Electron Shells and Subshells

The number n, associated with each electron energy shell is known as the principle quantum number or energy quantum number.

Each electron shell can be further broken down into one or more smaller units called subshells.

Each of these subshells also has an associated quantum number, l.

• For a given shell, l can take on any integer value from 0 to n-1.

• Each value of l is associated with a subshell.

• We also use letters (s, p, d, f...) to identify these different subshells. s is used for l=0, p for l=1, etc.

• Each subshell can be represented by a symbol which combines the numerical value of n (1,2,3, etc.), with the symbolic value for l (s,p,d,f), as in: 3p    for n=3   and  l= 1 = symbol p

One can determine the number of subshells for a given shell from the value of n for that shell.

Here's how things break down for the first four energy shells. Note that everytime you increase "n", an additional subshell is added.

Energy Ordering of the Subshells

Within a given shell, the ordering of the energy of the subshells is given by:

Each subshell consists of one or more orbitals. These orbitals can be thought of as representing, in an average way, the region of space that the electrons inhabit. We'll be talking about these more later in the course. The type of subshell determines the number of orbitals in the subshell and the total number of electrons the subshell can hold, as follows:

You may notice the the number of electrons is twice the number of orbitals. This is because each orbital can hold two electrons.

Putting this information together with the number of subshells allowed in each shell, we come up with a more detailed picture of how many electrons are allowed in each energy shell.

• Shell 1 (n=1): one subshell, the 1s. An s subshell holds 2 electrons, so a maximum of 2 electrons fit into the n=1 level.

• Shell 2 (n=2): two subshells, the 2s and 2p. An s subshell holds 2 electrons, a p holds 6, so a maximum of 8 electrons fit into the n=2 level.

• Shell 3 (n=3): three subshells, the 3s, 3p and 3d. An s subshell holds 2 electrons, a p holds 6, and a d holds 10, so a maximum of 18 electrons fit into the n=3 level.

Here's the above in tabular form with the addition of the n=4 level.

Writing Electron Configurations

The electron configuration for an atom is a way of writing down how electrons of an atom occupy the different energy shells and subshells.

Electron configurations for atoms are written by first grouping electrons into subshells. Next, write the designation of each subshell (nl) followed by a superscript indicating the number of electrons in that subshell.

Terms for each subshell are placed after one another until all subshells containing electrons are included. An electron configuration looks something like this:

But, how do we get there? Use the following rule:

• Electrons fill the lowest energy subshell available. Once that is full, electrons are placed into the next lowest subshell available.

Let's start with hydrogen (H). Hydrogen, with atomic number 1, has 1 electron. The lowest energy subshell is the 1s level, so the electron is placed there, and the configuration looks like:

Helium, atomic number 2, has 2 electrons. The second electron fills the 1s subshell (remember, s subshells can only hold 2 electrons).

Lithium, atomic number 3, has 3 electrons. The first two filled the 1s orbital, so the third one has to go into the next subshell, the 2s:

Next in line is Beryllium (Be), with 4 electrons.

When we get to boron (B), with 5 electrons, we have to begin a new subshell because the 2s is filled. The 2p in next in line:

As we proceed up in atomic number, we fill he 2p subshell and eventually have to start filling the 3s level. The electrons for the first 18 elements are placed into subshells in the following order: 1s, 2s, 2p, 3s, 3d. Their configurations are below:

Noble Gas Notation

A simplified way of writing electron configurations makes use of the noble gas notation.

Consider the electron configuration of Li:

Noting that 1s² is the electron configuration of He, this can also be written as:

Similary, for sodium, we can replace 1s²2s²2p⁶ with [Ne]:

Beyond the first 18 elements

Beyond the first 18 elements, things get a little more complicated. Basically, the energy shells overlap. For example, the 4s subshell actually has a lower energy than the 3d. Thus, the n=3 and n=4 levels overlap a bit. Electrons will fill the lowest energy subshell, so they will fill the 4s BEFORE the 3d. Below is a table of the energy ordering for the various subshells. As you go up vertically in the table, the subshells increase in energy. Note the overlapping shells.

Energy Level Ordering for Subshells

				4f
						6s
					5p
				4d
					5s
				4p
			3d
				4s
			3p
			3s
		2p
		2s
	1s

Electron Configurations After Element 18

The 4s subshell lies lower in energy than the 3d subshell, thus it is filled before the 3d.

The electron configuation of potassium (K), element 19 is:

Using the simplified ''noble gas notation'' we can write this in the simplified way:

where [Ar] represents the electron configuration of an argon atom.  

The electron configuation of calcium (Ca), element 20 is:

or

Starting with scandium (Sc, atomic number 21), we begin to fill the 3d:

Once the 3d is filled, we can return to the n=4 shell by beginning to fill the 4p subshell with the element gallium (Ga, atomic number 31):

A table of the elements K through Kr is given below. Note the there are a few exceptions due to the fact that 1/2 filled subshells are especially stable, hoever this is not something you will be held responsible for.