Electron Waves in the Hydrogen Atom
An electronA negatively charged, sub-atomic particle with charge of 1.602 x 10-19 coulombs and mass of9.109 x 1023 kilograms; electrons have both wave and particle properties; electrons occupy most of the volume of an atom but represent only a tiny fraction of an atom's mass. in an atom differs in two ways from the hypothetical electron in a box. First, in an atom the electron occupies all three dimensions of ordinary space. This permits the shapes of the electron waves to be more complicated. Second, the electron is not confined in an atom by the solidA state of matter having a specific shape and volume and in which the particles do not readily change their relative positions. walls of a box. Instead, the electrostatic force of attraction between the positive nucleusThe collection of protons and neutrons at the center of an atom that contains nearly all of the atoms's mass. and the negative electron prevents the latter from escaping.
In 1926 Erwin Schrodinger (1887 to 1961) devised a mathematical procedure by which the electron waves and energies for this more complicated situation could be obtained. A solutionA mixture of one or more substances dissolved in a solvent to give a homogeneous mixture. of the Schrodinger wave equation is beyond the scope of a general chemistry text. However, a great many chemical phenomena can be better understood if one is familiar with Schrodinger’s results, and we shall consider them in some detail.
The distribution of electron density predicted by the solution of Schrodinger’s equation for a hydrogen atom which has the minimum possible quantity of energyA system's capacity to do work. is illustrated in Fig. 1. A number of general characteristics of the behavior of electrons in atoms and molecules may be observed from this figure.
First of all, the hydrogen atom does not have a well-defined boundary. The number of dots per unitA particular measure of a physical quantity that is used to express the magnitude of the physical quantity; for example, the meter is the unit of the physical quantity, length. area is greatest near the nucleus of the atom at the center of the diagram (where the two axes cross). Electron density decreases as distance from the nucleus increases, but there are a few dots at distances as great as 200 pm (2.00 Å) from the center. Thus as one gets closer and closer to the nucleus of an atom, electron density builds up slowly and steadily from a very small value to a large one. Another way of stating the same thing is to say that the electron cloud becomes more dense as the center of the atom is approached.
A second characteristic evident from Fig. 1 is the shape of the electron cloud. In this two-dimensional diagram it appears to be approximately circular; in three dimensions it would be spherical. The following Jmol is a three-dimensional dot-density diagram for the orbital of the hydrogen atom shown in Figure 1. This lowest-energy orbital, called the 1s orbital, appears spherically symmetric. You can rotate the orbital around to verify this. In two dimensions, this can be illustrated more readily by drawing a circle (or in three dimensions, a sphere) which contains a large percentage (say 75 or 90 percent) of the dots, as has been done in the figure above. Since such a sphere or circle encloses most of (but not all) the electron density, it is about as close as one can come to drawing a boundary which encloses the atom. Boundary-surface diagrams in two and three dimensions are easier to draw quickly than are dot-density diagrams. Therefore chemists use them a great deal.