Arrangements of electrons in the orbitals of an atom is called its electron configuration. And we use the Pauli exclusion principle and other rules to arrange the electrons. To designate the electron configuration we use the level number and the letter of the sublevel and a superscript number to represent the number of electrons contained in the sublevel. Writing the electron configuration requires that we recall how many orbitals are contained in each type of sublevel

For example hydrogen with one electron has an electron configuration of 1s¹. The orbital diagram for hydrogen can be represented in the following way.

This notation uses a box to represent the orbital, the label for the orbital and an arrow to represent the electron. The electronic configuration for hydrogen can be written as 1s¹. This is a short-hand notation which identifies the level, the sublevel and the number of electrons in the sublevel. We can also display the energy level diagram for the hydrogen atom. A portion of the energy level diagram is shown,

So we have three ways to represent the electron arrangement in an atom. The orbital diagram, the electron configuration and the energy diagram. All three ways are useful.

The next atom is helium with 2 electrons. So the second electron could go into the 1s orbital with the opposite spin of the first electron or it could go into the next orbital in the n = 2 level. It turns out that the energy required to accommodate two electrons in the 1s orbital is significantly less than the energy required to place the second electron into the higher energy n = 2 level. The orbital diagram for helium is,

So while hydrogen has the electron configuration of 1s¹, helium has the electron configuration of 1s². The energy diagram for helium is shown as here. Notice that there has been a change in the relative energies of the 2s and 2p orbitals. This is an important point that must be addressed at this point.

In the hydrogen atom the sublevels in each principle level are degenerate. In multi-elecron atoms the degeneracy of the energy of the sublevels is lost.

When the third electron is to be placed it must go into the second level. The first level is filled and can not accommodate any more electrons. When the electron is added to the second level it can go into the 2s orbital or the 2p, the question is which orbital is the electron placed? The primary criteria, the Aufbau principle, states the electrons are to be placed into the orbital of lowest energy. So we must consider which orbital, when the electron is placed into it, has the lowest energy? This is answered by considering some complicated mathematical calculations. The essence of these calculations is that when an electron is placed into the 2s orbital the electron is likely to spend more time closer to the nucleus than an electron in a 2p orbital. If the electron spends more time closer to the nucleus the electron will experience a greater attraction to the nucleus and it is lower in energy. It can be stated the 2s orbital penetrates closer to the nucleus than does a 2p orbital.

So the orbital diagram for lithium is shown below. The electron configuration for lithium is 1s²2s¹.

The energy level diagram, on the left shows the relative energy of the 2s and 2p orbitals based on the ability of the sublevels to penetrate to the nucleus.

The next element is beryllium which has four electrons. The orbital diagram for beryllium is shown here. The electron configuration is 1s²2s². The fourth electron is placed in the 2s orbital. The energy required to pair the first 2s electron is less than the energy required to place the electron into the 2p orbital.

The next element is boron with 5 electrons. The orbital diagram for boron as shown has the one electron in the 2p orbital. The electron can be placed in any of the three 2p orbitals. The electron configuration for boron is 1s²2s²2p¹.

The energy level diagram for boron is show below.

For the next element, carbon, the sixth electron must be placed in the correct orbital. The question becomes whether the next electron should be pair the other electron or whether the electron should be placed in an empty 2p orbital.

According to Hund's rule the most stable arrangement in a set of degenerate orbitals is that with the most number of unpaired electrons. So carbon has two unpaired electrons.

The electron configuration for carbon is 1s²2s²2p². Notice the electron configuration does not clearly indicate the number of unpaired electrons in the element. The number of unpaired electrons is evident from the orbital diagram. The orbital energy diagram for carbon is shown below.

Nitrogen has seven electrons. The placement of the next electron must follow Hund's rule. The orbital diagram shows three unpaired electrons. The electron configuration for nitrogen is 1s²2s²2p³.

For oxygen the eighth electron must pair with one of the electrons in the 2p orbitals. The orbital diagram for oxygen is shown on the left. The electron configuration for oxygen is 1s²2s²2p⁴.

The orbital diagrams for fluorine and neon are shown. The next two electrons continue to pair those electrons that are unpaired to fill up the 2p orbitals.

With neon the second level is filled with electrons. Completed levels are a characteristic of all noble gases. If we look at the energy level diagram for neon the completed second level means the next electron must go into the third level. In the hydrogen atom the three sublevels, 3s, 3p and 3d were all degenerate in energy. In the multi-electron atom the three sublevels do not have the same energy. The relative energies of the three sublevels again depend on the ability of the electron to penetrate to the nucleus. As in the case of the second level the 3s orbital is lower in energy than the 3p which is lower in energy compared to the 3d.

So as we progress from sodium across the period to argon the electrons are placed in the orbitals just as they were for the second period.

The orbital diagrams for the eight elements are shown below.

The electron configurations for the next eight elements are as follows:

Na 1s²2s²2p⁶3s¹

Mg 1s²2s²2p⁶3s²

Al 1s²2s²2p⁶3s²3p¹

Si 1s²2s²2p⁶3s²3p²

P 1s²2s²2p⁶3s²3p³

S 1s²2s²2p⁶3s²3p⁴

Cl 1s²2s²2p⁶3s²3p⁵

Ar 1s²2s²2p⁶3s²3p⁶

When we come to potassium more interesting changes are observed. Chemically potassium behaves like sodium, as an alkali metal. It appears the next electron is in an s orbital, not a 'd' orbital. It turns out the energy of the 4s orbital is very close to the energy of the 3d orbital at potassium. But the energy of the 4s orbital is lower in energy compared to the 3d. So the next electron is placed into the 4s orbital. At calcium the electron is paired. For scandium we might consider whether the electron goes into the 3d or the 4p. It turns out the energy of the 3d is lower than the 4p so the d sublevel begins to fill with scandium. The electron configuration for scandium is [Ar]4s²3d¹. As electrons are added in titanium and vanadium the configuration is [Ar]4s²3d² and [Ar]4s²3d³. The next element, chromium, would be expected to have a configuration of [Ar]4s²3d⁴, however this is not the case. It turns out that as a result of the similarity in energy of the 4s sublevel and the 3d sublevel in this group that an interesting phenomena occurs at chromium. Instead of [Ar]4s²3d⁴ the electron configuration is [Ar]4s¹3d⁵. We might suggest that a half-filled d sublevel has extra stability. The next element, manganese, the additional electron is added to complete the half-filled 4s sublevel and the configuration is [Ar]4s²3d⁵. From iron through nickel ([Ar]4s²3d⁶, [Ar]4s²3d⁷, [Ar]4s²3d⁸) the electrons spin-pair in the 3d sublevel. At copper another reversal occurs. The electron configuration for copper is [Ar]4s¹3d¹⁰ not [Ar]4s²3d⁹. Zinc has an electron configuration of [Ar]4s²3d¹⁰.

At gallium we begin filling the 4p sublevel and continue to krypton. Rubidium fills the 5s, yttrium the 4d and indium the 5p. Cesium fills the 6s and lanthanum bigins the first available f sublevel, the 4f. The f sublevel is filled from lanthanum through ytterbium. Throughout this period there are strange reversals of configurations. The details of these changes are not critically important to us.

Having gone through this exercise it is interesting to study the periodic table in light of the position of the valance electrons of each atom. The periodic table displayed uses color to denote the location of the outer-most electrons. All of the alkali metals have the outer most, or valence electron, in an s orbital. For lithium the outer most electron is in the 2s orbital, for sodium the 3s, for potassium the 4s, etc. We say the general electron configuration for the alkali metals is ns¹. For the alkaline earth elements it is ns².

The periodic table can be used to write the electron configuration for any element. The trick is locate the particular element in the correct level and sublevel. The level numbers are located to the left of each period. The sublevels are identified by noting the section of the periodic table the element is located. (Describe the colors of the periodic table and do an example using the periodic table.)

It is useful to understand the observed trends in particular physical properties of the elements in relation to their location in the periodic table. The idea is note the physical properties and then understand the observe behavior in terms of the nature of the electron.