Electronic structure: shells and orbitals

In a nutshell

Understanding electronic structure is crucial for understanding the chemistry of reactions. Here, we will review how to deduce electronic configurations of atoms and explain what is meant by the terms shells, subshells and orbitals.

Electron shells

Electrons orbit the nucleus in electron shells, called quantum shells which are given principal quantum numbers. Each quantum shell contains different types of subshells. Each subshell contains a different number of orbitals. The four types of subshells and the number of electrons they can hold are summarised below.

subshell	number of orbitals	maximum electrons
$s$	$1$	$1\,\times\,2\,=\,2$
$p$	$3$	$3\,\times\,2\,=\,6$
$d$	$5$	$5\,\times\,2\,=\,10$
$f$	$7$	$7\,\times\,2\,=\,14$

And the subshells and electrons in the first four quantum shells are summarised below.

shell	subshells	number of electrons
$1^{st}$	$1s$	$2$
$2^{nd}$	$2s\,2p$	$2\,+\,(3\,\times\,2 )\,=\,8$
$3^{rd}$	$3s\,3p\,3d$	$2\,+\,(3\,\times\,2)\,+\,(5\,\times\,2)\,=\,18$
$4^{th}$	$4s\,4p\,4d\,4f$	$2\,+\,(3\,\times\,2)\,+\,(5\,\times\,2)\,+\,(7\,\times\,2)\,=\,32$

Orbitals

Each subshell contains different numbers of orbitals, which can hold up to two electrons. Orbitals have characteristic shapes.

$s$ orbitals are spherical.
$p$ orbitals are shaped like dumbbells, of which there are three.

Below is an $s$ -orbital.

Chemistry; Atomic structure and the periodic table; KS5 Year 12; Electronic structure: shells and orbitals

Below is a $p$ -orbital, of which there are three kinds; $p_z$ , $p_y$ and $p_x$ .

Chemistry; Atomic structure and the periodic table; KS5 Year 12; Electronic structure: shells and orbitals

Note: Electrons in each orbital spin in opposite directions, this is called 'spin-pairing'.

Deducing electronic configuration

A simple set of rules must be followed to work out electronic configuration.

Rule	explanation
1. Arrows in boxes	Electrons in orbitals are represented by arrows in boxes. Each box represents one orbital and an arrow represents one electron.
2. Lowest energy subshells first	Electrons fill up the lowest energy subshells first. From low to high, the order is: $1s\,2s\,2p\,3s\,3p\,4s\,3d\,4p\,4d\,4f$ . Note, unusually, $4s$ is filled before $3d$ because it is lower in energy, even though it's principal quantum number is bigger; this is an exception you must remember. Below is the electronic configuration of calcium.
3. Single before double	Electrons fill orbitals singularly before they start to pair up. 1. Nitrogen's electron arrangement. 2. Oxygen's electron arrangement.

To represent electronic configuration, you can either draw out the energy levels (as in the image for Rule 2. above) or use subshell notation.

Example

For potassium, the subshell notation is: $1s^22s^22p^63s^23p^64s^1$ . You can check this is correct by adding the total of the superscripts. Here, it equals $19$ , which tells you it is correct as that is the number of electrons in a $K$ atom.

Note: Noble gas symbols (i.e $Ar$ or $Ne$ ) are sometimes used for simplicity. For potassium, it is also correct to write the configuration as [ $Ar$ ] $4s^1$ , since the [ $Ar$ ] corresponds to $1s^22s^22p^63s^23p^6$ .

Using the periodic table

The periodic table can be used as it is split into s-block, p-block and d-block elements.

Chemistry; Atomic structure and the periodic table; KS5 Year 12; Electronic structure: shells and orbitals — A. s-block elements

B. d-block elements

C. p-block elements

s-block elements have an outer shell configuration of $s^1$ or $s^2$ .
p-block elements have an outer shell configuration of $p^1$ to $p^6$ .
d-block elements have an outer shell configuration of $d^1$ to $d^{10}$ .

Remember: $4s$  must be filled to $4s^2$ , and only afterwards $3d$ can be filled.

Exception to the rule

$Cr$ and $Cu$ don't fit the usual rule. Their 4 $s$ shell only ever fills to $4s^1$ as they donate the second electron to the $3d$ subshell as it's more stable.