Chemistry
Development of the Quantum Mechanical Model
quantum theory.doc
The following is a brief compilation of information found on the Internet about the development of the quantum
mechanical model of the atom.
1. Planck developed Quantum Theory in 1900 to explain the energy emitted by a “blackbody”. A blackbody is an
object that absorbs all the energy that strikes it. A blackbody is also a perfect emitter of energy. The energy
depends only on the temperature of the object and the frequency of the radiation. E = hv Planck’s explanation
only fit the data when he assume that energy was released in discrete amounts, called quanta.
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/The_Quantum_age_begins.html
2. In 1905 Einstein examined the photoelectric effect. The photoelectric effect is the release of electrons from
certain metals or semiconductors by the action of light. The electromagnetic theory of light does not agree with the
experimental evidence. Einstein proposed a quantum theory of light to solve the difficulty and then he realized that
Planck’s theory made implicit use of the light quantum hypothesis. By 1906 Einstein had correctly guessed that
energy changes occur in jumps which are multiples of hv where h is Planck’s constant and v is the frequency. He
proposed a “particle” of light (photon) that carried a quantum of energy.
http://www-gap.dcs.st- and.ac.uk/~history/HistTopics/The_Quantum_age_begins.html
3. In 1913 Neils Bohr was the first person to apply the quantum theory to atomic structure. Bohr’s theory
accounted for the series of lines observed in the spectrum of light emitted by atomic hydrogen. Bohr was able to
determine the frequencies of these spectral lines to considerable accuracy by expressing them in terms of the charge
and mass of the electron and Planck's constant. To do this, Bohr also postulated that an atom would not emit
radiation while it was in one of its stable states but rather only when it made a transition between states. The
frequency of the emitted radiation would be equal to the difference in energy between those states divided by
Planck's constant. This meant that the atom could neither absorb nor emit radiation continuously but only in finite
steps or quantum jumps. The energy of an allowed state can be calculated from En=-Rh(1/n2) where n=1, 2, 3…
http://web.fccj.org/~ethall/quantum/quant.htm
4. Making use of matrix algebra, Heisenberg, in 1925, developed a system called matrix mechanics. It consisted of
an array of quantities which when appropriately manipulated gave the observed frequencies and intensities of
spectral lines. The consequence of Heisenberg's work is his revolutionary (1927) “uncertainty principle”,
qp > h
The uncertainty of position (q) of an electron in an atom multiplied by the uncertainty of its momentum (p) must
be greater than Planck's constant (h). The uncertainty principle tells us that all observable quantities are subject to
changes determined by Planck's constant and we cannot know position and momentum simultaneously. While a
photon will not disturb an object like a house, it does alter position and momentum when bounced off an electron.
Heisenberg is out for a drive when he's stopped by a traffic cop. The cop says, "Do you know how fast you were
going?" Heisenberg says, "No, but I know where I am."
http://web.fccj.org/~ethall/quantum/quant.htm
5. In 1924 de Broglie speculated that nature did not single out light as the only entity to exhibit wave-particle
duality. He proposed that ordinary particles such as electrons could also exhibit wave characteristics in certain
circumstances. de Broglie assumed that an electron has associated with it a system of "matter waves." These waves
possess crests that disappear at one point and appear an instant later at another point. The distance between
successive crests () is the de Broglie wavelength and it is calculated from  = h/mv, where h is Planck's constant
and mv is momentum. http://web.fccj.org/~ethall/quantum/quant.htm
6. In 1925, Wolfgang Pauli proposed a new quantum theory property called "two-valuedness." This fourth
quantum number is known as electron spin. Originally spin suggested an actual clockwise or counterclockwise
rotation of the electron. Now we use spin to distinguish between the two electrons that can occupy a single orbital.
The exclusion principle is now stated as, "No two electrons in an atom can have the same set of four quantum
numbers."
7. In 1926, adopting the proposal by Louis de Broglie that particles of matter have dual nature and in some
situations act like waves, Erwin Schrödinger produced the basic equation of quantum mechanics. The Schrödinger
equation treats electrons as matter waves:
The following is taken from The God Particle by Leon Lederman:
Leaving his wife at home, Schrödinger booked a villa in the Swiss Alps for two weeks, taking with him his
notebooks, two pearls, and an old Viennese girlfriend. Schrödinger's self-appointed mission was to save the
patched-up, creaky quantum theory of the time. The Viennese-born physicist placed a pearl in each ear to
screen out any distracting noises. Then he placed the girlfriend in bed for inspiration. Schrödinger had his
work cut out for him. He had to create a new theory and keep the lady happy. Fortunately, he was up to the
task.
The only problem with Schrödinger's equation was his interpretation of the matter wave was wrong. He described
as the density distribution--some regions rich in electron matter while others scarce. But it was Max Born who
figured out what the equation actually predicts. http://web.fccj.org/~ethall/quantum/quant.htm
7. In 1926, Max Born collaborated with his student Werner Heisenberg who had formulated the first laws of
quantum mechanics in order to develop the mathematical formulation that would adequately describe it. When
Schrödinger put forward his quantum mechanical wave equation, Born showed that the solution of the equation has
a statistical meaning of physical significance. Born's interpretation of the wave equation proved to be of
fundamental importance in the new theory of quantum mechanics. Schrödinger believed that the electron was
spread out in space and its density given by the value of 2. Almost immediately Born proposed what is now the
accepted interpretation: 2 gives the probability density of finding the electron. The distinction between the two
interpretations is important. If 2is small at a particular position, the original interpretation implies that a small
fraction of an electron will always be detected there. In Born's interpretation, nothing will be detected there most of
the time, but when something is observed, it will be a whole electron. The concept of the electron as a point particle
moving in a well-defined path around the nucleus is replaced in wave mechanics by clouds that describe the
probable locations of electrons in different states. These probability densities give the shapes of the s, p, d and f
orbitals. http://web.fccj.org/~ethall/quantum/quant.htm
Note: Max Born was Olivia Newton John’s grandfather.
This photograph of well-known
scientists was taken at the
international Solvay Conference in
1927. Among those present are
many whose names are still known
today. Front row, left to right: I.
Langmuir, M. Planck, M. Curie, H.
A. Lorentz, A. Einstein, P.
Langevin, C. E. Guye, C. T. R.
Wilson, O. W. Richardson. Second
row, left to right: P. Debye, M.
Knudsen, W. L. Bragg, H. A.
Kramers, P. A. M. Dirac, A. H.
Compton, L. V. de Broglie, M.
Born, N. Bohr. Standing, left to
right: A. Piccard, E. Henriot, P.
Ehrenfest, E. Herzen, T. De Donder,
E. Schroedinger, E. Verschaffelt, W.
Pauli, W. Heisenberg, R. H. Fowler,
L. Brillouin.
http://www.genesisquest.org/ideas/solvay.html