Motion of electrons in orbitals and shape of orbitals

[AudioFlux]

Why don't electrons move only along the surface of orbitals?
Moreover, how do electrons move within orbitals, random movement or do they follow a definite path?
In a p-orbital, does one lobe consist of only one electron?
Why is the p-orbital dumbbell shaped and not spherical?

 

[BruceW]

The true physical reality of atoms is described by Quantum Mechanics.
The concepts of position and momentum are different in quantum mechanics. Think of the position as being spread out in space. (Not technically true, but its a good way to describe it). So the electron doesn't go round in a specific path.
If you've seen a picture of the p-orbital, it likely represents a single electron, with a particular magnetic quantum number. If you average over all possible magnetic quantum numbers, then the p-orbital is spherical.

 

[AudioFlux]

If you've seen a picture of the p-orbital, it likely represents a single electron, with a particular magnetic quantum number.

But doesn't each orbital represent the electron cloud of two electrons?

If you average over all possible magnetic quantum numbers, then the p-orbital is spherical.

If you average all the magnetic quantum numbers, won't you get 0?

So the electron doesn't go round in a specific path.

If the electron does not go around the nucleus in a circular path, won't it come crashing to the nucleus?

 

[Mike H]

Why don't electrons move only along the surface of orbitals?
Moreover, how do electrons move within orbitals, random movement or do they follow a definite path?
In a p-orbital, does one lobe consist of only one electron?
Why is the p-orbital dumbbell shaped and not spherical?

The representation of atomic orbitals in terms of their electron densities just tells you that the majority of said electron density is mostly localized within that volume - not that the electron is bound to the surface contour that is plotted.

Strictly speaking, an orbital is a one-electron wavefunction.

To (over)simplify the discussion, an electron in a p orbital has non-zero angular momentum. When one works through the math for this case, you get the dumbbell-looking electron density.

If the electron does not go around the nucleus in a circular path, won't it come crashing to the nucleus?

Welcome to quantum mechanics. Classical reasoning breaks down here. The notion that electrons "orbit" the nucleus is incorrect.

 

[BruceW]

But doesn't each orbital represent the electron cloud of two electrons?

It can represent one or two electrons. This is due to a property of the electron called intrinsic spin.

If you average all the magnetic quantum numbers, won't you get 0?

No, you can have an electron which is in a quantum superposition of all the possible magnetic quantum numbers for the p-orbital, and the wavefunction describing this particle will be symmetric. (not dumbell shaped.)

If the electron does not go around the nucleus in a circular path, won't it come crashing to the nucleus?

Nope. Classical physics < Quantum physics :)

 

[tex43]

"If you average over all possible magnetic quantum numbers, then the p-orbital is spherical".


Surely for a p-orbital with an orbital angular momentum quantum number of 1 the wavefunction describes a dumbell shape. In order for the wavefunction to descibe a spherical orbital the orbital angular momentum quantum number must be 0.
If a p-orbital were indeed spherical almost all of the chemistry associated with multiple bonds would be difficult to explain.