6 - Order of Atomic Orbitals
Abstract (TL;DR):
The arc on orbital chemistry ends with an explanation of two very important rules: the Aufbau Principle, which states that electrons must fill lower energy orbitals before filling higher energy ones, and Hund’s Rules, which state that (1) all subshells must be filled with one electron before being completed by an electron with an opposite spin and (2) the electrons that enter the subshells and half-fill them must have the same spin. Finally, we cover the specific order that electrons fill orbitals according to the Madelung Rule (or diagonal rule), which allows you to add both the principle and orbital quantum numbers (n + l) to determine what the lowest energy orbitals are (to satisfy the Aufbau Principle), and we explain that Noble Gases are unreactive because all of their orbitals are filled.
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Image by jimmymm-ilustra
Did you notice that the scale of what we discuss is getting bigger? However, no matter how large things get, there’s always going to be a ribbon to tie things up with. That’s the beauty of science having its gentle fingers on every pulse.
The ribbon around everything that we’ve discussed in the last 5 chapters is the Aufbau Principle, which describes the order of how electrons organize. Specifically, electrons seek stability according to the rules of the Pauli Principle, which states that there can only be two electrons in any one orbital.
In addition, the Aufbau principle, from the German word “build-up”, states that electrons must occupy the orbitals with the lowest energy before going into higher energy orbitals. That makes sense, right? Electrons have no need nor desire to be at a high energy level; if they can exist in a lower energy state, they will be.
The Building-Up
Before we begin, you might want to keep a periodic table handy.
Image via ScienceNotes
Building from chapter 4 and 5, the organization of each orbital conventionally takes the form of Principle-Orbital-Spin (n-l-s). The Aufbau Principle dictates that we start from lowest to highest energy level. As such, it’s surprisingly trivial to label these orbitals to see just how electrons organize themselves along the periodic table.
Image by William Reusch via Michigan State University
The first number, the Principle Quantum Number is what shows the energy level, and, thus, the electron shell of an element. If we are trying to occupy the lowest energy states first, we start with 1 – ground state energy. Next, the Orbital Quantum Number, the subshell number. Its lowest value is 0, corresponding to its label - s. Last, the Spin Quantum Number gives you whether one or both electron spins have been filled. The two spins - negative and positive - of each subshell must be filled before moving to the next subshell, which we designate as either 1 or 2, since we can’t tell which is “spinning” negatively or positively.
The unnamed Magnetic Quantum Number, the subshell orientation number, is necessary for telling how a subshell is filled by electrons. As a reminder, telling how many orientations there are is as simple as looking at the orbital quantum number and counting the spectrum from negative to positive. For example, if the orbital number is 0, there’s only 1 subshell. If it’s 1, there are 3 (-1, 0, 1).
The n-l-s system dictates that the lowest possible energy state is 1s1. This value is the numerical representation of an orbital. This particular orbital corresponds to hydrogen.
But remember, there are two electrons, "spinning" oppositely, per subshell. With the addition of the second electron, we hit 1s2. This state corresponds to helium.
Once all subshells’, and, therefore, the entire shell’s electrons have been filled, according to the Aufbau Principle, the next shell can be filled. We know that the next principle number, 2, marks an increase in energy states, which also means that the distance that electrons are from the nucleus increases. Ergo, the more energy electrons have, the more capacity they have to break away from the attractive forces of the nucleus.
With the increase in distance and the addition of even more electrons comes increases in possible electron configurations, resulting in not only new subshells, but also new orientations. Yet each orbital follows the Aufbau Principle. As such, you see an organization like the following picture.
This is an orbital diagram. Each arrow represents an electron and its spin.
Remember, p represents an orbital quantum number of 2. That means there’s a magnetic quantum number of 5, representing 5 subshells. Since the p orbital has three different orientations, each able to have two electrons, it allows for 6 electrons in total.
Image via PrintableDiagram
Attack of the Hund’s
When it comes to elements that have multiple orbitals orientations in a subshell, which is every element with a principle number of 2 or above, each orbital subshell must have one electron spin occupied before it is occupied with the electron with the opposite spin. This is one of Hund’s Rules, named after Friedrich Hund, a German physicist who frequently worked with Schrödinger and other quantum physicists during this time.
You could likely guess the reason for this rule’s existence now, but, just in case you haven’t understood the only motivation that electrons have yet, it is to reduce energy.
Two electrons grouping together in an orbital is already hard – the negative charges naturally repel each other. To reduce the effects of repulsion, the electrons inhabit the orbitals with similar energy levels first. Each spin direction has a similar energy level to an electron with the same spin. That means, since Pauli’s Principle prevents two electrons with the same spin from existing in the same subshell, each subshell will be filled with one spin direction before they are filled with the opposite spin. This is the second of Hund’s Rules.
This is why, in the above picture, instead of carbon (C)’s first 2p subshell being filled with an electron in the opposite spin, the second 2p subshell is filled with an electron (that has the same spin as the one in the first 2p subshell) instead. It is only when you get to oxygen (O) that the first subshell is filled with an oppositely-spinning electron.
Any orbital diagrams will show that electrons fill each orientation with the same upward spin before filling each orientation with the opposite downward spin. The necessity of having similar spin is based off the observed principle that like spins repel less.
A respectable analogy is something that you’ve likely experienced. Have you ever been reading a book at a library or bookstore with plenty of empty chairs dispersed around? How would you feel if, then, someone sits right next to you, occupying your space? Doesn’t that just feel wrong? Maybe a little inconvenient? How about if someone sat directly across from you. Now that would just be awkward; imagine you looking up from your riveting novel only to see a pair of peering eyes looking back at you. But, if all of the seats in the socially appropriate places are already taken, then there’s less of an issue with people taking the remaining seats next to or across from you. That’s, essentially, how electrons feel. They want to fill the empty, most distant seats before filling in the inconvenient seats.
For clarity, here is another orbital diagram with 36 elements. Notice Hund’s Rule being applied from boron (B) to neon (Ne) and from aluminum (Al) to argon (Ar).
Notice how here, the 2p orbital is divided into its three dimensional configurations, 2px, 2py and 2pz. Both ways of writing the 2p orbital are acceptable.
Image via Meta-Synthesis
Diagonal Rule
There’s one more curve ball that you should be aware of.
Electrons tend to fill orbitals in a unique, but organized way after the 2p subshell in most cases. When you get to the third principle number, you gain yet another subshell – the d subshell.
As we’ve said 1s1 is hydrogen and 1s2 is helium. With each element in the periodic table, the number of electrons within the system grows by one. But when you get to Argon (Ar) and move to Potassium (K), it goes from 3p to 4s. Why would we skip the 3d shell? After all, we went from 1s, to 2s-2p, then 3s-3p. Shouldn’t 3d come next?
There was a little factor that I purposely did not mention until this point. You can actually define the energy of orbitals by adding the principle quantum number and the orbital quantum number – n + l. This is called the Madelung Rule, which gives the order that orbitals are filled in. So, if we take hydrogen, for example, with an n of 1 and an l of 0, or s, we see that it has an energy level of 1, which is the lowest. Hydrogen and helium, technically, both fit into this 1s category, but we know that helium has two electrons, while hydrogen has only one. Therefore, helium has more energy in the system.
To belabor the point, it would be as if you had a solitary magnet on the table. It won’t move on its own until you put something of a similar pole near it, in which case it will move away. Electrons experience a similar reaction to each other, and therefore, the element itself is more energetic the more electrons there are.
But, returning to potassium (K), which has an n of 4 and an l of 0 (4s), it has an energy level lower than Scandium (Sc), which has an n of 3 and an l of 2 (3d). Potassium, which occupies the 4s orbital, has an energy level of 4, while scandium has an energy level of 5. Therefore, the 4s level is filled first.
This staggering creates a well-known diagonal. In fact, we can easily tell how to fill orbitals by following this Diagonal Rule.
Image via HyperPhysics
It’s simply amazing how we manage to organize something as chaotic as an electron. I suppose, however, that this is how they organize; we are just observers in this game, of which we are a sentient and thinking part.
There’s one more amazing thing that these orbitals reveal about the periodic table. It explains the Noble Gases.
The Noble Gases
Time for another callback. Remember in third article, when I mentioned noble gases and valence electrons? I said that noble gases were almost completely nonreactive.
Look at this periodic table.
Image via Chemistry LibreTexts
This puts a little more attention on the electron configuration. Do me a favor: take a look at the noble gas group, or the column most to the right.
Their orbitals are completely filled! There is not one spin arrow that is unaccompanied. You might have noticed that beryllium (Be) and magnesium (Mg) also fit this criterion. However, recall that every principle quantum number over 2 has a p or higher orbital. Those two elements, and all other elements in Group 2, don’t fill the p orbital, like neon and argon do in their respective rows.
Noble gases are nonreactive because there are no electrons required to complete their electron shells. Therefore, an element paired with a noble gas will lead to no result; there is no response to the phone call, as it were. Without space free for more electrons, there’s almost no way for elements to communicate.
If you look at your complete periodic table and the image of the orbital diagram used in the Diagonal Rule section, you can see this is the case for Argon (Ar) and Krypton (Kr) as well. Yes, Superman is from a very noble planet indeed.
Conclusion
With orbitals fully explained, you now have a basic understanding of modern atomic theory and, consequently, the Elemental Flow arc has come to its end. Now that you know what electrons are, in terms of how they move and organize themselves in an element, you are well equipped to understand how elements combine. In fact, I’ve already given you the answer to that. But, I suppose we will see soon, as we move with the flow eternal.