Understanding S-Orbital When l = 0

[mendes]

Hello,

When the azimutal quantum number l = 0, for the s-orbital, the orbital momentum itself is 0, as it is proportional to l(l+1), so how can we understand this ? Is the electron not orbiting around the nucleu or what ? :) Thanks

 

[Simon Bridge]

In general electrons do not orbit nuclei - this is a discarded model.

 

[mendes]

In general electrons do not orbit nuclei - this is a discarded model.

Ok, but how could we understand the fact that the orbital momentum is zero ?

 

[MSLion]

Quantum mechanics is just different, there are purely quantum effects you cannot understand in terms of classical mechanics.
You cannot think of the electron as orbiting, as someone already pointed out. It is delocalized around the nuclei.
As long as you do not try to picture the electron as a planet going around the sun on a planar orbit, there is no paradox.

 

[Simon Bridge]

What he said - the electron does not need any angular momentum as it is not orbiting.

You can understand electron angular momentum in terms of the available interactions. The behavior of an electron in an atomic bound state includes some terms in the math which look like those that are used in classical mechanics to describe angular momentum and spin. The name is a hold-over from the Bohr model. It's like I know a guy whose name is Carpenter, but he isn't a carpenter. However, one of his ancestors was. His name is a hold-over from that time.

What this means, if anything, depends on what you want to do.

I know this makes things difficult to think about at first - you keep wanting to think of an electron as a kind of very small ball doing something, but that's not how it works. Don't worry, you'll get used to it.

 

[Darwin123]

Ok, but how could we understand the fact that the orbital momentum is zero ?

There is a classical approximation of quantum mechanics referred to as stochastic electrodynamics (SED). The major hypothesis of is that the universe is filled with background of classical electrodynamic radiation that has a Lorentz invariant spectrum. The electromagnetic modes of the zero point radiation have random phases. It is this background, sometimes referred to a zero point radiation, that causes many of the effects thought of as quantum mechanical.
The "randomness" of motion is caused by the randomness of the phase of the electromagnetic modes. This is an entirely classical model. The electron is a particles and the electromagnetic radiation is a fluctuating continuous field.
In the SED, the ground state of an electron caused by an exchange of energy between the mechanical energy of the electron and the zero point radiation. The electron loses mechanical energy through radiation damping but absorbs energy due to absorption of zero point radiation.
Even the ground state spin of the electron can be explained by visualizing the electron as a finite sphere with electric charge distributed. The spin is also caused by the zero point radiation.
The ground state of the hydrogen atom can't be thought of as a Keplerian orbit in the usual sense. The motion of the electron is being forced by the zero point radiation. The zero point radiation causes essentially random motion. Hence, the expectation value of the angular momentum of the ground state is zero.
SED has turned out to be only an approximation of quantum mechanics. However, it is probably the best way to "visualize" the motion of the ground state in classical terms.