Review of Quantum Theory History• John Dalton – atoms are indivisible, no discussion of sub-atomic particles.

• J.J. Thomson – discovers the electron using the cathode ray tube, assigns it a negative charge.

• Goldstein – given credit for “finding” the proton (first particle) five years before Thomson discovers the electron.

• Accepted model of the atom at this point is the “plum-pudding” model.

• Rutherford discovers that the atom has a nucleus where all of the protons are located and that the “electron cloud” is mostly empty space. This is the gold foil experiment and leads to the “Rutherford model”.

• Niels Bohr proposes that the electrons move about the nucleus in fixed circular orbits. This leads to the “solar system” model of the atom.

• Max Planck calculates the energies that electrons may have. Also determines that electrons may absorb or emit “photons” as they gain or lose energy. This leads to the phrase “quantum theory”.

More Review• Heisenberg writes the “Uncertainty Principle” which becomes the precursor to the field of Statistical Mechanics.

• Schrodinger develops the “Schrodinger Equation” that proposes that science should utilize probabilities to describe the location of electrons having energies defined by Planck.

And then there was deBroglie…

deBroglie and Wave Mechanics

• Louis deBroglie was a French physicist who would eventually win a Nobel Prize for his “Duality of Light” theory.

• In this theory, he offers a solution to a great debate by suggesting that light is both a particle and a wave form of energy.

• Remember that Planck has demonstrated that electrons will give off light as they fall from higher energies to lower energies.

• deBroglie suggests that electrons should be thought of as being like light, and therefore they will follow the principles outlined in his theory.

• This idea gains wide acceptance and the “Quantum Wave Model” of the atom is adopted.

Elements of the Wave Model

• The study of waves includes a number of measurements. The simplest of these is the “wavelength” which is the distance between identical points on successive waves.

-1.5

-1

-0.5

0

0.5

1

1.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

1 wavelength

1 wavelength

• deBroglie submits that electrons having different energies will most likely be in 3-dimensional zones that have sizes representing the differences in energy.

• Zones with greater energy will surround zones that have less energy. These zones become known as “principal energy levels” and are called SHELLS in most textbooks.

• We currently recognize that the electron cloud has seven (7) of these shells. Each of them has a designation. Labeling from closest to the nucleus, we have

K, L, M, N, O, P, Q

K

L

M

N

O

P

Q

Energy Sub-levels

• The shells themselves are divided into different shaped regions that correspond to very specific energies within the shells.

• These regions are technically called energy sub-levels, but most books refer to them as orbitals.

• There are four (4) different types of orbitals, each corresponding to an energy within a shell.

• These orbitals are designated s, p, d, f

The shape of the “s” orbital

• This orbital is the easiest of the orbital types to comprehend. It is simply

spherical.

The shape of the “p” orbital

• Depending upon which book you read, this orbital will be described as “figure-8” shaped, or “dumb-bell” shaped. You can think of it as two inflated balloons tied together.

The “p” orbital becomes more difficult to understand because nature presents them in sets of 3.

Each will be aligned with an axis on a three-dimensional cartesian coordinate system with the intersection of the three orbitals being the nucleus.

Now for the “d” orbital…• This orbital is more complicated than the “p” orbital.

• Textbooks will typically describe it as “cloverleaf” shaped.

The ‘d” orbital occurs in sets of 5. Four of the set are easy to understand, but the 5th is simply weird…

And finally, there is the “f” orbital• There is no single term to describe the shape of this orbital, it is far too complex.

The “f” orbital occurs in sets of 7. They are all bizarre.

How does this all fit together???• Remember that all of these orbitals are simply regions in space corresponding to specific energies that electrons may have.

• There are no walls or barriers between the orbitals or shells.

• Electrons are able to move within a single orbital if they have the energy associated with that orbital.

• However, if an electron gains energy (absorbs a photon), it will move to a new orbital that corresponds to its new energy.

• Conversely, if an electron loses energy (emits a photon), it will “fall” to a lower energy orbital.

• The most difficult aspect of all of this is that these orbitals are “superimposed” over and through each other. An electron’s “location” is defined by the energy it is assumed to possess.

• The net result of all of these orbitals and all of these shells is essentially a spherical electron cloud.

Representation of the s and p orbitals of the K and L shells. The nucleus will be at the very center of the 1s orbital in the image on the right.