Absolutely Small - Michael D. Fayer [65]
FIGURE 11.1. Energy level diagram for atoms with many electrons. The spacings between the levels are not to scale. The energy depends on the principal quantum number, n, and the angular momentum quantum number, l, in contrast to the hydrogen atom (Figure 10.1), where the energy only depends on n. For n = 4, there is a single s orbital (l = 0), three different p orbitals (l = 1), five different d orbitals (l = 2), and seven different f orbitals (l = 3).
THE THREE RULES FOR PUTTING ELECTRONS IN ENERGY LEVELS
The hydrogen atom has a nucleus with charge +1 and a single negative electron. The helium atom has a nucleus with charge +2 and two negative electrons. Next comes the lithium atom (symbol Li) with a +3 charge on the nucleus (atomic number 3) and three negative electrons, which is followed by beryllium (Be) with a +4 nucleus and four negative electrons, and so on. The question is if we have an atom with a certain number of electrons, like beryllium with four, which energy levels do these four electrons go into? For hydrogen, the lowest energy state is the one in which the single electron is in the 1s orbital. If we excited the hydrogen 1s electron to say a 2p state (adding energy by absorbing light or with an electrical arc), it will fall back to the lowest energy state and conserve energy by emitting a photon. Such photon emission from the various energy levels of the hydrogen atom gives rise to its line spectrum discussed in Chapters 9 and 10. But it is not clear what to do when there is more than one electron. Should the four electrons of beryllium all go in the 1s orbital? It turns out that this is impossible.
Quantum theory, confirmed by countless experiments, has given us three rules that tell us how to place the electrons into the energy levels (Figure 11.1) to obtain the configuration of electrons for the various atoms. We use what is called the Aufbau procedure, that is, the build-up procedure. The three rules tell us how to place the electrons in the energy levels in the correct order to represent atoms. We will build up the atoms and construct the periodic table by “putting” more and more electrons for bigger and bigger atoms into the proper energy levels. Many properties of atoms, their tendency to gain or lose electrons to form ions, and the number of chemical bounds they form will be understandable from this Aufbau procedure, which gives rise to the form of the Periodic Table.
Rule 1—the Pauli Exclusion Principle
Rule 1 is the Pauli Exclusion Principle. It states that no two electrons in an atom (or molecule) can have all four quantum numbers identical. There are four quantum numbers, n, l, m, and s. For hydrogen we only used the first three, but now s is important. s can only have two values, s = +1/2 or -1/2. Therefore, a given orbital defined by the quantum numbers n, l, m can have at most two electrons in it. One of the electrons will have s = +1/2 and one will have s = -1/2. For example, the 1s orbital has n = l, l = 0, m = 0, and s = +1/2 or -1/2. Therefore, two electrons can go into the 1s orbital, one with “spin” +1/2 and one with spin -1/2. For the 2p orbitals, n = 2, l = 1, m = 1, 0, -1 and s = +1/2 or -1/2. The orbitals are px, py, and pz (see Figure 10.7). Each of these can have two electrons in it, one with s = +1/2 and the other must have s = - 1/2. Therefore, there can be a total of six 2p electrons, two in each of the three orbitals. 3d orbitals have quantum numbers n = 3, l = 2, m = 2, 1, 0, -1, -2, and s = +1/2 or -1/2. There are five 3d orbitals, and two electrons can go in each (s = +1/2 or -1/ 2) for a total of 10 d electrons, two in each of five orbitals. Finally, there are seven 4f orbitals with quantum numbers, n = 4, l = 3, m = 3, 2, 1, 0, -1, -2, -3, and s = +1/2 or -1/2. The result is a total of 14 f electrons, two in each of seven orbitals.
When two electrons are in a