Wave Mechanics

Bohr's model was the first to propose that electrons were found in specific energy levels, which he called orbits; with his model, he was able to correctly predict the emission spectrum of hydrogen atoms (H) and other one-electron systems. However, his model could not correctly predict the spectra of atoms or ions with more than one electron. It also had other important failings that are not worth getting into here.

The Bohr model was a tremendous paradigm-changing breakthrough, and was a powerful tool for explaning some basic physical phenomena. But it was quickly superseded by more sophisticated wave mechanical models for the behavior of electrons.

What Bohr got right was preserved by the wave mechanical model: it retains his idea the electrons only have certain allowed energies, and that these energies are related to the wavelengths of the electrons (hence, "wave mechanics"). However, the simplistic view of electrons as little planets, orbiting a sun-like nucleus, was jettisoned. The wave mechanical model embraced an interpretation of electrons as occupying complex three-dimensional shapes, spread out through space in ways that defy easy intuition.

This paradigm shift involved a change in terminology that is unfortunately rather subtle. Bohr's model described electron behavior in terms of orbits - simple circular paths through space. The complex 3D shapes that we will see described below were named orbitals. While this naming helps pay homage to Bohr and his ideas, it is unfortunately quite confusing for many students.

Orbitals

An orbital is a mathematically-defined region in the space around the nucleus in which there is a high probability of finding the electron. Like Bohr’s orbits, there are an infinite number of orbitals, but they can only have certain allowed energies. Different orbitals have different three-dimensional shapes as well.

An orbital is not a physical object any more than an orbit is. When we speak of an electron being “in” a particular orbital, we mean that the electron has the potential energy, and is found in the region, defined by that orbital. In a sense, an orbital is a visual and mathematical means of describing an energy state that an electron may have in an atom. The details of the energy state are influenced by the charge on the nucleus and by the presence of other electrons. For that reason, no two atoms or ions have exactly identical orbitals. However, they are similar enough that we use a common set of names to designate them.

Energy Levels

The orbitals in an atom are grouped into energy levels, called “main energy levels,” which are labeled 1 (the first main energy level), 2 (the second main energy level), and so on. The higher the energy level, the larger it is, the higher the energy of the electrons it contains, and the farther they are from the nucleus.

Note that the "energy" referred to here is potential energy, not kinetic. The situation is similar to a flower pot sitting on your front porch stoop – a low potential energy state – compared to a flower pot on the upstairs balcony – the higher potential energy state. Neither flower pot is moving, so neither one has appreciable kinetic energy. But the flower pot on the upstairs balcony has greater potential to do damage if it's dropped to the ground than the one on the porch.)

The electrons are attracted by the nucleus but repelled by each other. (Remember that opposite charges attract and like charges repel.) In the first main energy level, there is not much room and adding more than a couple electrons would result in electron-electron repulsions that are far larger than their attraction to the nucleus. In the second main energy level there is much more room, so more electrons can occupy it without being too repelled by each other. The shapes and orientations of the orbitals minimize electron-electron repulsion and maximize the attractive force from the nucleus.

Electron Organization

The chart below (easiest to read from the bottom up) lays out systematically the sublevels and orbitals that occur within each energy level. It should definitely be apparent by now that the orbital model is far more complex than Bohr's simple idea of orbiting planets.

You will notice that there is only one "s" orbital in each main energy level, that "p" orbitals always occur in groups of three, "d" orbitals in groups of five, and "f" orbitals in groups of seven. The pattern continues with later orbitals as well. Each letter group of orbitals within a main energy level is called a sublevel.

It is the sublevels that can hold different numbers of electrons because they contain different numbers of orbitals.

• Since s sublevels only ever have one orbital, they can always hold a maximum of two electrons

• Likewise, p orbitals always occur in groups of three, so a p sublevel can always hold up to six electrons, no matter what main energy level it's in.

• Continuing on, d orbitals always occur in groups of five, so a d sublevel can always hold up to ten electrons, two per d orbital in the sublevel.

• And finally, f orbitals always occur in groups of seven, so an f sublevel can hold up to fourteen electrons.

The distinction between main energy levels, sublevels, and orbitals is frequently confusing to students. The fact that the sublevels and the orbitals have the same names does not help. A 2p sublevel contains three 2p orbitals. A 3d sublevel contains five 3d orbitals.

At this point you may be feeling a bit overwhelmed with all the details involved in the wave mechanical model of the atom. For now it will be enough if you understand some of the basics about the wave mechanical model and have a general idea of how this model differs from the Bohr model. In the next lesson we will use the periodic table to see how its arrangement relates to the wave mechanical model of the atom, and how the chemical behavior of all matter is, at its heart, dependent on these patterns in the arrangement of electrons into orbitals, sublevels, and energy levels.

We will give a peak at these ideas in the next and final section of this lesson, and dive more fully into them in Lesson 6.