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 shells, subshells, and orbitals.* The Pauli exclusion principle requires that no two electrons in an atom may have identical values of all four quantum numbers. Because each orbital corresponds to a unique set of the first three quantum numbers and the spin quantum number has only two possible values, two electrons with opposite spins may occupy a given orbital. In Chapter 8 we will see that the properties of the nucleus are also dictated by quantum mechanics, and that the nucleus may also be thought of as having a shell structure.
Each shell corresponds to a different value of the principal quantum number. The periodic nature of chemical properties reflects the filling of successive shells as additional electrons (and protons) are added. Each shell corresponds to a ‘period’, or row, in the periodic table. The first shell (the K shell) has one subshell, the 1s, consisting of a single orbital (with quantum numbers n = 1, l = 0, m = 0. The 1s orbital accepts up to two electrons. Thus period 1 has two elements: H and He. If another proton and electron are added, the electron is added to the first orbital, 2s, of the next shell (the L shell). Such a configuration has the chemical properties of lithium, the first element of period 2. The second shell has 2 subshells, 2s (corresponding to l = 0) and 2p (corresponding to l = 1). The p subshell has 3 orbitals (which correspond to values for m of −1, +1, and 0), px, py, and pz, so the L shell can accept up to eight electrons. Thus, period 2 has eight elements.
There are some complexities in the filling of orbitals beyond the M shell, which corresponds to period 3. The 3d subshell is vacant in period 3 element in their ground states, and in the first two elements of period 4. Only when the 4s orbital is filled do electrons begin to fill the 3d orbitals. The five 3d orbitals are filled as one passes up the first transition series metals, Sc through Zn. This results in some interesting chemical properties, because which of the 3d orbitals are filled depends on the atom's environment, as we shall see in Chapter 7. Similarly, the second and third transition series metals correspond to filling of the 4d and 5d orbitals. The lanthanide and actinide rare earth elements correspond to the filling of the 4f and 5f shells (again resulting in some interesting properties, which we will consider subsequently). The predicted sequence in which orbitals are filled and their energy levels are shown in Figure 1.2. Figure 1.3 shows the electronic configuration of the elements.
Figure 1.2 The predicted sequence of orbital energies for electrons in atoms. S levels can hold 2 electrons, p, d, and f can hold 6, 10, and 14 respectively.
Figure 1.3 The periodic table of naturally occurring elements showing the electronic configuration of the elements. Only the last orbitals filled are shown, thus each element has electrons in the orbitals of all previous Group 18 elements (noble gases) in addition to those shown. Superscripts indicate the number of electrons in each subshell.
1.5.3 Some chemical properties of the elements
It is only the most loosely bound electrons, those in the outermost shells, that participate in chemical bonding, so elements sharing a similar outermost electronic configuration tend to behave similarly. Elements within the same column of the periodic table, or group, share outer electronic configurations and hence behave in a similar manner. Thus, the