Atoms with Three or More Electrons

Increasing the charge on the helium nucleus by one more proton produces lithium. It takes about 122 eV to remove the single electron from a Li2+ ion (i.e. nine times the ionization energy of a hydrogen atom), and it takes about 74 eV to remove one of the two electrons from a Li+ ion. However, it turns out that only about 5 eV is required to remove one of the three electrons from a neutral Li atom. No singly ionized ion requires more energy than Li+ to make it doubly ionized, yet the lithium atom itself is rather easily ionized, much more easily than the helium atom or the hydrogen atom.

The key to understanding why is to consider what happens when a third electron is added to the ground state of Li+, to make a neutral lithium atom. As you saw in Chapter 3, there are only two quantum states that have quantum numbers n = 1 and / = 0, i.e. there are only two Is states, each of them has m, = 0, one of them has ms = +1/2, and the other has ms = -1/2. You can think of these hydrogen-like states as though they can each be “occupied” by a single electron. So, the ground state of lithium cannot correspond to a quantum state of lslsls.

The principle that bans the third electron from being in a similar state to the other two is a crucial result of quantum physics; it was suggested by Wolfgang Pauli in 1925. The Pauli exclusion principle bans any two electrons in the same atom from occupying the same quantum state.

Remember that for any value of n, there are two “s” states, six “p” states, ten “d” states, and so on. Each quantum state corresponds to a different allowed combination of the four quantum numbers. According to the exclusion principle, each of these quantum states can accommodate only one electron.

Because there are only two Is states, the third electron in a lithium atom must occupy a 2s state. The ground state of the lithium atom can therefore be represented as lsls2s. The third electron in the lithium atom has principal quantum number n = 2, which makes it much more remote from the nucleus. As a result, one of the three electrons in the lithium atom is rather weakly bound, because it experiences a net charge that is not much greater than the one unit of the Li+ ion. The other two units of nuclear charge are effectively screened by the other two more tightly bound electrons. A rough estimate of the ionization energy of the lithium atom would be somewhat greater than that for the 2s or 2p state of hydrogen, namely: 13.60 eV/22 = 3.40 eV. In fact, it is 5.39 eV, indicating that the other tw'o electrons do not completely screen two units of nuclear charge.

It is a remarkable fact that lithium is a highly reactive metal, but helium is an extremely inert gas, yet the only difference between them is that lithium atoms contain three electrons surrounding a nucleus containing three protons, whereas helium atoms have two electrons surrounding a nucleus with two protons. The difference in properties is all due to the ionization energy difference between the two atoms, which in turn is due to the fact that quantum physics and the Pauli exclusion principle place a limit on the number of electrons in different quantum states. In the final section of this chapter, these ideas are taken even further to explore the basis of chemistry.

The Periodic Table of the Elements

As you have seen, for simple atoms such as He and Li, it is possible to be quite prescriptive about the states occupied by the two or three electrons that now' have to be considered. For the helium atom, both electrons can occupy Is states, so the ground state of helium is lsls. For the lithium atom, you have seen that the ground state is lsls2s.

With more electrons, this notation soon gets unw'ieldy. To avoid this problem, a more compact way of describing the organization of the electrons around a nucleus is used, referred to as the electron configuration. For the helium atom w'ith a ground state of lsls, the electron configuration is written as Is2, and for the lithium atom with a ground state of lsls2s, the electron configuration is written as Is2 2s1. It is important to realize that the superscripts here do not refer to “powers” of numbers, they are merely labels indicating the number of electrons that occupy the states specified by the n and / quantum numbers.

It is often quite convenient to think of electrons as “filling up” successive subshells in the atom. For instance: the Is subshell can accommodate two electrons because there are two Is quantum states, the 2s subshell can accommodate tw'o more electrons, and the 2p subshell can accommodate a further six electrons because there are six 2p quantum states. Subshells are filled in order of increasing energy so that the atom as a whole has the lowest possible energy level. The start of the sequence of filling states in order of increasing energy turns out to be Is, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p ... w'hich gets as far as atomic number 54 (corresponding to xenon). Although such terminology is not entirely accurate, owing to the interactions between electrons, it provides a useful simplification. For atoms that contain several electrons the states are somew'hat different from the “hydrogen-like” quantum states, because the interactions between the electrons complicate matters.

This can be seen as the origin of the wonderful structure encapsulated by the periodic table of the elements, first laid out by the Russian chemist Dmitri Mendeleev around 1869 (Figure 5.2). He arranged the various elements in a grid such that

The periodic table of the elements

FIGURE 5.2 The periodic table of the elements.

elements with similar properties appeared in the same column (or Group) of the table, and each row (or Period) of the table is now recognized as containing the elements in order of increasing atomic number.

Lithium (Li), sodium (Na), and potassium (K), known as the alkali metals, each lie in the first Group of the table, because they are each similarly very reactive. The outer electron in each of these elements is a solitary electron occupying an “s” subshell. The electron configurations of these three elements are: Li: Is2 2s1, Na: Is2 2s2 2p6 3s1, and K: Is2 2s2 2p6 3s2 3p6 4s1, corresponding to atomic numbers of 3, 11, and 19. That single outer electron is what makes each of these elements so chemically reactive, since it is not tightly bound and so can readily exchange with other elements.

The right-most Group of the table contains the inert (or so-called noble) gases helium (He), neon (Ne), argon (Ar), and krypton (Kr). The outermost electrons of each of these elements comprise a full subshell. The electron configurations of these four elements are: He: Is2, Ne: Is2 2s2 2p6, Ar: Is2 2s2 2p6 3s2 3p6, and Kr: Is2 2s2 2p6 3s2 3p6 3d10 4s2 4p6, corresponding to atomic numbers of 2, 10, 18, and 36. That full outer subshell is what makes each of these elements so chemically unreactive, since there are no loosely bound electrons to share with other elements in chemical reactions.

As a final example, the penultimate Group on the right-hand side of the table contains a group of elements known as the halogens, which include fluorine (F), chlorine (Cl), and bromine (Br). The outermost electrons of each of these elements comprise a subshell with a single vacancy. The electron configurations of these three elements are: F: Is2 2s2 2p5, Cl: Is2 2s2 2p6 3s2 3p5, and Br: Is2 2s2 2p6 3s2 3p6 3dl() 4s2 4p- corresponding to atomic numbers of 9, 17, and 35. The vacancy in the outer subshell means that these elements readily accept an electron from another atom (such as those in the first Group) to form strongly bonded compounds. This is why sodium chloride (NaCl), whose crystals are formed from sodium and chlorine atoms bound together, is such a widespread substance on Earth, known as common salt.

All the richness of chemistry and chemical reactions essentially stems from these simple quantum rules for how the electrons are distributed in atoms. Although this section of the book focusses on the smallest scale structures of the Universe, the behaviour of materials on an everyday scale that we see around us is firmly rooted in this quantum world. The behaviour of solids, liquids, and gases, the differences between metals, organic compounds, and other materials are all determined by the simple rules that operate at an atomic scale.

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