Quantum Mechanics! Electrons in s-orbitals.

According to my chemistry book, electrons in s-orbitals are the only ones which can “penetrate” to the nucleus, because they have no angular momentum. Electrons in p, d, f, etc orbitals cannot “penetrate” to the nucleus, because “Physically, electrons with angular momentum are moving around the nucleus, not toward it.”

So then how are electrons in s-orbitals moving? In straight lines? I dont understand how an electron in an s-orbital (or any orbital, for that matter) can move in anything other than a circle, and I dont understand how an electron would move in a straight line. But I cant think of how else it could move.

Any quantum-mechanically inclined Dopers out there who know the answer?

Bottom line is, we don’t know how electrons move in an atom. It’s really a mistake to think of them following any specific path. Electrons, like all subatomic particles, don’t have a location until we make a measurement. So they don’t follow a set path, much less a nice circular orbit, at all.

It’s better to think in terms of probability: How likely is it that I will find an electron this far away from the nucleus? A little further? Electrons in the s orbitals (again, the word “orbital” is a misnomer carried over from an incorrect model of the atom) are found within a spherical region centered at the nucleus. Their position and energy is described by a wavefunction, and it so happens that the probability density of the s orbital wavefunction has a peak at the center. What that means is, the likelihood of finding the electron is much higher at the center than further out.

Electrons in s orbitals don’t have angular momentum. Angular momentum comes in discrete packets of energy, and s orbital electrons don’t have enough energy to get even one packet. Electrons in all the other orbitals do have angular momentum. That doesn’t mean we can imagine a p-orbital electron spinning around the nucleus. Think of it as a p- or d- or f-orbital electron having too much energy to do anything but be barely contained by the nucleus near the outer edges of the fuzzy atom.

Thank you Spatial Rift 47 - of the many things I dont understand about quantum mechanics, the whole deal with angular momentum is one of them, and while I still dont understand it, what you wrote helps me not understand it a little bit less. If you are bored and feel like posting more stuff about quantum mechanics, please feel free.

The first thing you have to do is discard the usefulness of macroscopic analogies. Even in non s orbitals you can’t think of the electron as actually moving, because an accelerating charged particle would continuously radiate. (It’s true that you can say that the electron doesn’t radiate in this manner because it can only emit energy in quantas, but that’s really saying the same thing)

When you observe a non s electron it does have angular momentum, but even so you can’t think of it as moving between observations. Another strange unintuitive quantum fact is that when working with radial probabilities the effective potential is a function of the angular velocity even though the electron doesn’t actually move.

Also intrinsic angular momentum (spin) is sort of like what would occur if a charged sphere spun about its axis, but the electron is a point particle and therefore can’t spin. And even if you ascribed it a finite size (of Bohr radius) its surface velocity would have to exceed c.

This is true per unit volume, but the total volume is much greater at the Bohr radius and the radial probability actually peaks there, not at the nucleus.

Wow, was that ever a poorly written post please excuse me.

In fact ignore it completely-- Bohr radius for an electron?? May God have mercy on me.

Spatial Rift 47 gives a nice way of thinking about what electron orbitals are. I must nitpick and point out that s-electrons do have angular momentum (spin) even though they do not have orbital angular momentum.

If you have two 1s-electrons (say in a helium atom), then the whole system has a total angular momentum of zero, since neither s-electron has orbital angular momentum and their spins of opposite sign and equal magnitude (+/- 1/2) cancel.

Here is kind of a nice visualization tool for hydrogenic (single-electron) orbitals. You’ll see that p-, d-, f-… wavefunctions all have nodes at the nucleus (where r=0), because their wavefunctions contain powers of r (as well as exponential dependence on r that causes the wavefunction to decay at large distances from the nucleus). Therefore electrons in those states have zero probability of being coincident with the nucleus (or, ah, “penetrating” it).

In contrast, the r-dependence of s-orbitals appears only in the exponential term, which means they have a finite probability of overlapping the nucleus. They are, therefore, very effective at screening the nuclear charge from other electrons, if you care to start piling on electrons.

This is giving me flashbacks to 1998 when I was “studying” pchem (or rather, trying to flunk less badly then my peers, thereby earning a grade of “B”). I just wanted to say that I love all the people who responded here for taking the time to do so, and who were able to do so in a manner that was much more effective than my former professor.
There’s also something to be said for having almost ten years to ruminate on a subject and to understand it without being under the gun of a formal assessment of one’s understanding.
I love this place.

Yes, you are correct. There are two kinds of angular momentum: spin and orbital. S-orbital electrons have no orbital angular momentum, but any electron anywhere always has spin angular momentum of 1/2h-bar.

I believe the classical analogue of an s-orbital electron is something like this guy oscillating back and forth through the center of the earth. To echo other posters, this is a lame-ass analogy; what’s really happening is a wave function, or something nobody really understands that’s described by a wave function.

The amazing part, is that even decent professors make the mistake of trying to ascribe motion to electrons. While I was writing up my dissertation, I got into a debate over a specific mechanism that could either occure as a four electron process or a six electron process. Technically, four electron processes are not allowed (due to symmetry rules), but previous publications had allways described it as a four electron process. I then found a publication that demonstrated that the reaction could be a six electron process, but my old boss resisted because that’s not what had been published.

He then told me to have our computational chemist calculate which process was occuring. This can’t be done. Computers calculate the wavefunction of an electron in a system that is effectively stationary (Born-Oppenheimer approximation). There is no usefull way to calculate the “motion” of electrons. Mechanisms as we draw them in organic chemistry, are models that explain the behavior of systems but they have little relevance to reality. Electrons just don’t move like that.

illoe, that website is awesome. I greatly enjoy sticking it to the old hydrogenics - confuse me, will you? How do you like having principal quantum number 20? Take that! And that! And - hmm, that actually looks kind of cool.

And Christopher - I have no idea what you are talking about in most of your post, but I totally know what the Born-Oppenheimer approximation is! Which is exciting.

Most of this quantum mechanics stuff makes me wish I was oscillating back and forth in through the center of the earth, like the guy in coffeecat’s link. You would think, I have how many electrons in my body, doing this stuff all the time? Surely one of them would man up and figure out some way to explain it to me. But no. Alas. And so I must turn to the Straight Dope.

Thanks all!

My post was just a long winded way of stating that considering the motion of electrons on a molecular scale is only academic, and has no basis in reality. When considering electrons in a molecule, think of the shape of the wave-function and nothing else.

My specific example simply demonstrated that even the professionals get it wrong. Don’t fret it.

standard qm cannot answer that, but there is another well known interpretation- the de broglie bohm interpretation that would satisfy you. it is also called the pilot wave theory or bohemian mechanics. it is totally consistent with standard qm except for the interpretation part, for it highly deals with causuality and determinism without violating bells inequality.

anyway, the answer to your question according to it is that the electrons of s orbitals are at rest. there is a “quantum potential” (derived from Schrödinger eqn) that counters the nuclear attraction

Aaaiiieeee! Quantum zombies!