Electronic configuration of elements based on sub shells

Every atom has a very small, heavy nucleus at its centre, and its electrons move around that nucleus. The path in which electrons revolve around the nucleus of an atom is called an orbit or shell. Starting from the one closest to the nucleus, the shells are named K, L, M and N. They are also given the numbers 1, 2, 3 and 4. This number is called the shell number and is written as n, so the K shell is n = 1 and the N shell is n = 4.

A shell is not a single track where all its electrons sit side by side. Each shell is divided into one or more subshells, and each subshell contains one or more orbitals. The electrons are found in these orbitals. So the address of an electron has three parts: the shell, the subshell inside that shell, and the orbital inside that subshell.

A school building helps to picture this. The floors of the building are like shells. Each floor has one or more classrooms, and these are like subshells. Each classroom has benches, and these are like orbitals. A student is always on a bench, inside a classroom, on some floor. In the same way an electron is always in an orbital, inside a subshell, in some shell.

You can already write the electrons of an atom shell by shell. Sodium has 11 electrons, and it is written as 2, 8, 1: two electrons in K, eight in L and one in M. This is the electronic configuration based on shells. It tells how many electrons sit in each shell, but it could not explain all the properties of elements. Through their research, scientists found that the electrons of one shell do not all have the same energy. So they developed the electronic configuration of elements based on subshells, which shows exactly which subshell each electron occupies.

The number of subshells in a shell is equal to its shell number. There are 1, 2, 3 and 4 subshells in the K, L, M and N shells respectively. A subshell is named by writing the shell number followed by the letter s, p, d or f. The subshell in the K shell is 1s. The L shell has 2s and 2p. The M shell has 3s, 3p and 3d. The N shell has 4s, 4p, 4d and 4f.

Look at the pattern down the table. Every shell begins with an s subshell. A p subshell appears only from the L shell onwards, a d subshell only from the M shell onwards, and an f subshell only from the N shell onwards. The K shell is so small that it has room for nothing except 1s.

Each kind of subshell has a fixed maximum number of electrons. The s, p, d and f subshells can accommodate a maximum of 2, 6, 10 and 14 electrons respectively. Notice that each kind holds 4 more than the one before it. This limit is the same in every shell: 2s holds 2 electrons just as 1s does, and 3p holds 6 just as 2p does.

When every subshell of a shell is completely filled, adding their electrons gives the largest number of electrons that shell can hold. A full subshell is written with its electron count raised above it, so 2p⁶ means the 2p subshell holding 6 electrons.

Every piece of a subshell configuration carries three facts. Take 2p⁵ as an example:

• The number in front, 2, is the shell number, so this subshell belongs to the L shell.
• The letter, p, names the subshell.
• The small raised number, 5, is the number of electrons in that subshell. It is not the number of subshells and not the shell number.

When a whole configuration is written, the subshells of one shell are kept together and a comma separates one shell from the next. Fluorine, with atomic number 9, is written as:

\[ 1s^2, 2s^2 2p^5 \]

In a neutral atom the number of electrons equals the atomic number, so the raised numbers of a correct configuration always add up to the atomic number. For fluorine:

\[ 2 + 2 + 5 = 9 \]

Imagine building an atom by adding its electrons one at a time. Which subshell does each new electron go into? The answer is given by Aufbau's principle. Aufbau is a German word meaning building up, and the electronic configuration of elements on the basis of subshells is guided by this principle.

So the subshell with the lowest energy fills first, and a subshell is filled completely before the next one starts. Electrons cannot be filled in the 2s subshell until the 1s subshell is completely filled. In the same way, 2p waits until 2s is full.

The order of energy does not simply follow the shell number. The 4s subshell has lower energy than 3d, so 4s is filled before 3d even though it belongs to a higher shell. The same thing happens later with 5s before 4d and 6s before 4f. The order of subshells according to their increasing energies is:

\[ \begin{aligned} &1s < 2s < 2p < 3s < 3p \\ &< 4s < 3d < 4p < 5s \\ &< 4d < 5p < 6s < 4f \\ &< 5d < 6p \ldots \end{aligned} \]

This order is easy to rebuild with a diagonal diagram. Write the subshells of each shell in a row, one row for n = 1, the next for n = 2, and so on, keeping all the s subshells in one column, the p subshells in the next, then d, then f. Then draw parallel arrows slanting from upper right to lower left, starting at the top. Reading the arrows one after another gives the filling order.

• Arrow 1 passes through 1s.
• Arrow 2 passes through 2s.
• Arrow 3 passes through 2p and then 3s.
• Arrow 4 passes through 3p and then 4s.
• Arrow 5 passes through 3d, then 4p, then 5s.
• Arrow 6 passes through 4d, then 5p, then 6s.
• Arrow 7 passes through 4f, then 5d, then 6p, then 7s.

Put together, electrons are filled serially in the order 1s, 2s 2p, 3s 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p and onwards. The energy ladder below shows the same idea for the first twenty elements. The 4s step sits lower than the 3d step, which is why the 19th and 20th electrons climb to 4s rather than into 3d.

Any subshell configuration can be written by following the same short method.

• Step 1: Find the atomic number. It tells you how many electrons must be placed.
• Step 2: Take the subshells in Aufbau order: 1s, 2s, 2p, 3s, 3p, 4s and onwards.
• Step 3: Fill each subshell to its maximum (s 2, p 6) before moving to the next one.
• Step 4: Stop when all the electrons are placed. The last subshell may be only partly filled.
• Step 5: Check that the raised numbers add up to the atomic number.

Example 1: Sodium, atomic number 11.

Step 1: Sodium has 11 electrons. Filling 1s with its maximum of 2 leaves 9 electrons:

\[ 1s^2 \]

Step 2: Filling 2s with 2 and then 2p with 6 uses 8 more electrons, leaving 1:

\[ 1s^2, 2s^2 2p^6 \]

Step 3: The next subshell in the order is 3s, so the last electron goes there:

\[ 1s^2, 2s^2 2p^6, 3s^1 \]

Step 4: Checking by adding the raised numbers:

\[ 2 + 2 + 6 + 1 = 11 \]

Example 2: Potassium, atomic number 19.

Step 1: Potassium has 19 electrons. Filling 1s, 2s and 2p places 10 of them, leaving 9:

\[ 1s^2, 2s^2 2p^6 \]

Step 2: Filling 3s with 2 and 3p with 6 places 8 more, so 18 electrons are placed and 1 is left:

\[ 1s^2, 2s^2 2p^6, 3s^2 3p^6 \]

Step 3: By Aufbau's principle 4s comes before 3d, so the last electron enters 4s:

\[ \begin{aligned} &1s^2, 2s^2 2p^6, \\ &3s^2 3p^6, 4s^1 \end{aligned} \]

Step 4: Checking the total:

\[ 2 + 2 + 6 + 2 + 6 + 1 = 19 \]

This explains something the shell method alone cannot. The M shell of potassium still has an empty 3d subshell, yet its 19th electron goes to the N shell. That is why potassium's shell configuration is 2, 8, 8, 1 and not 2, 8, 9.

Using the same method for every element from hydrogen to calcium gives the table below. The shell configuration is shown beside each one so that the two can be compared.

Reading down the table shows the Aufbau order at work:

• Hydrogen and helium fill the 1s subshell. Helium ends with 1s², a full K shell.
• Lithium and beryllium fill 2s. Boron to neon then fill 2p one electron at a time, and neon ends with 2p⁶, a full L shell.
• Sodium and magnesium fill 3s. Aluminium to argon fill 3p, and argon ends with 3p⁶.
• Potassium and calcium put their new electrons into 4s, and the 3d subshell stays empty.

A shell configuration can always be read off a subshell configuration. Add the raised numbers of all the subshells that share the same shell number. Chlorine is 1s², 2s²2p⁶, 3s²3p⁵, so the electrons in each shell are:

\[ \begin{aligned} \text{K} &: 2 \\ \text{L} &: 2 + 6 = 8 \\ \text{M} &: 2 + 5 = 7 \end{aligned} \]

So chlorine's shell configuration is 2, 8, 7. The subshell configuration is a more detailed form of the shell configuration. The shell configuration says how many electrons are in each shell. The subshell configuration also says how those electrons are shared among the subshells of that shell, and it follows the order in which they were filled. Both always give the same total number of electrons.