Electron Shells and Orbitals

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What is it?

Electrons supposedly move around the nucleus of atoms. For a long time it remained obscure how they would do such a thing1(see also: wave-particle duality). In the beginning of the 20th century a series of clever concoctions resulted in the electron shell theory, which is merely an extension of everyday quantum mechanics2. According to this theory, electrons move randomly around the nucleus, concentrated within regions called 'orbitals', which are defined as the volume where an electron is most likely to be, and which bear more resemblance to a cloud or a propeller, than to the orbit of a planet around a star. These orbitals have defined shapes and the electrons moving in there obey certain laws. The orbitals are classified according to their shape, with a letter-code (in order of increasing shape complexity3: s, p, d, f, g, h, i,...) to confuse lay people and students. To confuse even more, orbitals always come in groups: There is one s-orbital, three p-orbitals, five d-orbitals, seven f-orbitals, etc... All of these orbitals arrange forming shells which also have number and letter-codes starting from the closest to the nucleus:

# (code)  
set of orbitals
1 (K)s
2 (L)s,p
3 (M)s,p,d
4 (N)s,p,d,f
5 (O)s,p,d,f,g
6 (P)s,p,d,f,g,h

It should be stressed, that the existence of these orbitals is independent from the presence of electrons. That means: The orbitals are there, empty so to speak. The next thing to learn, will be how to fill these shells and orbitals with electrons. Doing this for the neutrally charged atoms will result in the arrangement of the periodic table of the elements4

How to Fill Shells and Orbitals with Electrons

As mentioned it is difficult to visualize the behaviour of the electrons. One consequence of the theory is that there are only certain defined orbitals in which the electrons can move. Another one is that only two electrons (each having a quality called 'spin' but which has noting to do with real-life spinning) can occupy one orbital at a time (this is also known as the Pauli Exclusion Principle5).

Smart scientists have calculated the shapes and positions of the orbitals, and the energy electrons would have if they were moving in the respective orbitals. They concluded that electrons will tend to occupy orbitals in which they will be able to move in a simple low-energy manner. Meaning: Electrons will tend to move in a shell as close as possible to the nucleus and in an orbital with a shape as simple as possible. But, just to make things a little bit more complicated: In certain cases the shape of the orbital is so complicated, that the electron would rather take a simpler orbital in a more distant shell than having to move within a complicated shape.

Luckily a simple orbital-filling-order scheme has been found, and only minor exceptions do not follow the scheme. Electrons will fill the orbitals in the following order:

1s(2) 2s(2) 2p(6) 3s(2) 3p(6) 4s(2) 3d(10) 4p(6) 5s(2) 4d(10) ...

Where the number in parenthesis corresponds to the maximum number of electrons in the set of orbitals (always 2 per orbital, but there are three p-orbitals, five d-orbitals and so on. Example: The electronic configuration of Iron (Fe); Iron (uncharged) has 26 electrons, so its electronic configuration would be:


Adding the numbers in the parenthesis will give 26. As for notation, the complete s and p orbitals can be abbreviated using the symbol of the corresponding noble gas6;

In our example Fe: [Ar] 4s(2)3d(6)

Remark: In some textbooks the number in the parenthesis can be found superscript (like 4d7), but that is a minor detail.

And what is that good for?

The existence of defined orbitals and shells can be used in technology in numerous ways. For example:

-To analyse the atomic composition of anything (from fruitcakes or atmospheres of planets to sun-spots)

-To generate colourful light in neon, xenon or mercury-lamps (cf. emission lines) and lasers

-To calculate the shape of molecules like enzymes and Aspirin

-To predict properties of metals, like their usage in photovoltaic devices

-To calculate properties of doped and undoped semi-conductors (which are used to build microchips)

1Even more obscure is the question why they would do something like that2Which is a perversely complicated piece of science, which only three or four people on this planet understand (R.P.Feynman)3The original designation of those orbitals was done according to their spectral appearence, namely: sharp, principal, diffuse, fundamental hence the letter code, the remaining letters are ordered alphabetically4This is also the reason why the elements are arranged in that particular way on the table. The period number is also the shell number, and the group number is associated with the filling of the orbitals (e.g. the transition metals are sometimes called d-block elements, because their d-orbitals are being filled. Cf. How to Fill Shells and Orbitals with Electrons)5Named after the Austrian scientist Wolfgang Pauli (1900-1958) who invented it in 1925 and went Nobel in 19456Or by looking at the periodic table, the element on the far right side one line above

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