# Electron Orbitals

#### Misha Kuznetsov

Hello,

At first, I wasn't sure why p-orbitals are shaped as they are. I looked through the posts of others here and it makes some sense now. My understanding is that they are dumbbell shaped because electrons repel from each other and are attracted by the nucleus.

Then why is an s-orbital spherical? If there are two electrons in it, wouldn't they repel and also make more of a lobed shape?

I have a guess though: do electrons pairs act as one particle with double the charge? That would seem to make sense.

Thanks

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#### Khashishi

The shape of orbitals are more based on convenient mathematics than reality. Actual images of electron densities usually look spherical. http://io9.com/the-first-image-ever-of-a-hydrogen-atoms-orbital-struc-509684901
Spherical harmonics are just a choice of basis functions for deconstructing an arbitrary function over the surface of a sphere, similar to how a Fourier series lets you deconstruct an arbitrary periodic function into sinusoidal components. The quantum numbers n and l are not arbitrary--they actually affect the atom's energy. But the m quantum number is arbitrary since it depends on choice of coordinates. You can't actually get a dumbbell shape unless you have something to establish a "z" direction in your atom (such as an external magnetic field). If you average over possible "m" values, you get back a spherical distribution.

The lobed shape of the p orbital has nothing to do with electrons repelling each other. It's just the shape of the spherical harmonic #Y_1^0#

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#### blue_leaf77

Homework Helper
I have a guess though: do electrons pairs act as one particle with double the charge? That would seem to make sense.
They are connected through the repulsion force between them but they have their own degree of freedom. If you want to know more about two electron system, you can easily find materials on the Helium atom.

#### Misha Kuznetsov

This is directly from the forum I read on: "So the placement of electron orbitals is determined by the conflicting requirements of electrons to get close to the nucleus, but far from each other."

If the same quantum microscope was somehow used on carbon, we wouldn't see dumbbell shaped orbitals?

#### Khashishi

The forum post sounds wrong (possibly taken out of context). The classic orbital shapes are defined for hydrogen, which has just one electron.
If you looked at carbon under a quantum microscope, you would see a bigger spherical electron cloud than hydrogen. You can't distinguish the different electrons, so you can't look at the orbital of a single electron in the cloud. IF there was an external magnetic field to break the degeneracy in m, then maybe you could see some shape there. At sufficiently low temperature, you might see the "pancake" shaped p orbital with m=-1, not the dumbbell p orbital with m=0.

If the temperature is higher than the energy spacing between the m states, then the m states will be scrambled and it will look spherical again.

#### blue_leaf77

Homework Helper
I guess that post was referring to the presence of potential barrier due to the angular momentum of electron.

#### Misha Kuznetsov

Ok, thank you. This has helped a lot

#### Nugatory

Mentor
This is directly from the forum I read on: "So the placement of electron orbitals is determined by the conflicting requirements of electrons to get close to the nucleus, but far from each other."
Where exactly did you read this? Physics Forums has a rule requiring that sources be properly cited; otherwise we have no way of knowing whether you've misunderstood what you've been reading or whether your source is just plain wrong.

Mentor

#### blue_leaf77

Homework Helper
Lol, that's what you get when someone forces the intuition of everydaylife into an atomic world, although it may work for those who are only interested in the practical parts of QM. For instance you don't even need an "atom" to observe the angular distribution exhibited by the spherical harmonics, for example see the toy problem 'spherical well'. Whenever the system has a radial symmetry, the angular distribution in that system will very likely be represented by spherical harmonics.

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