*NOTE: I forwarded it to this question to my son who’s a theoretical quantum physical chemist.
No, I don’t understand half of what he said either.*
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*I went to a local tutor last Saturday to ask some of these questions, but though she gets good grades in her college chem classes, these were things that had never really come up.
Atoms are often depicted as being basically round, but the shapes of the actual orbitals are mostly not. I’m assuming you’ve seen diagrams of p or d orbitals.
- Are all orbitals in “shell 4” really of a similar energy? If so, why do they fill so far apart, like the 4s and the 4d? Isn’t the energy shell number really more of a bookkeeping method?*
In the ideal one-electron atom, such as Hydrogen, positronium, or He+, all orbitals of shell N are exactly the same energy. Thus the hydrogen 2p is exactly the same energy as the hydrogen 2s.
In a multi-electron atom this is not true. First electron repulsions raise the energy of any shell already occupied. Thus although the Carbon 2px, 2py, and 2pz are in the same energies when empty, the electrons preferentially singly occupy shells. Second, there is an energy called exchange. This comes from pure quantum mechanics and raises the energies of antiparallel spin. In other words, if the first p in carbon is spin up, chances are the second is also. Together those two effects cause something called Hund’s Rule.
The last effect is one called electron screening. Electrons orbiting behind another shell do not experience the full nuclear attraction as they are being repelled by the electron in their way. Subshells with higher order angular momentum have an average distance from the nucleus greater than those of lower order. The 2p orbital shoots out beyond the 2s for example. Because this orbital is extending through an already occupied orbital, it is destabilized by the screening. Classically, the same effect happens when you stick a magnet oriented the wrong way in between two magnets that attract. They don’t stick together as strongly, because the magnet in the middle exerts a force that is pushing them apart. “Similarly”, the repulsion of an inner electron forces the outer electron to spend more time in the farther extent of the orbit, although, in the quantum world, my professors would kill me for making such a statement. This lowers the attractive forces of those upper level electrons, and it raises the energy level of the higher subshells. The 3d electrons are so screened by the 3s and particularly the 3p electrons that the energy level is bumped above the 4s. In an ion however, where the nuclear charge is greater, the s electrons are often emptied first, as the loss of an entire shell is a more favorable configuration than some s and some d.
There are also relativistic contractions dealing with the electrons in higher order elements “orbiting” so fast, that they approach the speed of light. This “contracts” certain shells and make it harder to ionize electrons from them. Thus thallium often has a +1 state, where it loses its p electron, but not its s. Relativistic contraction is somewhat complicated, and predicting it is a matter for upper level inorganic.
2. Do the electrons fill the entire space of the orbital, or do the stay close to the surface of the “balloon” (as the orbitals are often kind of shown)? Her book seemed to show that they fill the space.
Whether an electron fills space or occupies the surface of a balloon is a difficult thing to say in quantum mechanics. An orbital is a line of isoprobability, so for example an electron in the 1s state has a 90% probability of being somewhere in the 1s orbital. In that sense electrons fill space. We can go further and say that there is more of a chance it is in this part or that part. But it’s not really filling space in the same way that ketchup fills a bottle.
*3. Her book also said that the reason the 4s orbital fill before the 3d is that it “allows closer penetration of the electron to the vicinity of the nucleus.” Why is that? *
This is as I said. If you integrate a distance function across the 4s and 3d, you will find that the 4s electron is closer to the nucleus on average than the 3d electron. This doesn’t mean that the 4s orbital is actually closer, but it does mean there is more likely to be interference between the 3d electron and electrons from more inner orbitals. So the screening will be higher.
4. Are all these orbitals intersecting each other? The 4p must be running through all fouelonr s orbitals, just for one example.
You are quite right. Orbitals intersect. But the electrons don’t crash into each other.
5. Are electrons considered to be point charges that have variable paths, or are they so small that the de Broglie wave function literally makes their location spread out? I thought the wave function meant that the point charge had a variable path and that the “charge cloud” nomenclature was a way of describing it in practical terms, as that’s how it acts in human perception.
Both are true. An electron is a point charge in that it doesn’t have any physical volume. Experiments designed to measure the “Cross-section” of an electron report that they take up as little space as could possibly be described.
However a moving electron is quite literally smeared over an area. One can do a position measurement on it and nail down where it is, but trying to measure any property afterwards will smear out the electron again. This is not just a human perception thing. Electrons are waves. We can refract and focus them just like light or sound waves. And they interfere with each other and form ripple patterns on screens, like water does on a pond. The charge cloud is what an electron physically does. It is physically tangible.
At the same time if I bounce particles off of it, they will interact with the electron in the charge cloud as if it were a point particle. Quantum Physics is disconcerting.
- How do Americans pronounce de Broglie? Even the internet has failed me on this one.
Something like Dee Bray. French is weird.