OBJECTIVE: To understand how the electron’s position is represented in the wave mechanical model.
By the mid-1920s it had become apparent that the Bohr model was incorrect. Scientists needed to pursue a totally new approach. Two young physicists, Louis Victor de Broglie from France and Erwin Schrödinger from Austria, sug- gested that because light seems to have both wave and particle characteristics (it behaves simultaneously as a wave and as a stream of particles), the electron might also exhibit both of these characteristics.
When Schrödinger carried out a mathematical analysis based on this idea, he found that it led to a new model for the hydrogen atom that seemed to apply equally well to other atoms—something Bohr’s model failed to do. We will now explore a general picture of this model, which is called the wave mechanical model of the atom.
In the Bohr model, the electron was assumed to move in circular orbits. In the wave mechanical model, on the other hand, the electron states are described by orbitals. Orbitals are nothing like orbits. To approximate the idea of an orbital, picture a single male firefly in a room in the center of which an open vial of female sex-attractant hormones is suspended. The room is extremely dark and there is a camera in one corner with its shutter open. Every time the firefly “flashes,” the camera records a pinpoint of light and thus the firefly’s position in the room at that moment. The firefly senses the sex at- tractant, and as you can imagine, it spends a lot of time at or close to it. How- ever, now and then the insect flies randomly around the room.
When the film is taken out of the camera and developed, the picture will probably look like Figure 11.18. Because a picture is brightest where the film has been exposed to the most light, the color intensity at any given point tells us how often the firefly visited a given point in the room. Notice that, as we might expect, the firefly spent the most time near the room’s center.
According to the wave mechanical model, the electron in the hydrogen atom can be pictured as being something like this firefly. Schrödinger found that he could not precisely describe the electron’s path. His mathematics enabled him only to predict the probabilities of finding the electron at given points in space around the nucleus. In its ground state the hydrogen electron has a probability map like that shown in Figure 11.19. The more intense the color at a particular point, the more probable that the electron will be found at that point at a given instant. The model gives no information about when the electron occupies a certain point in space or how it moves. In fact, we have good reasons to believe that we can never know the details of electron mo- tion, no matter how sophisticated our models may become. But one thing we feel confident about is that the electron does not orbit the nucleus in circles as Bohr suggested.