years now...

4. Dec 24, 2004

### Louis Cypher

Re: clouding the discussion

And of course its a cloud, and we cant be sure of its energy state, and that its so fantastically complicated we've only produced clouds for the most basic elements, apart from that it's fine:-)

5. Dec 24, 2004

### pervect

Staff Emeritus
You should say "the orbital angular momentum of electrons causes them to have an orbital magnetic dipole moment, just as if they were revolving around the nucleus.

It's OK to say that electrons have orbital angular momentum, (see for instance

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qangm.html

but it's in questionable taste to say that they actually revolve. (You can get away with saying they act as if they revolve if you don't actually say that they revolve, though). Similarly, it's OK to say that an electron iin free space has momentum, it's questionable to say that it is "moving" or has a "velocity" (well, sometimes you can get away with saying that an electron in free space has a velocity, but other times someone will complain when you say that).

Hope this helps :-)

6. Dec 28, 2004

### ConcealedDreamer

I was told that the electron can be a particle or frequency around the nucleus