HS Chemistry - Essentials

Electrons, Energy Levels, & Atomic Orbitals

Overview of The Page

This page will cover:

• Where do electrons reside in the atom?
• How do electrons fill up their energy levels?
• What is an atom's electron configuration? What is an atom's box notation?

Atoms are made up of three subatomic particles: protons, neutrons, and electrons.

Electrons are different from protons and neutrons. While the protons and neutrons reside in the nucleus of the atom, the electrons orbit the atom in shells. Electrons are also really tiny compared to protons and neutrons - so small that when calculating atomic mass, electrons have a mass of 0 amu, compared to 1 amu for protons and neutrons $electrons aren't actually massless, they just have a really tiny mass$.

There are 7 electron shells surrounding the nucleus in which electrons are found. The 1^st shell is the innermost shell, closest to the nucleus, and the 7^th shell is the outermost shell, furthest from the nucleus. Not all atoms have all 7 electron shells, however. As the number of electrons increases, so does the number of shells. This means that atoms with a lower atomic number have fewer electron shells. For example, Helium, which is in the 1^st period of the Periodic Table, has only one electron shell. Similarly, Iodine, which is in the 5^th period of the Periodic Table, has five electron shells. The number of electron shells an atom has can be determined from the period number.

Furthermore, each electron shell is made up of subshells. Each subshell contains orbitals, and each orbital contains two electrons.

There are 4 types of subshells. In order from lowest energy level to highest energy level, they are:

• The s subshell
• The p subshell
• The d subshell
• The f subshell

Each of these contains a different number of orbitals:

• The s subshell contains 1 orbital.
• The p subshell contains 3 orbitals.
• The d subshell contains 5 orbitals.
• The f subshell contains 7 orbitals.

However, just as not every atom contains all 7 shells, not every shell contains all 4 subshells:

• The first shell contains the s subshell.
• The second shell contains the s and p subshells.
• The third shell contains the s, p, and d subshells.
• The fourth shell contains the s, p, d, and f subshells.
• The fifth shell contains the s, p, d, and f subshells.
• The sixth shell contains the s, p, and d subshells.
• The seventh shell contains the s and p subshells.

The maximum number of electrons that a shell can hold is 2x², where x is the number of subshells in that shell.

Note that x is not a formally used variable, and is just used for instructional purposes.

Aufbau Principle

Although every shell contains its respective subshells, not every atom has electrons in those subshells.

For instance, take Lithium. It has 3 electrons. First, electrons will go into the first shell. Since the first shell contains only the s subshell, and the s subshell has one orbital, the first shell will contain 2 electrons. Then, electrons will go into the second shell. The second shell contains the s subshell, which has one orbital, and the p subshell, which has three orbitals. With a total of four orbitals, the second shell can contain a maximum of 8 electrons. However, since there is only 1 electron remaining, that electron will go into the second shell's s subshell, rather than the p subshell.

If we take Beryllium, which has 4 electrons, the electrons will first go into the first shell, leaving two electrons for the shell. Then, those two electrons will go into the second shell's s subshell, completely filling it up, rather than the p subshell.

If we take Boron, which has 5 electrons, the electrons will first go into the first shell, then into the second shell's s subshell, leaving 1 electron, which will then go into the second shell's p subshell.

The electrons went into the second shell's s subshell, which has a lower energy level, before going into the second shell's p subshell, which has a higher energy level. This is because of the Aufbau principle: electrons will fill lower-energy subshells before they fill higher-energy subshells. However, this does not mean that each shell is completely filled up before moving on to the next shell.

The order in which electrons fill up subshells can be shown using the following diagram:

This diagram is cross-hatched to show the order in which electrons fill up subshells:

As can be seen from the diagram, after the 3p subshell is filled, the electrons first go into the 4s subshell, then the 3d subshell. Similarly, after the 6s subshell, the electrons fill up the 4f subshell, then they go into the 5d subshell, then they go into the 6p subshell, and then they go into the 7s subshell.

The shape of the Periodic Table also matches up with this. If we mark the elements on the Periodic Table to match their highest energy level subshell:

We can see that the Transition Elements in the middle all have a d subshell as their highest energy level subshell, and the Lanthanide and Actinide series at the bottom have a f subshell as their highest energy level subshell.

We can also use this information to show how the electrons are distributed in an atom.

Electron Configuration

The electron configuration of an atom shows how the electrons are distributed in an atom. It shows which subshells are in an atom, and how many electrons each subshell has.

For instance, take Calcium $Ca$, element 20:

It has 20 electrons. In accordance with the Aufbau principle, first the 1s subshell will be filled with two electrons. To write the electron configuration, we first write the shell number, then the subshell letter, and then the number of electrons occupying that subshell as a superscript:

Electron configuration of Calcium $Ca$ so far: 1s²

At this point, we still have 18 electrons remaining. The 2s subshell will be filled with two electrons:

Electron configuration of Calcium $Ca$ so far: 1s²2s²

At this point, we still have 16 electrons remaining. The 2p subshell will be filled with six electrons:

Electron configuration of Calcium $Ca$ so far: 1s²2s²2p⁶

At this point, we still have 10 electrons remaining. The 3s subshell will be filled with two electrons:

Electron configuration of Calcium $Ca$ so far: 1s²2s²2p⁶3s²

At this point, we still have 8 electrons remaining. The 3p subshell will be filled with six electrons:

Electron configuration of Calcium $Ca$ so far: 1s²2s²2p⁶3s²3p⁶

At this point, we still have 2 electrons remaining. The 4s subshell will be filled with two electrons:

Electron configuration of Calcium $Ca$ so far: 1s²2s²2p⁶3s²3p⁶4s²

Now we have 0 electrons remaining. The complete electron configuration of Calcium is 1s²2s²2p⁶3s²3p⁶4s²

We would follow the same process if we were writing the electron configuration for an element that didn't completely fill up one of its subshells, as well as for an element that had electrons in a d subshell. For example, take Zirconium $Zr$, element 40, with 40 electrons:

It has two electrons in the 4d subshell, so it satisfies both these conditions. Its electron configuration would be:

Electron configuration of Zr: 1s². 38 electrons remaining.

Electron configuration of Zr: 1s²2s². 36 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶. 30 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶3s². 28 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶3s²3p⁶. 22 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶3s²3p⁶4s². 20 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰. 10 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶. 4 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s². 2 electrons remaining.

Electron configuration of Zr: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d². 0 electrons remaining.

Thus, Zirconium's electron configuration is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d².

But this takes quite a while to write out. It would take even longer if we had to write out the electron configuration of an element like Uranium $element 92$.

Fortunately, there is a shorter method of writing electron configurations, called the shorthand electron configuration. It takes the electron configuration of the largest noble gas with less protons than the element, and adds the remaining electron configuration.

For Zirconium, the largest noble gas with less protons than Zirconium is Krypton $Kr$:

Krypton's electron configuration is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶.

Zirconium's electron configuration is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d².

Zirconium's electron configuration is very similar to Krypton's electron configuration. The only difference is that Zirconium has 5s²4d² added at the end. Therefore, instead of writing the full electron configuration of Zirconium, we can just write:

Zirconium's shorthand electron configuration: [Kr] 5s²4d²

This is much quicker than writing the full electron configuration. This can also work for larger elements, like Uranium.

Box Notation

Electron configuration shows how the electrons are distributed among the subshells, but box notation can take it one step further.

Box notation shows how the electrons are distributed in the orbitals by showing electrons as arrows. For example, the box notation for Argon $Ar$, element 18, is shown below:

Each orbital is a box. As can be seen, a box by itself represents an s subshell, and three boxes joined together represent a p subshell. Similarly, five boxes joined together would represent a d subshell. It is, however, difficult to determine shell numbers this way, unless one labels them like in the diagram below:

There is also a shorthand method for writing box notations. It follows much the same rules as the shorthand method for writing electron configurations. For example, the box notation for Calcium (Ca)\, element 20, is shown below:

The shorthand box notation for Calcium $Ca$ would be:

Note that the subshell labels underneath the boxes are not necessary.

Finally, it should be mentioned that the reason why the arrows point in opposite directions inside a box is because electrons in the same orbital move in opposite directions.