Topic 2 · page 10 of 15

Orbitals, sub-shells and shells

Electrons live in orbitals, each holding at most two. Orbitals are grouped into sub-shells (s, p, d) and sub-shells into shells. This page gives the shapes, the capacities and the energy order you need to fill them.

13 min read2.92.122.16

Read first: Successive ionisation energies, First ionisation energy of elements 1 to 36

Orbitals 2.9

The ionisation energy evidence says that electrons sit in shells, and that shells are divided into sub-shells. The next step is to describe what a sub-shell is made of.

An electron cannot be pinned to a path round the nucleus. It is better to think of a cloud: the orbital is the region where there is a high chance of finding the electron.

Each electron also has a property called spin, which can point one of two ways. In diagrams the two spins are shown as arrows, ↑ and ↓. Two electrons can share one orbital only if their spins are opposite: ↑↓. A third electron cannot join them.

The shapes of s and p orbitals 2.12

Orbitals have shapes, set by where the electron is likely to be.

The shapes of orbitals: an s orbital is a sphere; each p orbital has two lobes along one axis; the three p orbitals lie at right angles along the x, y and z axes. — An s orbital and the three p orbitals. The nucleus is the black dot at the centre.

An s orbital is spherical, centred on the nucleus. Every shell has one. The 2s orbital is a larger sphere than the 1s.
A p orbital is dumbbell-shaped: two lobes, one on either side of the nucleus. There are three p orbitals in a p sub-shell, lying at right angles to each other along the x, y and z axes. They are called $p_x$ , $p_y$ and $p_z$ . They are the same shape and energy but point in different directions.

The first shell has no p orbitals. They start in the second shell.

Shells, sub-shells and orbitals 2.16

The structure has three levels:

A shell is labelled by a number, n = 1, 2, 3, 4, and so on. A higher n means a greater average distance from the nucleus and a higher energy.
Each shell is divided into sub-shells, called s, p, d and f.
Each sub-shell is made of orbitals, which each hold up to 2 electrons.

Sub-shell	Orbitals	Maximum electrons
s	1	2
p	3	6
d	5	10
f	7	14

Shell n contains n sub-shells, which gives the table you must know.

Shell, n	Sub-shells	Orbitals	Maximum electrons
1	1s	1	2
2	2s, 2p	1 + 3 = 4	8
3	3s, 3p, 3d	1 + 3 + 5 = 9	18
4	4s, 4p, 4d, 4f	1 + 3 + 5 + 7 = 16	32

The maximum in shell n is 2n². Check: 2 × 4² = 32 for the fourth shell. No element up to krypton has any electron in 4d or 4f, so the first four shells matter only as far as 4s, 3d and 4p.

Energy order

Electrons fill the lowest-energy sub-shell first. Up to krypton the order is:

\text{1s} < \text{2s} < \text{2p} < \text{3s} < \text{3p} < \text{4s} < \text{3d} < \text{4p}

Energy ladder of sub-shells up to krypton from 1s at the bottom to 4p at the top, with one box for each orbital. The 4s sub-shell is lower than 3d. — Energy order up to krypton. Each box is one orbital.

Check yourself

Define the term orbital.
How many electrons can there be in (a) one 2p orbital, (b) the 2p sub-shell, (c) the 3d sub-shell, (d) the third shell?
Describe the shape of an s orbital and of a p orbital. How many p orbitals are there in a p sub-shell?
Explain the difference between an orbit and an orbital.
List the sub-shells in the third shell, with the number of orbitals in each.
Put these sub-shells in order of increasing energy: 3d, 4s, 3p, 2s, 4p, 1s.

Answers cover these until you have tried the questions

A region within an atom that can hold up to two electrons, with opposite spins.
(a) 2. (b) 3 orbitals × 2 = 6. (c) 5 orbitals × 2 = 10. (d) 2 × 3² = 18 (3s: 2, 3p: 6, 3d: 10).
An s orbital is spherical. A p orbital is dumbbell-shaped, with two lobes either side of the nucleus. There are three p orbitals, at right angles to each other along the x, y and z axes.
An orbit is a fixed path round the nucleus. An orbital is a region of space in which there is a high probability of finding an electron, and it can hold two electrons with opposite spins.
3s (1 orbital), 3p (3 orbitals) and 3d (5 orbitals): 9 orbitals in total.
1s < 2s < 3p < 4s < 3d < 4p