Origin of the Quantum Mechanics theory

Erwin Schrödinger and the development of the new theory

Later, one year after the suggestion of de Broglie (electrons like waves), Erwin Schrödinger developed a theory of the atom that used three-dimensional standing waves to describe the orbits of the electron about the nucleus, within the next five years Schrödinger and other scientist worked out the details of a much deeper theory, now known as Quantum Mechanics. This theory provides a very different view of the atom:

1. The electron doesn’t exist in well-defined circular orbits: rather, the electron, because of its wave nature, is spread out in space as a "cloud" of negative charge.
2. Electron cloud (called Orbital) must be interpreted as a probability distribution to find the electron at a certain position in space.

For a better understanding, the following draw shows the ground state of the hydrogen atom.

We have to talk about the "orbital" of the ground state (orbital is the region of space where the probability to find the electron is not zero) We leave the word "orbit" because the depiction of a definite trajectory of the electron in the atom is meaningless.

Fig.1. Orbital of the Ground state for the hydrogen atom. (The nucleus is at the origin of the three axis). 

The area where the dots are denser represents the region where the probability to find the electron is higher. We can’t predict the exact path the electron will follow, we can only calculate the probability to find it at different points. This limit grows up directly from the texture of the nature in itself as demonstrated by Werner Heisenberg with his UNCERTAINTY PRINCIPLE: It’s impossible to measure at the same time and perfectly well both Position and Momentum of a definite object. This statement (As we will see) doesn’t disturb in the macroscopic world, on the contrary it becomes crucial for micro-objects like electrons in the atoms. It makes no sense talking about orbits inside an atom, because electrons in atoms are not to be treated like particles with definite Position and Momentum , a more successful way to describe them is by treating them as wavelike entities.

The size and shape of the electron cloud (orbital) can be calculated for a given state of an atom. For the ground state in the hydrogen atom, the electron cloud is spherically symmetric (as shown in the previous figure). The electron cloud may not have a distinct border, atoms do not have a precise boundary or a well defined size. Observe the orbital of the hydrogen atom with the  java applet at:

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

Not all electron clouds have a spherical shape: complex atoms with more than one electron have more complex orbitals. For instance see the images at:

http://www-wilson.ucsd.edu/education/gchem/atomorbs/images/39.Fullscreenorbitals.jpeg

http://www-wilson.ucsd.edu/education/gchem/atomorbs/images/40.Fullscreenorbitals.jpeg

and try to build different orbitals changing your perspective with the applet at: