Carbon has 6 electrons: 2 in the K shell and 4 in the L shell, as Atomic structure counted them. Shells get those counts right. They say nothing about where the electrons are, or what shape of space they fill.
Shape is what a chemist needs. It explains why methane, CH₄, is a tetrahedron (a pyramid with four triangular faces, the carbon at its center), why a C=C double bond refuses to twist, and why benzene, a ring of six carbons, is flat. This page replaces shells with orbitals, the shapes electrons actually occupy. Everything later in the course builds on them.
What an orbital is
Start with hydrogen: one proton and one electron. The electron does not circle the nucleus on a track. Take a snapshot of where it is, then another, and another, and each snapshot finds it somewhere new. Mark every sighting with a dot. The dots build a round cloud, thickest near the nucleus and thinning out with distance.
Now draw a boundary around the region where the electron is found 90% of the time. That region is an orbital: a region of space where an electron is likely to be found. It is a cloud of probability, not a path. Hydrogen's electron sits in an orbital called 1s.
Every orbital belongs to a shell. The shell number is written n: the K shell is n = 1, the L shell is n = 2 and the M shell is n = 3. In an orbital's name, the number is its shell and the letter is its shape. So 1s is the s-shaped orbital of the K shell.
Two electrons per orbital: the Pauli principle
Helium has two electrons, and both sit in the 1s orbital. They differ in one property, called spin. Each electron behaves like a tiny magnet that points one of two ways, spin up or spin down, drawn ↑ and ↓. Helium's two electrons have opposite spins: ↑↓.
Lithium's third electron cannot join them. It has to go into the next shell. The rule behind that is the Pauli exclusion principle: no two electrons in one atom can have both the same orbital and the same spin. An orbital therefore holds at most 2 electrons, and those two have opposite spins.
s orbitals: spheres
Hydrogen's 1s orbital is a sphere centered on the nucleus. Every shell has exactly one s orbital, starting with 1s in the K shell. The L shell's s orbital is 2s. It is a bigger sphere, because an n = 2 electron spends most of its time farther from the nucleus.
Inside the 2s sphere is a node: a surface where the electron is never found. For 2s the node is a small sphere around the nucleus. The electron can be inside it or outside it, but never on it.
p orbitals: two lobes and a nodal plane
The L shell also has orbitals of a second shape, called p. Take one of them, 2px. It has two lobes, rounded regions on opposite sides of the nucleus, lying along the x axis. The shape is often called a dumbbell. The lobes pinch to nothing at the nucleus itself.
Between the lobes lies a flat nodal plane. It passes through the nucleus at right angles to the x axis, and the electron is never found on it.
The two lobes are one orbital, not two. An electron in 2px can turn up in either lobe, and the whole orbital still holds at most 2 electrons.
Three p orbitals, at right angles
The L shell has three 2p orbitals, not one. The second, 2py, lies along the y axis. The third, 2pz, lies along the z axis, which points straight out of the page. Each one sits at 90° to the other two.
The three 2p orbitals have the same shape and the same energy. They differ only in direction. Orbitals with exactly equal energy are called degenerate. The five 3d orbitals, met below, are another degenerate set. Every shell from n = 2 on has one set of three p orbitals; the K shell has none.
Those 90° angles leave a puzzle. Methane's H–C–H angles are 109.5°, not 90°. Hybridization shows how carbon gets from one to the other.
d and f orbitals, and what a shell holds
Heavier atoms use two more shapes. d orbitals are mostly four-lobed cloverleaves, and each shell from n = 3 on has five of them. f orbitals have still more lobes, and each shell from n = 4 on has seven. Organic chemistry happens almost entirely in s and p orbitals. You need to recognize d and f, not draw them.
Now count the M shell, n = 3. It has one 3s, three 3p and five 3d orbitals: nine in all. At 2 electrons each, it holds 18. The n = 4 shell adds seven f orbitals and holds 32.
| Orbital type | Shape | Orbitals per shell | First shell | Electrons per set |
|---|---|---|---|---|
| s | sphere | 1 | n = 1 | 2 |
| p | two lobes, nodal plane between | 3 | n = 2 | 6 |
| d | mostly four lobes | 5 | n = 3 | 10 |
| f | more lobes still | 7 | n = 4 | 14 |
These numbers match the shells you already know. The K shell is the single 1s orbital, so it holds 2. The L shell is 2s plus the three 2p orbitals, four orbitals in all, so it holds 8. Nothing about the counting changes. What orbitals add is the shape of the space the electrons fill, and that shape sets the shape of molecules.
The periodic table's rows are 2, 8, 8, 18, 18, 32 and 32 elements long, built from the same numbers. Row 3 stops at 8 rather than 18 because of the filling order, set out below.
Phase: what the two shades mean
Look back at the p orbital. Its two lobes are drawn in two shades. The shades show phase. An electron in an orbital behaves like a wave, and a mathematical function called the wavefunction describes that wave. Like a wave on water, it has a plus part and a minus part. The shades mark those two signs. They are not electric charges.
A 1s orbital has one sign all over, and either sign is allowed. A 2s orbital has both: one sign inside its node and the other outside. The node is where the sign changes.
Phase matters when orbitals on two atoms overlap. Bring two hydrogen atoms together with their 1s orbitals in the same phase, and the two waves add up between the nuclei. The electron pair gathers there and holds both nuclei: a bond.
Bring the same two atoms together in opposite phase, and the waves cancel between the nuclei. A node appears there, and the electrons are kept out of the space that would hold the atoms together. This combination is called antibonding. It does not make a bond.
A bond, then, is overlap between orbitals on two different atoms. Keep that apart from Hybridization, the next page, in which one atom mixes its own orbitals into new shapes before it bonds.
You can set phase aside for a while, but it returns. Bonding uses it to build single and double bonds. Aromatic Chemistry uses it to explain aromaticity, the extra stability of certain flat rings such as benzene.
Filling order: lowest energy first
Lithium has 3 electrons. Two fill 1s. The third goes into the n = 2 shell, and it goes into 2s, not 2p. Boron, with 5, puts 2 in 1s and 2 in 2s, and only its fifth electron goes into a 2p orbital.
The rule is that electrons fill the lowest-energy orbitals first. This is the Aufbau principle, from the German for "building up". Within one shell, energy rises in the order s < p < d < f, so 2s fills before 2p.
An atom's filling is written as its electron configuration. Each subshell, meaning all the orbitals of one type in one shell, is written with a superscript giving its electrons. The 2p subshell is the three 2p orbitals together. Boron's configuration is 1s² 2s² 2p¹.
Why s fills before p: shielding and penetration
Take lithium's third electron. The nucleus pulls on it with a charge of +3. The two 1s electrons sit closer in, and they repel it, cancelling part of that pull. This is shielding: inner electrons screen an outer electron from the nucleus.
Now compare a 2s electron with a 2p electron. The 2s electron spends a little of its time right by the nucleus, inside the 1s electrons. The 2p electron gets inside the 1s electrons too, but less, and never reaches the nucleus itself, which sits on its nodal plane. Getting in close like this, inside the inner electrons, is called penetration.
More penetration means less shielding. Less shielding means the electron feels a stronger pull from the nucleus, and a stronger pull means lower energy. So 2s lies below 2p. The same argument puts p below d, and d below f.
When 4s fills before 3d
Potassium has 19 electrons. The first 18 fill 1s, 2s, 2p, 3s and 3p, exactly as in argon. The 19th could go into 3d or 4s. It goes into 4s.
Here penetration beats the shell number. A 4s electron penetrates far more than a 3d electron, so 4s lies lower in energy even though 4 is larger than 3. Potassium and calcium fill 4s before any element fills 3d. That is why the d-block starts in row 4 of the periodic table, not row 3.
Configurations get long, so chemists write a filled core as the group 18 element (a noble gas) that has it. [Ar] stands for argon's 18 electrons, 1s² 2s² 2p⁶ 3s² 3p⁶. Potassium is then [Ar] 4s¹.
Hund's rule: spread out, then pair
Nitrogen has 7 electrons. Four fill 1s and 2s, which leaves three for the three 2p orbitals. They go one to each orbital, all with the same spin, and none of them pair.
That is Hund's rule: when electrons fill a set of degenerate orbitals, each orbital takes one electron, all with the same spin, before any orbital takes a second. The spreading comes from repulsion. Two electrons in one orbital share one region of space and push against each other. An empty orbital of equal energy lets them stay apart, so they take it. An electron alone in its orbital is called unpaired.
Carbon has 6 electrons. 1s takes 2 and 2s takes 2, which leaves 2 for the 2p set. Hund's rule puts them in separate 2p orbitals. Result: 1s² 2s² 2p², with two unpaired electrons and one 2p orbital empty.
Nitrogen (7 electrons) is 1s² 2s² 2p³, with one electron in each 2p orbital. Three unpaired electrons mean three bonds. The 2s pair is already paired, and that pair becomes the lone pair in ammonia, NH₃. In ammonia itself the pair no longer sits in a pure 2s orbital; Hybridization shows where it goes.
Oxygen (8 electrons) is 1s² 2s² 2p⁴. The first three 2p electrons take one orbital each, and only the fourth has to pair. Two unpaired electrons mean two bonds. The two pairs in the n = 2 shell, one in 2s and one in 2p, become oxygen's two lone pairs.
Fluorine (9 electrons) is 1s² 2s² 2p⁵. Two 2p orbitals are full and the third holds one electron. That gives one unpaired electron, one bond and three lone pairs.
Read down the four. Nitrogen, oxygen and fluorine form as many bonds as they have unpaired electrons: three, two and one. Carbon breaks the pattern. Its configuration predicts two bonds, yet carbon forms four. The last section of this page takes that up.
Reading the periodic table by blocks
Sodium's last electron goes into 3s. Carbon's last electron goes into 2p, and chlorine's into 3p. The periodic table groups elements by the subshell their last electron fills. Those groupings are its blocks.
- The s-block is groups 1 and 2, the two leftmost columns.
- The p-block is groups 13 to 18, the six columns on the right. Essentially every element of organic chemistry lives here: C, N, O, F, S, P, Cl, Br and I.
- The d-block is groups 3 to 12, the ten middle columns: the transition metals (group 12 is not always counted as transition metals).
- The f-block is the two rows pulled out beneath the table, the lanthanides and actinides.
Read this way, the table stops being a chart to memorize. It becomes a map you can work out. An element's position gives its last-filled subshell, that gives its valence configuration, and that tells you how it bonds.
The periodic table tool (the ⚛ button) shows every element in its group and row, so you can read off its block there. Its colors mark categories such as halogens and noble gases, not blocks.
That counting argument does not cap row 3 at eight, because the n = 3 shell has nine orbitals, not four. Sulfur, for example, forms SF₆, with six bonds to one sulfur. Lewis structures sets out how such compounds are drawn and how best to describe their bonds.
The problem this leaves behind
Carbon's ground-state configuration (its lowest-energy arrangement), 1s² 2s² 2p², has only two unpaired electrons. Taken at face value, that predicts two bonds, giving something like CH₂. But carbon forms four bonds in essentially every stable organic compound you will draw. Methane is CH₄, with four identical bonds at identical angles.
So something must happen to carbon's orbitals before it bonds. That is the subject of the next page, Hybridization, and its answer is the single most useful idea in structural organic chemistry.