Shells, subshells, orbitals. Three words that sound like synonyms and are not. They nest inside one another like rooms inside floors inside a building, and once that picture is clear, writing electron configurations becomes bookkeeping.
📚 What you need to know
Electrons occupy principal energy levels (shells) numbered by n.
Each shell holds a maximum of 2n2 electrons: 2, 8, 18, 32.
Shells are divided into subshells: s, p, d and f.
Subshell energy rises in the order s < p < d < f within a shell.
Subshells contain orbitals: s has 1, p has 3, d has 5, f has 7.
Each orbital holds a maximum of two electrons, so s holds 2, p holds 6, d holds 10, f holds 14.
Orbitals in the same subshell are degenerate — equal in energy. 4s fills before 3d because it is lower in energy.
Shells, subshells and orbitals
A shell is the coarse level given by n. It splits into subshells of slightly different energies, and each subshell contains a set number of orbitals, each of which is a region where up to two electrons can be found.
Every capacity in the table below comes from this one picture: count the orbitals in a subshell, then multiply by two.
Shell (n)
Subshells present
Orbitals in total (n2)
Maximum electrons (2n2)
1
1s
1
2
2
2s, 2p
4
8
3
3s, 3p, 3d
9
18
4
4s, 4p, 4d, 4f
16
32
Subshell
Number of orbitals
Maximum electrons
s
1
2
p
3
6
d
5
10
f
7
14
The shapes of orbitals
An orbital is not a path. It is a region of space in which there is a high probability of finding an electron, and the shape of that region depends on the subshell.
The dot at the centre of each diagram is the nucleus. Notice that the p orbitals have no electron density at the nucleus itself, which is one reason p electrons are held less tightly than s electrons.
The energy order, and where it goes strange
Within a shell, s is lowest and f is highest. Between shells, higher n means higher energy. Put those two rules together for n = 3 and above and the subshells start to overlap.
This single overlap is responsible for the whole shape of the d block, and for why transition metals lose their 4s electrons before their 3d ones when they form ions.
Students often try to memorise a long list of exceptions here. There is really only one thing to remember at this level: 4s is lower in energy than 3d. Everything else follows the plain order. And notice that “fills first” and “is lost first” point in opposite directions — once 3d starts filling it drops below 4s, so the 4s electrons become the outermost and go first when an ion forms.
WORKED EXAMPLE
State the number of orbitals and the maximum number of electrons in the n = 3 shell, and show how both follow from the subshells present.
List the subshellsThe third shell contains 3s, 3p and 3d.Count the orbitals3s: 1 + 3p: 3 + 3d: 5 = 9 orbitalsWhich matches n2 = 32 = 9.Count the electrons9 orbitals × 2 electrons = 18Which matches 2n2 = 2 × 9 = 18.9 orbitals, 18 electronsThe two formulas are not separate facts to learn. n2 counts the orbitals and every orbital holds two.
WORKED EXAMPLE
Explain what is meant by degenerate orbitals, and give an example.
The definitionDegenerate orbitals are orbitals that have exactly the same energy as one another.An exampleThe three 2p orbitals, 2px, 2py and 2pz, are identical in energy and differ only in the direction they point.the three orbitals of any p subshellWhy it mattersBecause there is no energy reason to prefer one over another, an electron entering a p subshell has a free choice of three empty orbitals. That is what makes Hund’s rule possible, as you will see on the next page.
WORKED EXAMPLE
The n = 4 shell can hold 32 electrons. Show this from the subshells it contains, and state which subshell fills first in practice.
Subshells in the fourth shell4s, 4p, 4d and 4f.Add the capacities2 + 6 + 10 + 14 = 32Or by orbitals: 1 + 3 + 5 + 7 = 16 orbitals, and 16 × 2 = 32.32 electrons, matching 2n2 = 2 × 16Which fills first4s, and in fact it fills before the 3d subshell of the shell below, because 4s is lower in energy than 3d.Capacity and filling order are separate questions. A shell’s capacity never changes; the order in which its subshells get used depends on energy.
💡 Exam tip
Learn the capacities as orbitals first: 1, 3, 5, 7 — then double them.
Use 2n2 for shell capacity and n2 for the number of orbitals.
Describe an orbital as a region of high probability, never as a path or orbit.
Say s orbitals are spherical and p orbitals are dumbbell-shaped and perpendicular.
Know the term degenerate and be able to give the p orbitals as an example.
Remember the one overlap: 4s is lower in energy than 3d.
⚠️ Common mix-up
Using “shell”, “subshell” and “orbital” interchangeably. They are three different levels of structure.
Thinking a p subshell is one orbital holding six electrons, rather than three holding two each.
Putting more than two electrons in an orbital. Two is an absolute limit.
Describing orbitals as circular paths around the nucleus.
Assuming 3d fills before 4s because 3 is less than 4.
Expecting a d subshell in the n = 2 shell. The first d subshell appears at n = 3.
Up next: Writing Electron Configurations — you now have the boxes and their capacities. The next page fills them in the right order, including the two elements that famously refuse to cooperate.
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