Quantum Mechanical Models

Bohr’s model was eventually superseded by models based on quantum mechanics, a branch of physics that tries to make sense of the strange wave-like behaviors of electrons and other subatomic particles. The first full theory of quantum mechanics was developed a little more than a decade after Bohr proposed his model of the atom. It provided many further insights about the structures and behaviors of atoms, but also revealed some rather astounding things about the fundamental nature of physical reality. Some basic features of quantum mechanical models will be explained on the next few pages; the theory itself—and its startling implications about reality—will be discussed in chapter 7.

According to quantum mechanics, electrons don’t follow simple circular orbits but behave in more complex ways. Still, the theory upholds Bohr’s insightful hypothesis: electrons do not obey the laws of classical physics (Newton’s laws and Maxwell’s equations), but follow an entirely different set of laws. As Bohr suggested, electrons behave in some respects like waves and in some respects like particles. And because they behave as both waves and particles, only certain energies are allowed. That was Bohr’s most important innovation, which led quickly to the development of quantum theory.

In quantum mechanical models of atomic structure, the Bohr orbits are replaced by wave-like states called orbitals. Unlike the orbits in the Bohr and Rutherford models, orbitals are not circles. They are three-dimensional shapes. The orbital with lowest energy is simply a sphere that surrounds the nucleus, but at higher energies orbitals have complex shapes, as shown in the figure below. These shapes correspond to various types of three-dimensional standing waves that an electron can form around the nucleus.

The borders of an orbital are not precisely defined. In other words, orbitals have no definite boundaries: they do not begin or end at any particular location. This is because electrons don’t have definite locations, even when they are behaving more or less like particles. The smallest particles we can see with our eyes—particles of dust and the like—always appear to be located at specific places, i.e. specific points in space. But electrons aren’t like that. An electron tends to spread itself over a region of space, and this region has no definite boundaries. Some experiments suggest that an electron can even exist in numerous places at once! We’ll talk about that in chapter 7. For now, the important thing to know is simply that electrons don’t have exact positions, and for this reason atomic orbitals have no definite edges or boundaries. They’re sort of “fuzzy,” so to speak.

The structure of an atomic orbital is represented by a probability density function—a mathematical function that specifies the chance of finding an electron in any given region near the nucleus when the electron’s position is measured. We can picture this density function as a hazy cloud that surrounds the nucleus of an atom, a cloud that may be wispy in some places and thicker in others. Denser parts of the cloud represent areas where the electron is more likely to appear if you try to detect it; thinner areas represent regions where the electron is less likely to appear. The electron might be detected anywhere within the cloud, but it really has no definite location, at least until it interacts with the detector. (That’s what quantum mechanics seems to imply, anyway. We’ll discuss this in chapter 7.)