Section 2: Early Models of the Atom
The foundation for all that follows is the periodic table that Russian chemist Dmitri Mendeleev formulated by arranging the chemical elements in order of their known atomic weights. The table not only revealed the semi-periodic pattern of elements with similar properties, but also contained specific holes (missing elements, see Figure 4) that allowed Mendeleev to actually predict the existence and properties of new chemical elements yet to be discovered. The American chemist G. N. Lewis then created an electron shell model giving the first physical underpinning of both Mendeleev's table and of the patterns of chemical bonding. This is very much in the current spirit of particle physics and the Standard Model: symmetries, "magic numbers," and patterns of properties of existing particles that strongly suggest the existence of particles, such as the Higgs boson, yet to be discovered.
Figure 5: The father and son of chemical periodicity: Mendeleev and Lewis.
Source: © Left: Wikimedia Commons, Public Domain. Right: Lawrence Berkeley National Laboratory. More info
J. J. Thomson
When Mendeleev assembled his periodic table in 1869, he was the giant standing on the shoulders of those who, in the 6 decades before, had finally determined the relative masses of the chemical elements, and the formulae of those simple combinations of atoms that we call "molecules." In this arduous task, early 19th century chemists were greatly aided by using techniques developed over several millennia by the alchemists, in their attempts to, say, turn lead into gold. This latter idea, which nowadays seems either antiquated or just silly, did not seem so to the alchemists. Their view is reinforced by the realization that even as Mendeleev produced his table: No one had any idea what the chemical elements, or atoms as we now call them, were made of. Mendeleev's brilliant work was empiricism of the highest order. John Dalton, following Democrates, had believed that they weren't made of anything: Atoms were the fundamental building blocks of nature, and that was all there was to it.
Figure 6: Plum pudding (or raisin scone) model of the atom.
Source: © William P. Reinhardt, 2010. More info
This all began to change with J. J. Thomson's discovery of the electron in 1897, and his proposed atomic model. Thomson found that atoms contained electrons, each with a single unit of negative charge. To his great surprise he also found that electrons were very light in comparison to the mass of the atoms from which they came. As atoms were known to be electrically neutral, the rest of the atom then had to be positively charged and contain most of the mass of the atom. Thomson thus proposed his plum pudding model of the atom.
Rutherford and Lewis
Thomson's model was completely overthrown, less than 15 years later, by Ernest Rutherford's discovery that the positive charge in an atom was concentrated in a very small volume which we now call the "atomic nucleus," rather than being spread out and determining the size of the atom, as suggested by Thomson's model. This momentous and unexpected discovery completely reversed Thomson's idea: Somehow, the negatively charged electrons were on the outside of the atom, and determined its volume, just the opposite of the picture in Figure 6. How can that be?
The fact that electrons determine the physical size of an atom suggested that they also determine the nature of atomic interactions, and thus the periodic nature of chemical and physical interactions as summarized in Mendeleev's Table, a fact already intuited by Lewis, based on chemical evidence. At ordinary energies, and at room temperature and lower, nuclei never come into contact. But, then one had to ask: How do those very light electrons manage to fill up almost all of the volume of an atom, and how do they determine the atom's chemical and physical properties?
Figure 7: The Lewis shell model for the first three atoms in the modern periodic table.
A start had already been made. In 1902, when Rutherford's atomic nucleus was still almost a decade in the future, American chemist G. N. Lewis, had already proposed an empirically-developed shell model to explain how electrons could run the show, even if he was lacking in supplying a detailed model of how they actually did so.
He suggested that the first atomic shell (or kernel as he originally called it) held two electrons at maximum, the second and third shells a maximum of eight, and the fourth up to 18 additional electrons. Thus, for neutral atoms and their ion, the "magic numbers" 2, 8, 8, and 18 are associated with special chemical stability. Electrons in atoms or ions outside of these special closed shells are referred to as valence electrons, and determine much of the physical and chemical behavior of an atom. For example, in Unit 8, we will learn that atoms in metallic solids lose their valence electrons, and the remaining ionic cores form a metallic crystal, with the former valence electrons moving freely like water in a jar of beads, and not belonging to any specific ion. In doing so, they may freely conduct electrical currents (and heat), or under special circumstances may also become superconductors, allowing these free electrons to flow without resistance or energy dissipation.
Lewis also assumed that chemical bonding took place in such a way that stable molecules had fully filled shells, and that they formed these full shells by sharing electrons in pairs. The simplest example is the formation of the hydrogen molecule. He denoted a hydrogen atom by H, where the is the unpaired electron in the atom's half-filled first shell. Why two atoms in a hydrogen molecule? The answer is easy in Lewis's picture: HH. This pair of dots denotes that two shared electrons form the bond that holds the H2 molecule together, where the subscript means that the molecule consists of two hydrogen atoms. As there are now no longer any unpaired electrons, we don't expect to form H3 or H4. Similarly, helium, which already has the filled shell structure He, has no unpaired electrons to share, so does not bond to itself or to other atoms.
Figure 8: Molecules in the Lewis shell picture: the pair bond for H2 and Li2.
Next, Lewis introduced his famous counting rule (still used in models of bonding in much of organic chemistry and biochemistry): As the electrons are shared in overlapping shells, we count them twice in the dot picture for H2, one pair for each H atom. Thus, in the Lewis manner of counting, each H atom in H2 has a filled shell with two electrons just like Helium: He. Here, we have the beginning of the concept of pairs or pairing, albeit in the form of a very simple empirical model. Such pairings will soon dominate all of our discussion.
How can those tiny electrons determine the size of an atom?
Lewis's model implies certain rules that allow us to understand how to build up an atom from its parts, and for building up molecules from atoms, at least for the electrons that determine the structure of the periodic table and chemical bonding. Another set of such rules tells us how to form the nucleus of an atom from its constituent neutrons and protons. The formation of nuclei is beyond the scope of this unit, but we should note that even these rules involve pairing.
We can take such a blithe view of the structure of the nucleus because this first discussion of atoms, molecules, solids, and macroscopic quantum systems involves energies far too low to cause us to worry about nuclear structure in any detail. It is the arrangement of and behavior of the electrons with respect to a given nucleus, or set of nuclei, that determines many of the properties of the systems of interest to us. However, we should not forget about the nucleus altogether. Once we have the basic ideas involving the structure of atoms and molecules at hand, we will ask whether these composite particles rather than their constituent parts are bosons or fermions. When we do this, we will suddenly become very interested in certain aspects of the nucleus of a given atom. But, the first critical point about the nucleus in our initial discussion involves its size in comparison with that of the atom of which it is, somehow, the smallest component.
Figure 9: Rutherford's model of a hydrogen atom.
Source: © Wikimedia Commons, Public Domain. Author: Bensaccount, 10 July 2006. More info
Although it contains almost all of the atom's mass and its entire positive electrical charge, the nucleus is concentrated in a volume of 1 part in 1015 (that's one thousand trillion) of the physical volume of the atom. The size of the atom is determined by the electrons, which, in turn, determine the size of almost everything, be it solid or liquid, made of matter that we experience in daily life. For example, the volume of water in a glass of water is essentially the volume of the atoms comprising the water molecules that fill the glass. However, if the water evaporates or becomes steam when heated, its volume is determined by the size of the container holding the gaseous water. That also applies to the gaseous ultra-cold trapped atoms that we first met in Unit 5 and will encounter again later in this unit as Bose-Einstein condensates (BECs). They expand to fill the traps that confine them. How is it that these negatively charged and, in comparison to nuclei, relatively massless electrons manage to take up all that space?
Atoms and their nuclei
The atomic nucleus consists of neutrons and protons. The number of protons in a nucleus is called the atomic number, and is denoted by Z. The sum of the number of protons and neutrons is called the mass number, and is denoted by A. The relation between these two numbers Z and A will be crucial in determining whether the composite neutral atom is a boson or fermion. The volume of a nucleus is approximately the sum of the volumes of its constituent neutrons and protons, and the nuclear mass is approximately the sum of the masses of its constituent neutrons and protons. The rest of the atom consists of electrons, which have a mass of about 1/2,000 of that of a neutron or proton, and a negative charge of exactly the same magnitude as the positive charge of the proton. As suggested by its name, the neutron is electrically neutral. The apparently exact equality of the magnitudes of the electron and proton charges is a symmetry of the type we encountered in Units 1 and 2.
Do electrons have internal structure?
Now back to our earlier question: How can an atom be so big compared to its nucleus? One possibility is that electrons resemble big cotton balls of negative charge, each quite large although not very massive, as shown in Figure 10 below. As they pack around the nucleus, they take up lots of space, leading to the very much larger volume of the atom when compared to the volume of the nucleus.
Figure 10: A cotton ball model of an atom.
Source: © William P. Reinhardt. More info
However, there is a rather big problem with the simple cotton ball idea. When particle physicists try to measure the radius or volume of an individual electron, the best answer they get is zero. Said another way, no measurement yet made has a spatial resolution small enough to measure the size of an individual electron thought of as a particle. We know that electrons are definitely particles. With modern technology we can count them, even one at a time. We also know that each electron has a definite amount of mass, charge, and—last, but not at all least, as we will soon see—an additional quantity called spin. In spite of all this, physicists still have yet to observe any internal structure that accounts for these properties.
It is the province of string theory, or some yet-to-be created theory with the same goals, to attempt to account for these properties at length scales far too small for any current experiments to probe. Experimentalists could seek evidence that the electron has some internal structure by trying to determine whether it has a dipole moment. Proof of such a moment would mean that the electron's single unit of fundamental negative charge is not uniformly distributed within the electron itself. Since the Standard Model introduced in Unit 1 predicts that the electron doesn't have a dipole moment, the discovery of such an internal structure would greatly compromise the model.
For now, though, we can think of an electron as a mathematical point. So how do the electrons take up all the space in an atom? They certainly are not the large cotton balls we considered above; that would make everything too simple, and we wouldn't need quantum mechanics. In fact we do need quantum mechanics in many ways. Ironically, the picture that quantum mechanics gives, with its probability interpretation of an atomic wavefunction, will bring us right back to cotton balls, although not quite those of Figure 10.