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Filling the Orbitals

Build any atom by dropping electrons into orbitals one by one, following a few simple rules: lowest energy first, no two electrons alike, and spread out before pairing up. This is the recipe behind every element.

One rule that changes everything

Here is the question this guide answers: if every electron would rather sit in the lowest-energy orbital, why don't all of an atom's electrons just pile into the n = 1 cloud together? The answer is a single, stern rule of nature — the Pauli exclusion principle: no two electrons in the same atom may have the same four quantum numbers. Each complete address (n, ℓ, m, spin) can be used by at most one electron. The lowest orbital fills, then electrons are forced upstairs, and that forcing is what gives atoms their layered structure.

Why this rule exists is deep: electrons belong to a class of particles called fermions, and fermions simply refuse to share a quantum state — it is built into the kind of thing they are. We will dig into the reason in the periodic-table guide. For now, take exclusion as the law of the land and notice its first consequence: since spin has two settings (up, down), each spatial orbital — each n, ℓ, m combination — holds exactly two electrons, one of each spin. Two, and never a third.

Aufbau — lowest floors first

To build an atom, add its electrons one at a time and always drop each into the lowest-energy orbital still available. This is the Aufbau principle — German for "building up." Like water filling a staircase from the bottom step, electrons settle into the cheapest seats first and only move higher when those are taken. The running tally of which orbitals an atom's electrons occupy is its electron configuration, written as a tidy list like 1s² 2s² 2p⁶ (the little numbers count electrons in each).

There is one twist that trips up beginners. In atoms with many electrons, the energy order is not simply 1, 2, 3 by shell, because electrons shield one another from the nucleus and shift the levels around. The upshot is that the 4s orbital fills before the 3d — the staircase has a couple of steps out of strict numerical order. There is a well-known diagonal chart for the exact order, but the principle never changes: always take the lowest energy gap available, whatever its label.

Hydrogen (1 electron):   1s1
Helium   (2 electrons):  1s2          <- 1s now full (2 max)
Lithium  (3 electrons):  1s2 2s1      <- third electron forced up to 2s
Carbon   (6 electrons):  1s2 2s2 2p2
Neon     (10 electrons): 1s2 2s2 2p6  <- 2nd shell full, very stable
Building atoms by Aufbau: each new electron takes the lowest open seat, with at most two per orbital.

Hund — spread out before pairing up

Aufbau tells you which subshell to fill next, but when a subshell has several orbitals of equal energy — the three p orbitals, say — it does not tell you how to share the electrons among them. That is Hund's rule: electrons spread out singly across equal-energy orbitals, each taking an empty one before any orbital gets a second electron — and the singles all keep their spins pointing the same way. Only once every orbital in the set has one electron do they start to pair up.

Put the three rules together and you have a complete recipe for any atom: fill from the lowest energy up (Aufbau), give each orbital at most two electrons of opposite spin (Pauli), and spread out across equal orbitals before doubling up (Hund). Run this recipe with the right number of electrons and you can write down the configuration of any element — and predict a great deal about how it behaves. In the final guide, we lay this filled-up ladder against the periodic table and watch the table's whole shape snap into focus.