In the last lesson we covered the quantum numbers, which describes individuals electrons and where they are located. In this lesson we will now look at how to represent the electrons of atoms and elements as a whole.

When representing the electrons of atoms and elements we must first determine how many electrons are present. We can determine this information from the atomic number in the periodic table. Although this number represents the total number of protons present in an atom it also represents the number of electrons in neutral atoms. Since the number of protons and electrons will be equal. If we have an ion we can still use the atomic number, but we have to add or subtract the additional or missing electrons.

For example, if we wanted to find the number of electrons in magnesium we would begin by determining Mg’s atomic number from the periodic table. Since it has an atomic number of 12 it has that many electrons since it is a neutral atom. If on the other hand, we wanted to represent Mg^{2+} we would need to subtract two electrons from magnesium’s atomic number. So Mg^{2+} would end up with a total of 10 electrons.

After we have determined how many electrons we have we will then determine what shells and subshells these electrons can occupy. This information is also pulled straight from the periodic table and follows the block and row organization.

For Mg we will count all of the shells and subshells up to the element. In this case we would have 1s, 2s, 2p, and 3s.

Next up we need to determine how many electrons can fit in each shell. This is wholly dependent on the shape of each sub-shell and the number of orbitals it contains. An s sub-shell has one orbital and therefore 2 electron spots. P sub-shells on the other hand have 3 p-orbitals and therefore 6 electrons spots. D sub-shells 5 d-orbitals and 10 electron spots and f sub-shells 7 f-orbitals and 14 electron spots. So long as you can remember that s has 2 electron spots you can add 4 to find the number of electron spots per successive sub-shell.

So in Mg we have 4 subshells with 6 orbitals and a total of 12 electron spots. We can demonstrate this by drawing lines to represent each orbital. We place large spaces between each individual sub-shell so we can determine which is which.

We can think of all of these shells, sub-shells, and orbitals like a housing complex for electrons. Each floor is a shell, each wing a sub-shell, and each individual room an orbital. Electrons want to be in the lowest energy state possible. Or if we are going with our apartment complex analogy no one wants to constantly walk up multiple flights of stairs. So when electrons begin to fill up the available orbitals they will start with the lowest shell or the first floor that has openings.

For Mg, the electrons would start by pilling into the lowest energy shell, which is 1s. There are only two spots on this floor though so the apartment complex spots fill up super quickly. It is onto the next floor then where both the 2s and 2p shell fill up. Then the next floor where the last two electrons fill the 3s shell. This idea of filling the lowest energy shell first is called the **Aufbau principle **and electrons will always fill the lowest energy shell that has room first.

Ions like Mg2+ will also follow the Aufbau principle, but here the 3s shell would be empty since it only has 10 electrons.

While little electron apartment complexes are cool we won’t be drawing them on the MCAT nor do chemists. Instead, we will represent each orbital by a line and each electron in that orbital as an arrow. We can’t just plop electrons in willy nilly though. They have a specific order and way they must be arranged.

First, electrons don’t want to share a room so they won’t unless they have to. This means that we will start by filling in each line with one arrow before adding another to the mix. So if we have 3 electrons and a p-subshell then each electron will fill its own p-orbital. This idea is called **Hund’s rule **so make sure you put one arrow in every available line prior to adding a second one.

When electrons do double up they will only double up in specific ways. Electrons are picky and only tolerate other electrons with opposite spins. Again going back to our analogy electrons only want to pair up with electrons on opposite schedules this way they will minimize their interaction with one another. So when we place a second electron into an orbital its arrow must always point in the opposite direction. The first electron always starts with spin up so the first arrow must always point up and therefore the second will always point down. Taken together these ideas are called the **Pauli Exclusion Principle** because once you have an up arrow all other up electrons are excluded from that room.

- Find the total number of electrons
- Determine the shells they can occupy
- Fill the lowest energy shells first (Aufbau Principle)
- One to a line (Hund’s Rule)
- Alternate arrows (Pauli Exclusion Principle)
- Use all the electrons up

Lines and arrows are better than apartment complexes, but still a bit unwieldy especially when we get to atoms with 10+ sub-shells to fill. So we can use electron shorthand to represent our atom as well. Here we start by stating the shells and sub-shells and using a superscripted number to define how many electrons are in each.

For example with Mg would be represented as Mg 1s^{2}2s^{2}2p^{6}3s^{2} and the Mg^{2+} ion as Mg^{2+} 1s^{2}2s^{2}2p^{6}.

Even still this notation can get a bit out of had when we get into the elements further down into the periodic table. As a way of shortening this even further, we can use noble gas notation. Here we will only represent the **valence electrons **of an atom or the electrons in the outermost shell using electron shorthand. For the rest of the electrons, they will be replaced by the nearest noble gas above the element of interest.

For example, the noble gas above Mg is neon (Ne) so [Ne] will replace all of the shells except for 3s giving Mg an electron configuration of Mg[Ne]3s^{2}. Mg^{2+}‘s electron configuration is [Ne] on the other hand since it has the electron configuration of a noble gas (Mg^{2+}[Ne]).

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