also applies to mathematics. Computer programmers call it the KISS (Keep It Simple, Stupid!) principle. In science, we call it parsimony, and can sum it up by saying: Don't make nature any more complex than it already is.
1.4.2 The scientist as skeptic
Although we often refer to scientific facts, there are no facts in science. A fact, by definition, cannot be wrong. Both observations and theories can be, and sometimes are, wrong. Of course, some observations (e.g., the Sun rises each morning in the East) and theories (the Earth revolves around the Sun) are so oft-repeated and so well established that they are not seriously questioned. But remember that the theory that the Sun revolves around the Earth was itself once so well established that Galileo was tried and sentenced to house arrest for questioning it.
One of the ways in which science differs from other fields of endeavor is that in science, nothing is sacred. It is best to bear in mind the possibility, however remote, that any observation or theory can be wrong. Conversely, we must also accept the possibility that even the wildest observations and theories might be correct: in quantum physics, for example, there is a great range of well-replicated observations that can only be labeled as bizarre (see, e.g., Gribbin, 1984). “Intuition” plays a greater role in science than most scientists might be willing to admit, even though scientific intuition is often very useful. Nevertheless, our intuition is based largely on our everyday experience, which is very limited compared with the range of phenomena that science attempts to understand. As a result, our intuition often deceives us. Sometimes we must put it aside entirely. That a clock will run slower if it moves faster, or that an electron can behave as both a wave and a particle, or that continents move great distances, are all very counter-intuitive observations, but all are (apparently) correct. Thus, skepticism is one of the keys to good science. In science, never totally believe anything, but never totally disbelieve anything, either.
1.5 ELEMENTS, ATOMS, CRYSTALS, AND CHEMICAL BONDS: SOME CHEMICAL FUNDAMENTALS
1.5.1 The periodic table
We'll begin our very brief review of chemical fundamentals with the periodic table (Figure 1.1). In Dmitri Mendeleyev's‡ day, chemistry and geochemistry were not as distinct as they are today. Chemists were still very much occupied with discovering new elements, and they sought them in natural materials. For a variety of reasons, therefore, the Mendeleyev's periodic table provides a good point of departure for us.
Mendeleyev's periodic table of the elements was the sort of discovery that produces revolutions in science. Chemistry had evolved tremendously through the first half of the nineteenth century. Between the publication of Lavoisier's The Elements of Chemistry, often considered the first modern text in chemistry, in 1789 and Mendeleyev's 1869 paper, the number of known elements had increased from 23 to 67. The concepts of the atom and the molecule were well established, and the role of electromagnetic forces in chemical interactions was at least partly understood. Nevertheless, the structure of atoms, and how this structure governed chemical properties of the atom, were to be twentieth-century discoveries (though there were some interesting prescient theories). Mendeleyev's great contribution was to show that properties of the elements are a periodic function of atomic weights. Like all good scientific theories, this one made predictions: Mendeleyev was not only able to predict the discovery of then-unknown elements, such as B, Sc, Ga, and Ge, but also their characteristics and the materials or minerals in which they were most likely to be found (Strathern, 2000). The periodic table led the way not only to the discovery of the remaining elements, but also to understanding the fundamental controls on chemical behavior.
Figure 1.1 shows the periodic table as we know it today. Like most theories, Mendeleyev's has gone through some revision since it was first proposed. Most importantly, we now organize the periodic table based on atomic number rather than atomic weight. The atomic number of an element is its most important property and is determined by the number of protons in the nucleus (thus the terms atomic number and proton number are synonymous). The number of protons in turn determines both the number of electrons in the neutral atom and how these electrons are organized.
The mass of an atom is a function of both the proton number and the neutron number, i.e., the number of neutrons in the nucleus. Generally, several possible numbers of neutrons can combine with a given number of protons to form a stable nucleus (we will discuss nuclear stability in greater detail in Chapter 8). This gives rise to different isotopes of the same element, i.e., atoms that have the same atomic number but different masses. For example, helium has two stable isotopes: 3He and 4He. Both 3He and 4He† have two protons (and a matching number of electrons), but 4He has two neutrons while 3He has only one.
Figure 1.1 The periodic table showing symbols and atomic numbers of naturally occurring elements. Many older periodic tables number the groups as IA-VIIIA and IB-VIIB. This version shows the current International Union of Pure and Applied Chemistry (IUPAC) Convention.
The atomic weight of an element depends on both the masses of its various isotopes and on the relative abundances of these isotopes. This bedeviled nineteenth century chemists. William Prout (1785−1850), an English chemist and physiologist, had noted in 1815 that the densities of a number of gases were integer multiples of the density of hydrogen (e.g., 14 for nitrogen, 16 for oxygen). This law appeared to extend to many elemental solids as well, and it seemed reasonable that this might be a universal law. But there were puzzling exceptions. Cl, for example, has an atomic weight of 35.45 times that of hydrogen. The mystery wasn't resolved until Thompson demonstrated the existence of two isotopes of Ne in 1918. The explanation is that while elements such as H, N, O, C, and Si consist almost entirely of a single isotope, and thus have atomic weights very close to the mass number of that isotope, natural Cl consists of about 75% 35Cl and 25% 37Cl‡.
1.5.2 Electrons and orbits
We stated above that the atomic number of an element is its most important property. This is true because the number of electrons is determined by atomic number, and it is the electronic structure of an atom that largely dictates its chemical properties. The organization of the elements in the periodic table reflects this electronic structure.
The electronic structure of atoms, and indeed the entire organization of the periodic table, is determined by quantum mechanics and the quantization of energy, angular momentum, magnetic moment, and spin of electrons. Four quantum numbers, called the principal, azimuthal, magnetic, and spin quantum numbers and conventionally labeled n, l, m, and ms, control the properties of electrons associated with atoms. The first of these, n, which may take values 1, 2, 3, ..., determines most of the electron's energy as well as its mean distance from the nucleus. The second, l, which has values 0, 1, 2, ... n−1, determines the total angular momentum and the shape of the orbit. The third, m, which may have values −l, ... 0 ... l, determines the z component of angular momentum and therefore the orientation of the orbit. The fourth, ms, may have values of –½ or +½ and determines the electron's spin. The first three quantum numbers result in the electrons surrounding the nucleus being organized into
