Electron Shells and Orbitals

     Electrons supposedly move around the nucleus of atoms. For a long time it remained a mystery how they would do such a thing1. At the beginning of the 20th Century a series of clever suppositions 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'. Orbitals 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 within them obey certain laws.

     Orbitals are classified according to their shape, with a letter code in order of increasing shape complexity: s, p, d, f, g, h, i... The original designation of those orbitals was done according to their spectral appearance, namely: sharp, principal, diffuse, fundamental, hence the letter code with the remaining letters being ordered alphabetically. To cause even greater confusion, orbitals always come in groups. There is one s-orbital, three p-orbitals, five d-orbitals, seven f-orbitals, and so on. All of these orbitals are arranged forming shells which also have number and letter-codes starting from the closest to the nucleus:

Shell #
Set of orbitals letter
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
... s,p,d,f,g,h,i...

     It should be stressed that the existence of these orbitals is independent from the presence of electrons. Or, in other words, the orbitals are always present whether or not there are any electrons about to fill them.


How to Fill Shells and Orbitals with Electrons:

     The next thing to consider is 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 elements. This 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 (eg, the transition metals are sometimes called d-block elements, because their d-orbitals are being filled).

     As mentioned, it is difficult to visualize the behavior of electrons. One consequence of this 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 nothing to do with real-life spinning) can occupy one orbital at a time. This theory is known as the Pauli Exclusion Principle, named after the Austrian scientist Wolfgang Pauli (1900-1958) who invented it in 1925 and received a Nobel prize in 1945.

     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 have concluded that 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. However, 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.

     A simple orbital filling order scheme has been found to which there are only minor exceptions. 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)3...

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

1s(2) 2s(2) 2p(6) 3s(2) 3p(6) 4s(2) 3d(6)

     Adding the numbers in the parentheses will give 26. As for notation, the complete s- and p-orbitals can be abbreviated using the symbol of the corresponding noble gas4.

In our example, Iron would be: [Ar] 4s(2) 3d(6)

Applications of the Principle

The existence of defined orbitals and shells can be used in technology in numerous ways.
To analyze the atomic composition of anything (from fruit cakes to atmospheres of planets to sun-spots)
To generate colorful light in neon, xenon or mercury-lamps (see also 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)


1.     Even more obscure is the question why they would do something like that (see also: wave-particle duality).
2.     Which is a perversely complicated piece of science, which 'only three or four people on this planet understand', according to RP Feynman.
3.     In some textbooks the number in the parentheses can be found superscripted (like 4d7), but that is a minor detail.
4.     The element on the periodic table at the far right side, and one line above.