Quantum Mechanical Model

GETTING TO KNOW ERWIN SCHRODINGER..

 Erwin Schrödinger was born on August 12, 1887, in Vienna, the only child of Rudolf Schrödinger, who was married to a daughter of Alexander Bauer, his Professor of Chemistry at the Technical College of Vienna.  He was a highly gifted man with a broad education. After having finished his chemistry studies, he devoted himself for years to Italian painting. After this he took up botany, which resulted in a series of papers on plant phylogeny.

Schrödinger's wide interests dated from his school years at the Gymnasium, where he not only had a liking for the scientific disciplines, but also appreciated the severe logic of ancient grammar and the beauty of German poetry.

From 1906 to 1910 he was a student at the University of Vienna, during which time he came under the strong influence of Fritz Hasenöhrl, who was Boltzmann's successor. It was in these years that Schrödinger acquired a mastery of eigenvalue problems in the physics of continuous media, thus laying the foundation for his future great work. He assistant to Franz Exner, he, together with his friend K. W. F. Kohlrausch, conducted practical work for students. It came as a result of his dissatisfaction with the quantum condition in Bohr's orbit theory and his belief that atomic spectra should really be determined by some kind of eigenvalue problem. For this work he shared with Dirac the Nobel Prize for 1933.

In 1936 he was offered a position at University of Graz, which he accepted only after much deliberation and because his longing for his native country outweighed his caution. With the annexation of Austria in 1938, Soon afterwards he managed to escape to Italy, from where he proceeded to Oxford and then to University of Ghent. After a short stay he moved to the newly created Institute for Advanced Studies in Dublin, where he became Director of the School for Theoretical Physics. He remained in Dublin until his retirement in 1955.

After his retirement he returned to an honored position in Vienna. He died on the 4th of January, 1961, after a long illness, survived by his faithful companion, Annemarie Bertel, whom he married in 1920

What is a quantum model?

The quantum model is a probability area an electron may be located in.  In 1923 Louis de Broglie suggested that an electron moves with a wavelength that completes a circle, which would explain the different energy levels as Bohr’s model did but would also explain the wave diffraction pattern obtained by C.J. Davisson and L.H. Germer.  In 1925 Erwin Schrödinger developed his wave equation which explained the motion of the electron by taking into effect the forces surrounding the electron.

Where did this model come from?
Bohr’s development of Rutherford’s planetary model had begun the process of introducing quantum theory to the structure of the atom (see developing a model of the atom: radioactive atoms). Bohr introduced the idea of stationary states in which the atom was stable. Transitions between these states explained the existence of spectral lines.

In the case of hydrogen, he was able to derive energy levels: transitions between his predicted energy levels matched the lines in the hydrogen spectrum. However, his model could not predict energy levels for any other atoms (though those of the hydrogen-like alkali metals could be approximated).
 
It took the work of Heisenberg and Schrödinger to separately come up with ways of describing more fully the quantized energy levels of atoms. Heisenberg used matrices and Schrödinger developed a wave equation. It is solutions of Schrödinger‘s equation that provide pictures of electrons’ probability densities around the nucleus of an atom.

MORE ABOUT THE QUANTUM MECHANICAL MODEL OF AN ATOM.

1930’s:

Erwin Schrödinger's most important contribution to the current Atomic Model was his development of the mathematical description that described the paths electrons would most likely follow in their orbits around the nucleus.  The formulas that Schrödinger developed in 1926 would be later called the basis of quantum mechanics, and awarded him a Nobel Prize. Eventually, Schrödinger determined that instead of Bohr's suggested orbits, there were actually orbitals. Instead of the idea of the electrons following a pre-determined path, the electrons would be moving around in an area. These ideas, including the quantum mechanical formulas, were presented in his "Wave Mechanical Formula." This model eventually became the new Modern Atomic Theory. 

Here is a quantum mechanical picture of a Hydrogen atom. The nucleus is not shown, but is located at the center of the picture. 

Some things to notice: 

You can see where the electron is most likely to be: near the nucleus.  

            You can't tell exactly where the electron is, just where it is most likely to be. 

The individual dots are not electrons. They are meant to be used in the context of how dense or heavy an area of dots appears. 

The more crowded (or heavier packed) the dots are in a particular region, the better chance you have of finding the electron there. 

Wave Mechanical Model: Power Boat Analogy

When a power boat is cruising on a lake, the wave which it produces has its greatest amplitude right at the boat, and the amplitude decreases as the distance from the boat increases. Thus you could locate the most probable location of the boat by analyzing the amplitude and energy of its associated water wave.

This is analogous to the wave mechanical model which visualizes the atom as a positive nucleus surrounded by vibrating electron waves. The Schrödinger Wave Equation describes the amplitude and other characteristics of the waves which are associated with the moving electrons, and thus it also is able to describe the energy and location of the orbiting electrons.

 

Here's a video about the features of a Quantum Mechanical Model of an Atom

Sources: 

http://www.youtube.com/watch?v=68friBTvHSw

http://www.umanitoba.ca/outreach/crystal/resources

http://www.britannica.com/EBchecked/topic/684121/chemical-bonding/43383/The-quantum-mechanical-model

http://nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html