Energy States in Atoms - 10

You've probably heard the term "semiconductor" used often in news reports and discussions about information technology.  The semiconductor industry produces the chips that drive all modern technology:  computers, telephones, clocks, watches, and other products too numerous to list.  We will tackle the issue of how computing devices can be produced from semiconductors later.  This reading will explore what exactly a semiconductor is and how it differs from other materials.
 
The behavior of electrons in atoms, and of the atoms themselves, can be described in terms of the potential energy of the electrons.  (Disclaimer)  We often use energy diagrams that show different values of energy as horizontal lines, with lines further toward the top of the page (or screen) denoting higher energies.  To the right is an energy diagram showing the decrease in gravitational potential energy as someone walks down a staircase into a basement.  Figure (a) shows the stairs themselves.  Figure (b) is the corresponding potential energy diagram.  We have set the energy at the top of the stairs to be zero, so the values of energy on individual stairs are negative.  Note how the lines are evenly spaced, indicating the same change in energy for each stair.  In this "system" of the person on the basement stairs, the lowest possible energy is achieved when the person is at the bottom of the stairs.  We call this lowest possible energy the "ground state" energy. (a) A person at the top of a flight of stairs; (b) the corresponding potential energy diagram, with the top of the stairs at zero energy.
An elevator in a subterranean weapons lab will only stop at specific heights. Like the energy levels in a staircase, energies in atoms are "quantized," which means only particular energies are possible.  In an atom, however, the energies are not uniformly spaced. Consider the workers in the subterranean weapons lab shown to the left.  The spacing of these levels is not uniform but decreases as you get closer to the surface.  This non-uniform spacing better resembles the spacing of energy levels in an atom.

A worker in this plant will have one of four particular values of gravitational potential energy, corresponding to the depth of one of the four levels.  You will not find a worker with, say, an energy halfway between that of Level 2 and Level 3.  A similar scheme is true in atoms.  Electrons cannot take any energy but must choose from the specific allowed energies characteristic of the material.  The figure to the right shows a few of these allowed energies for a silicon atom.  The lowest energy, marked n = 1, is the lowest energy possible for electrons in silicon.  Allowed energies are labeled by this "principle quantum number" n, with n increasing as energy increases.

We are following a fairly common convention of setting the energy to be zero when electrons just have enough energy to leave the atom.  Thus negative energies indicate that an electron is "bound" and remains in the atom an electron with positive energy is no longer bound to the nucleus and can leave an atom. 

The idea that electrons can exist with only specific energies was proposed by Niels Bohr in 1913.  Further explanation of this effect is found on numerous other sites listed on the References page.  For the purposes of this module it is sufficient to acknowledge that Bohr's theory about quantized energies was correct.
 

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Copyright © 2003 Doris Jeanne Wagner and Rensselaer Polytechnic Institute.  All Rights Reserved.