1924 - Louis-Victor de Broglie Studied the wave-particle duality of light as suggested by Albert Einstein and extended this idea to include other objects such as the electron. The energy of an object (E) in motion is equal to its mass (m) times the square of its speed (s):

The energy of a wave (E) is proportional to its frequency (v) which is proportional to its speed (s) and inversely proportional to its wavelength () where h is Planck's constant:

If an object acts as both a particle in motion and a wave, then the two equations can be combined:

Cancelling like terms and rearranging the equation to solve for the wavelength results in the following:

By defnition, momentum (p) of an object is equal to the product of its mass (m) times its speed (s), so p can be substituted for ms to get the de Broglie equation.

• de Broglie equation - The wavelength () of an object in motion is inversely proportional to its momentum (p) where h is Planck's constant (6.626 x 10^-34 J-s):

With this equation, if the mass of an object is too large (as it is with most objects), the wavelength would be negligible.  Very small particles such as electrons, however, are small enough to exhibit the properties of both waves and particles.

Since electrons act as waves as well as particles, they cannot be restricted to circular orbits, but rather must exist in three-dimensional space.  Atoms or ions with a single electron are simple enough to be explained using the Bohr model which assumes that electrons travel in circular orbits around the nucleus.  An atom or ion with any more electrons, however, is too complex to be explained by the Bohr model.

Next:  "Quantum Numbers"