Origin of the Quantum Mechanics theory

The Bohr’s model of the atom explains perfectly well the surprising regularities of the lines spectrum emitted by the atoms, but this model has some insubstantialities and defects:

1. As Bohr himself said, the model doesn’t explain why the electrons are compelled to cover only certain orbits. As a matter of fact Bohr assumed the Angular Momentum could have only discrete value (Third Postulate), but he didn’t know why.
2. The Bohr’s model talks about circular orbits, but circular orbits are two-dimensional while the atom is a more complex three dimensional object.
3. The model doesn’t explain the differences between the frequencies of the light emitted by the atoms and the rotation frequencies of the electron in the atom.

Starting from the ideas of Planck and Einstein, Louis de Broglie introduced a new hypothesis: since the light behaves in some cases as a wave and in others as made up of particles, why can’t particles themselves have the same dual nature too?

An electromagnetic wave (light) with frequency and wavelength , can be described as made up of particles called Photons, each Photons have Energy and Linear Momentum computed as follows

(is the Planck’s constant and is the speed of light into vacuum.)

A particle with mass , while moving with speed gets a linear Momentum and an energy . This particle can be thought as a wave irradiating  in space with a frequency and a wavelength computed by reversing the previous system and coupling it with the relationship

, ,

de Broglie relationships

is called de Broglie wavelength.

In this way if we know the Linear Momentum and the Energy of an electron, we can think it as a wavelike entity whose wavelength and frequency are given by de Broglie relationships.

By depicting electron in the atom like a standing wave on a circular orbit, de Broglie could easily explain Bohr’s Third Postulate:

In order to form a standing wave on a circular orbit, the wavelength of the electron must be restricted to values whose multiples equal the circumference of the orbit:

de Broglie condition on the electron standing wave

If this condition is not verified the electron standing wave can’t exist in the atom.

See the text figure 17.22 page 359 and try this interactive  java applet:

http://www.colorado.edu/physics/2000/quantumzone/debroglie.html

By solving the system

de Broglie condition explains and leads us to the third Bohr’s postulate on allowed orbits .

One year after the suggestion of de Broglie, Erwin Schrödinger  started to develop a theory of the atom that used three-dimensional standing waves to describe the orbits of the electron around the nucleus.