Shells, sub-shells and orbitals

Electron structure uses a hierarchy of ideas.

A shell is a main energy level around the nucleus. Shells are labelled by a principal number, n = 1, 2, 3, 4.... The first four shells can hold these maximum numbers of electrons:

The formula behind these values is 2n2, but the values themselves matter most here. The 4th shell maximum of 32 is the full shell capacity; in this lesson's configurations up to Z = 36, you only need the order as far as 4p.

A sub-shell is a group of orbitals within a shell. The sub-shell letters you need here are s, p and d.

That definition does a lot of work. It says an orbital is a region, not a fixed path. It also says a single orbital can be empty, hold one electron, or hold two electrons, but if it holds two electrons they must have opposite spins.

Worked example: capacity of the 3p sub-shell

A p sub-shell contains 3 orbitals. Each orbital can hold 2 electrons:

So a full 3p sub-shell is written as 3p6.

Orbital shapes and boxes

For this lesson, the only orbital shapes you need to know are s and p.

An s orbital is spherical. A p orbital is dumb-bell shaped, with two lobes on opposite sides of the nucleus. In a p sub-shell there are three p orbitals, usually described as being at right angles to each other, but the shape of one p orbital is still just one dumb-bell.

Orbitals can also be shown as boxes. Each box represents one orbital. Each arrow represents one electron. Two arrows in the same box show two electrons with opposite spins:

one orbital with two electrons: [up down]

In a real box diagram the arrows are drawn in opposite directions. In text, the important idea is that a pair in one orbital must have opposite spins.

Worked example: reading a box

If an orbital box contains one electron, the orbital is half-filled. If it contains two opposite-spin electrons, the orbital is full. An s sub-shell has one box, so 2s2 means the single 2s orbital is full.

Filling orbitals in order

Electrons fill orbitals in order of increasing energy. For the first three shells, plus the 4s and 4p orbitals, use this filling order:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p

The unusual-looking part is that 4s fills before 3d. That is the order you use when building configurations up to Z = 36.

There is one more filling rule. Orbitals with the same energy are occupied singly before any pairing happens. The three p orbitals in one p sub-shell have the same energy, so one electron goes into each p orbital before a second electron pairs with any of them.

Worked example 1: nitrogen

Nitrogen has atomic number 7, so a nitrogen atom has 7 electrons.

Fill in order:

1s2 2s2 2p3

The 2p3 part means three electrons are in the three 2p orbitals. Because equal-energy orbitals fill singly before pairing, the three 2p electrons occupy separate p orbitals. Nitrogen therefore has three unpaired electrons in the 2p sub-shell.

Worked example 2: oxygen

Oxygen has atomic number 8, so an oxygen atom has 8 electrons:

1s2 2s2 2p4

The first three 2p electrons occupy the three p orbitals singly. The fourth 2p electron has to pair in one of those orbitals, with opposite spin.

Writing atom configurations

An electron configuration in sub-shell notation tells you the shell number, the sub-shell letter and the number of electrons in that sub-shell.

For example:

1s2

means "two electrons in the 1s sub-shell". The final number is normally written as a superscript, but plain text configurations such as 1s2 2s2 2p4 are accepted in this lesson format.

To write a configuration for an atom:

1. Use the atomic number as the number of electrons.
2. Fill sub-shells in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p.
3. Stop when all electrons have been placed.
4. Check that no sub-shell exceeds its capacity: s2, p6, d10.

Worked example 1: sulfur, Z = 16

Sulfur has 16 electrons.

1s2 2s2 2p6 3s2 3p4

Check the total:

2 + 2 + 6 + 2 + 4 = 16

The 3p sub-shell is not full because it contains 4 electrons, not 6.

Worked example 2: calcium, Z = 20

Calcium has 20 electrons.

1s2 2s2 2p6 3s2 3p6 4s2

The 4s sub-shell is used before 3d, so calcium ends in 4s2.

Worked example 3: iron atom, Z = 26

Iron has 26 electrons.

1s2 2s2 2p6 3s2 3p6 4s2 3d6

Some mark schemes also allow the filled third-shell terms to be grouped as:

1s2 2s2 2p6 3s2 3p6 3d6 4s2

For learning the filling process, keep the order 4s before 3d.

Special neutral atoms: chromium and copper

Most configurations up to Z = 36 follow the simple filling pattern. The two common neutral-atom exceptions are chromium and copper:

Cr: 1s2 2s2 2p6 3s2 3p6 4s1 3d5
Cu: 1s2 2s2 2p6 3s2 3p6 4s1 3d10

This is a controlled exception note, not a new calculation method. You do not need a detailed quantum explanation here; just recognise that chromium has a half-filled 3d5 sub-shell and copper has a full 3d10 sub-shell.

Writing s- and p-block ion configurations

For ions in this lesson, stay inside the OCR boundary: s- and p-block ions up to Z = 36.

The method is:

1. Start with the atomic number.
2. Adjust for the charge.
3. Write the full sub-shell configuration for that number of electrons.

For a positive ion, subtract electrons. For a negative ion, add electrons.

Worked example 1: magnesium ion, Mg2+

Magnesium has Z = 12, so a magnesium atom has 12 electrons. A 2+ ion has lost 2 electrons:

12 - 2 = 10 electrons

The configuration for 10 electrons is:

Mg2+: 1s2 2s2 2p6

Worked example 2: chloride ion, Cl-

Chlorine has Z = 17. A 1- ion has gained 1 electron:

17 + 1 = 18 electrons

The configuration for 18 electrons is:

Cl-: 1s2 2s2 2p6 3s2 3p6

Worked example 3: bromide ion, Br-

Bromine is a p-block element with Z = 35, so Br- is inside this lesson's ion boundary:

35 + 1 = 36 electrons

Fill to 36 electrons:

Br-: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6

Do not use transition-metal ions as your main examples in this lesson. They are revisited later, where the 4s electrons are removed before 3d electrons when transition-metal ions form.