What is the noble gas shorthand?

It is a shortcut to avoid writing out long configurations. You write the symbol of the nearest noble gas that comes before your element in brackets, which accounts for all the core electrons, and then you only write the valence (outer) electrons that come after it. For example, Sodium is [Ne] $3s^1$.

How do I write an electron configuration for an ion?

For a negative ion (anion), add the extra electrons to the next available orbital. For a positive ion (cation), subtract electrons. Just remember to remove them from the highest principal energy level (highest $n$) first.

Why does $4s$ fill before $3d$?

Because energy levels overlap as they get further from the nucleus. The shape of the s-orbital allows its electrons to spend a little time very close to the nucleus, making the overall energy of the $4s$ state slightly lower than the $3d$ state in neutral atoms.

How do you write an electron configuration?

Writing an electron configuration means mapping out exactly where every electron in an atom lives. You do this by filling energy levels and subshells in a specific order, starting from the lowest energy level closest to the nucleus and working your way out. Think of an atom as a hotel for electrons. The floors are the energy levels, the types of rooms are the subshells (labeled s, p, d, and f), and the beds are the orbitals. To write the configuration, you just count the electrons and fill the "hotel rooms" following a few basic rules.

The Three Rules of Filling

To get the configuration right, you need three rules. The Aufbau principle states that electrons fill the lowest energy orbitals first (floor 1 before floor 2). The Pauli exclusion principle says that each orbital can hold a maximum of two electrons, and they must have opposite spins. Finally, Hund's rule tells us that when electrons fill a subshell with multiple orbitals (like the p subshell, which has three), they spread out first. One electron goes into each empty orbital before they start pairing up.

The Subshells: s, p, d, and f

Every floor (energy level, $n$ ) has a certain number of room types (subshells). The $s$ subshell has 1 orbital and holds up to 2 electrons. The $p$ subshell has 3 orbitals (up to 6 electrons). The $d$ subshell has 5 orbitals (up to 10 electrons). The $f$ subshell has 7 orbitals (up to 14 electrons). You write them by listing the energy level, the subshell letter, and a superscript for the number of electrons, like $1s^2$ .

Reading the Periodic Table

You do not need to memorize the filling order; the periodic table is a cheat sheet. The first two columns are the s-block, the right six columns are the p-block, the middle transition metals are the d-block, and the bottom two rows are the f-block. By reading the periodic table from left to right, top to bottom, you can track exactly which subshell is filling up at any given atomic number.

Where Students Slip Up

The biggest trap happens when the d-block starts. The $4s$ subshell is slightly lower in energy than the $3d$ subshell, so $4s$ fills first. However, when atoms like Iron (Fe) lose electrons to become ions, they actually lose their $4s$ electrons before their $3d$ electrons. Another common slip is forgetting the exceptions: Chromium (Cr) and Copper (Cu) borrow an electron from the $s$ subshell to make their $d$ subshell half-full or completely full, because that arrangement is more stable.

Worked through

Write the full electron configuration for a neutral atom of Oxygen (O).

First, find Oxygen on the periodic table. Its atomic number is 8, which means a neutral atom has 8 electrons. Step 1: Start at the lowest energy level. The first shell has only an s subshell, which holds 2 electrons. This gives us $1s^2$ . We have 6 electrons left. Step 2: Move to the second energy level. The $2s$ subshell fills next with 2 electrons. This gives us $2s^2$ . We have 4 electrons left. Step 3: Move to the $2p$ subshell. The p subshell can hold up to 6 electrons, but we only have 4 left. So, we put all 4 into this subshell, writing it as $2p^4$ . Putting it all together, the full electron configuration for Oxygen is $1s^2 2s^2 2p^4$ .

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Where this comes from: OpenStax Chemistry 2e, Chapter 6: Electronic Structure and Periodic Properties of Elements · Khan Academy, Unit: Electronic structure of atoms