How Atoms Work

Electrons Can Behave as Waves: The Quantum Model of the Atom

Although the Bohr model adequately explained how atomic spectra worked, there were several problems that bothered physicists and chemists:

Why should electrons be confined to only specified energy levels?
Why don't electrons give off light all of the time? As electrons change direction in their circular orbits (i.e., accelerate), they should give off light.
The Bohr model could explain the spectra of atoms with one electron in the outer shell very well, but was not very good for those with more than one electron in the outer shell.
Why could only two electrons fit in the first shell and why eight electrons in each shell after that? What was so special about two and eight?

Obviously, the Bohr model was missing something!

In 1924, a French physicist named Louis de Broglie suggested that, like light, electrons could act as both particles and waves (see De Broglie Phase Wave Animation for details). De Broglie's hypothesis was soon confirmed in experiments that showed electron beams could be diffracted or bent as they passed through a slit much like light could. So, the waves produced by an electron confined in its orbit about the nucleus sets up a standing wave of specific wavelength, energy and frequency (i.e., Bohr's energy levels) much like a guitar string sets up a standing wave when plucked.

Another question quickly followed de Broglie's idea. If an electron traveled as a wave, could you locate the precise position of the electron within the wave? A German physicist, Werner Heisenberg, answered no in what he called the uncertainty principle:

To view an electron in its orbit, you must shine a wavelength of light on it that is smaller than the electron's wavelength.
This small wavelength of light has a high energy.
The electron will absorb that energy.
The absorbed energy will change the electron's position.

We can never know both the momentum and position of an electron in an atom. Therefore, Heisenberg said that we shouldn't view electrons as moving in well-defined orbits about the nucleus!

With de Broglie's hypothesis and Heisenberg's uncertainty principle in mind, an Austrian physicist named Erwin Schrodinger derived a set of equations or wave functions in 1926 for electrons. According to Schrodinger, electrons confined in their orbits would set up standing waves and you could describe only the probability of where an electron could be. The distributions of these probabilities formed regions of space about the nucleus were called orbitals. Orbitals could be described as electron density clouds (see Atomic & Molecular Orbitals for a look at various orbitals). The densest area of the cloud is where you have the greatest probability of finding the electron and the least dense area is where you have the lowest probability of finding the electron.