Beginning Organic Chemistry (BOC)
1. Basic Knowledge
b. Electronic Structure of Atoms
i. A Deeper Look.

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Distribution of Electrons in Atoms.

The following is a very brief discussion of the main points of atom theory. You should consult a good general chemistry text or Internet sites for further information.


Matter, at the atomic level, differs greatly in its properties from matter that we can see around us. Because of its small mass and volume at the atomic level, the Heisenberg Uncertainty Principle must be applied, whereas at the mass, size, and volume that we see, this principle can be neglected.

Application of the uncertainty principle to electrons means that any attempt to know the position for an electron at the same time as knowing its energy is impossible. Essentially this means that we cannot apply the equations for particles (which assume that the position and energy of the particle can be measured simultaneously) to the electron in the atom. At this point in time, equations which can be applied are the equations of a wave (wave mechanics or quantum mechanics).

Wave Equations.

Solving the wave equations for an atom involves solving second order differential equations. Because of the number of interactions between the different electrons and between the electrons and the nucleus, this is impossible to do exactly except for the hydrogen atom, and so is done approximately, based on the solutions for the hydrogen atom. You may be able to visualize the different waves that can be on a stretched string, so with the atom, there are a number of different waves possible for electrons. These different waves can each be represented by a set of three quantum numbers (n, l, and ml). The "aufbau" approach has been developed to find which waves the electrons occupy in an atom.

"Aufbau", or "build-up".

The "aufbau" approach finds the 'ground state' for the atom by filling the electron waves of lowest energy. Using the common method of indicating a wave using only the n and l values (with these latter coded such that s indicates an l value of 0, p an l value of 1, and d an l value of 2), the energy of the waves in increasing order is:

1s < 2s < 2p < 3s < 3p < 4s < 4p.


The quantum mechanical approach to the atom inevitably leads to the problem of how to model the atom in a meaningful way when the electron is described by a three-dimensional wave equation. The adopted way is to plot a three-dimensional shape, within which volume the electron mostly resides. Such a shape is called an orbital. When we do this we find that orbitals differ in size with the value of the n quantum number, and in shape with the value of the l quantum number. Three-dimensional, rotatable models of some atomic orbitals are available from the University of Arizona.

Visualizing atomic orbitals

Some of the Arizona orbitals are imported for you on a separate page. Note that these files are moderately large and so may take time to download. They require the chime plug-in.

Look at atomic orbitals

Date created: 2005 06 08.