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Chemistry

Schrödinger's atom and Quantum Numbers

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Schrödinger's atom and Quantum Numbers

Outline

Calculating the Electron Orbital Locations

As we mentioned, the Bohr atom is a very much simplified model of the orbitals allowed to electrons in the hydrogen atom. A much more accurate model uses a wave equation to determine the most likely location of the electron for a given set of parameters, the electron's quantum numbers.

Schrödinger's Model

According to the Schrödinger model (the math of which you are mercifully too young to have to deal with yet), the wave functions describing the wave behavior limit the electron's location to specific volumes around the nucleus. But the electron function describes only the probability that an electron lies within a certain area; it does not describe the actual location of a specific electron at any point in time. There is a limit on what we can know: the wavelength of the electron dictates the amount of error in the momentum of the electron, which is the product of its mass times its velocity. The practical result of the Heisenberg Uncertaintly Principle is that the better we know the velocity of the electron, the less we know about its actual position, or vice versa.

Quantum Numbers

Since electrons in bonds are what holds atoms together in molecules, describing electron states become very important to chemists. There are some important rules to remember in this attempt:

  1. There are four quantum numbers describing the four characteristics of the electron.
    1. The n value is the principle quantum number. It can take any integer value from 1 to infinity. The n value indicates the energy level. Electrons with higher n values are further from the nucleus. Energy level is important: it indicates the kinetic energy the electron has in moving from one position to another within the atom, and it indicates the amount of work that must be done in order to change the position of the electron within the atom.
    2. The l value is the angular momentum number. It can take any positive integer value from 0 to n - 1. The l value indicates the angular momentum of the electron, and dictates the shape of the orbital (spherical, dumbell, convoluted). For historical reasons, the l values are matched with letters indication the shape of the orbital.
      1. l = 0 = s = spherical, one per level
      2. l = 1 = p = dumbell, three per level
      3. l = 2 = d = harder to draw!, five per level
      4. l = 3 = f = really hard to draw, nine per level
    3. The m value is the magnetic quantum number. It can take any integer value from -l to 0 to +l. The m value indicates the orientation of the orbital around the nucleus. For example, if the orbital shape is a dumbbell, there should be three: one along the X axis, one along the Y axis, one along the Z axis. The m di value indicates the X, Y, or Z direction of the electron's l-shaped orbital.
    4. The s value is the spin quantum number. It can be +1/2 or -1/2. It indicates the direction of spin of the electron.
  2. Each electron in an atom has a unique set of quantum numbers. Since the s value can have only 2 possible values for a given configuration of n, l, and m, only two electrons can have the same orbital.
  3. For purposes of chemical bond evaluation, only the quantum states of the valence electrons are important.

The quantum numbers explain the behavior of electrons in atoms, and the behavior of electrons in atoms explains chemical reactivity. Study the Periodic Table according to Electron orbital structure to see how the quantum values of its electrons can tell us how the atoms of an element will form bonds. You may also find Purdue's Chemistry Website useful.

Practice with the Concepts

What density pattern (shape of orbital in three dimensions) would you expect of a 3px orbital?

How many electrons can exist in an atom fully populated through level 3?

Discussion Questions

Optional Readings

For help with Electron Configurations, search out the links at the Woodrow Chemistry Teachers site.

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