IONIZATION ENERGIES

The sizes of the atoms and the chemical properties of the elements depend largely on how strongly the outer electrons in their atoms are bound to their nuclei. As a way of getting a sense of the strength of this binding, measurements have been made of the ionization energies that are required to break the outer electrons free from their atoms.

Measurements are typically tabulated in several series, each for the removal of one, two, or more electrons, respectively. The energies are obtained either by using electrical methods or through calculations on spectroscopic data using the quantum relationship between the energy of a photon and its wavelength (as discussed initially in Chapter 2). The ionization energies determined by either method agree quite well. Of the two methods, the spectroscopic method is the more accurate, and the data presented here were obtained mainly by that method.¹

The ionization energy needed to free a single outermost electron from its ground-state atom² is just the energy needed to boost the outermost electron from the negative energy of its bound outer-electron state to the zero of energy that makes it a free particle. (Refer back to Chapter 11 for a discussion of energy and “bound state” energies.) So the negative of this positive ionization energy is just a measure for each element of the depth of the negative energy that holds the electron trapped in its bound state, precisely what we have been describing throughout this book as the negative energy level of the outermost occupied electron state. The measurement of ionization energy thus gives us a bird's-eye view into this energy level for the more complex many-electron atoms for which energies are difficult to calculate or approximate. It also gives us a view into the differences in these highest occupied energy levels as we compare the atom of one element to that of another. Through this we explain bonding. I consider specific bonds in Chapter 15, but here I introduce the subject generally. I show what the energy levels of these outermost states tell us about the propensity to bond.

OUTER-ELECTRON ENERGIES AND THE SIZES OF ATOMS

Table D.1 (located second from last in the photo insert) is a partial periodic table showing the outer-electron energies and sizes of the atoms of 41 of the elements. (Note that this table is to be read looking from the right side of the two pages that it is spread across.) The table becomes simple and easily understandable if we define its features. The symbol for each element appears below a shaded sphere (where there is one, showing relative atomic size) in a ratio-like arrangement along with the superscripted symbol for its valence-subshell ion (to be defined further on in this chapter). For example, we have Mg/Mg²⁺. Below those symbols is a ratio giving the approximate radius of the atom and the radius of its valence-subshell ion (also to be defined further on), both in units of one-tenth of a millionth of a millimeter (where a millimeter is about the thickness of a dime). The outer-electron energies (the negative of the measured ionization energies) are shown in green as the lowest item below the spheres and symbols.

The elements are divided into the A-type and B-type Groups (types marked by the letters A or B after the Roman numeral that labels the Group, those elements in each column), as defined in Chapter 13. The Groups (columns) correspond to those in our periodic tables IV and B.2. (Note: I have placed the same periodic table in two places, labeled as Table IV in Chapter 13 and Table B.2 in Appendix B, to make examining the periodic table easier in relation to the discussion in the nearby text.)

The inset rectangular box in Table D.1 provides information on ten elements of the B-type groups, the transition metals. The surrounding rest of the table describes the properties of the atoms of each of 31 (main) A-type group elements at positions corresponding to the locations of those same elements as they are represented in the leftmost and rightmost two columns or first (bottom) several rows of the two periodic tables mentioned above. It is easiest to consider one group and one property at a time, and we start by examining the properties of the A-type groups of elements, starting with atomic size.

The first thing we notice in scanning across Table D.1 is a nearly continuous decrease in the sizes of the spheres in each row from left to right. These spheres represent the approximate overall sizes of the atoms of each of the elements.³ (They are essentially the sizes of the probability clouds of the outermost states occupied by the electrons in each atom. But, remember, all electron states are to be thought of as somewhat diffuse and cloudlike [as shown, for example, in Fig. 3.8], not like the hard spheres drawn in Table D.1. Only the electrons in the outer s states of the elements in the first two columns at the far left or in the completely filled shells of atoms in the last column at the far right are expected to actually have a spherical symmetry, and all of these “spheres” would appear “fuzzy” and diffuse.)

Note that sizes are not shown for the atoms of the noble gases, which are listed without spheres in Column VIIIA at the far right of each row. The atoms of these elements can be surmised to be just a bit smaller than the sizes of the atoms shown in the same row in the preceding column, Column VIIA (since the sizes of atoms are seen to change only gradually left to right across the last elements in each row toward Column VIIIA).

With a few exceptions, to be noted last, the outer-electron energies become steadily more negative (showing greater binding) as we scan through the elements left to right across each row of the table, and down each column. The size of each atom (conversely) generally decreases element to element across the rows (left to right), and this decrease is in rough correspondence with the more negative outer-electron energy, reflecting the stronger binding of the electron that more negative energy produces. And the size of each atom generally decreases element to element down the columns, and this decrease is in rough correspondence with the more negative outer-electron energies down each column, reflecting the greater binding of the electron.

Look at the steadily more negative outer-electron energy as we consider successively the elements in the last three columns of each row of the table. This more and more negative energy shows particularly well the general trend of the greater binding of the outermost electrons as we consider each successive element left to right in each row; that is, as we consider elements with successively more and more electrons. Each additional p-state electron in the atoms of these elements is apparently only partially shielded by its fellow electrons from the attraction of the nucleus, while the additional proton in that atom creates a greater attraction and binding of all of the electrons, as reflected in the more and more negative energy of the outermost electron.

Note that the outer-electron energy in each row of the table reaches a minimum (is most negative) for the Group VIIIA element at the end of each row, that is, for those elements completing the occupation of a full shell of electrons. The atoms of these elements hold onto their electrons so strongly that they tend not to have any stripped away in reaction with other elements. Nor do their atoms tend to gain an electron, since the outer-electron energy (as a measure of the tendency to attract and bind) of the state that the added Group VIIIA element's electron would go into is less negative in energy (and less binding) even than the relatively small outer-electron energy of the element starting the next row of the table. That is because the ion that would be formed by addition of an electron to the atom of the Group VIIIA element—though otherwise resembling the atom of the next higher-Z element starting the next row—would have one fewer proton in its nucleus than the atom of that higher-Z element. So the added outermost electron that it would acquire would be less tightly bound and less strongly attracted to the nucleus than the equivalent electron in the atom of the next higher-Z element. Thus an electron in another element would simply not be attracted to the atom of the noble gas, Group VIIIA, element. The lack of any tendency to lose an electron, and the lack of any tendency to gain one, together explain why the Group VIII elements do not tend to react to form an ionic bond. Nor do they tend to interact by sharing an electron to form a covalent type of bond. They thus tend to be noninteracting, aloof—and hence the name, “noble gases.”

Now, note the less strongly negative outer-state energy of the oxygen atom, represented by the symbol (O) in Row 2, and of that for sulfur, represented by (S) in Row 3 of Column VIA, relative to the outer electron state energies of the atoms of nitrogen (N) and phosphorous (P), respectively, in Column VA. These (O) and (S) less strongly negative energies interrupt the otherwise steady decrease in the outer occupied state energies of the atoms of elements from left to right. These singular energy increases in (O) and (S) (as one scans left to right) occur because oxygen and sulfur are the first elements in their rows to have electrons of opposite spin in their outer p subshell, that is, two electrons occupying the same p spatial state. And that, as mentioned in Chapters 13 and 14, causes a relatively large mutual repulsion of the two electrons in that state, making the energies of these outer electrons less negative so that they are less tightly bound and the ionization energy needed to remove either of them is correspondingly smaller.

THE PROPENSITY TO BOND

In nature, everything tends toward the lowest overall energy state. Atoms will tend to share or transfer electrons one to another as long as the sum of the energies of all of the electrons in both atoms (or ions, if they are formed) after the transfer is less than the sum of these energies beforehand. So, what determines an atom's (element's) propensity to gain or lose or share an electron (react chemically to bond) is the energy level of its last occupied state and that of the state just above it relative to those of the atoms of the other elements that it may bond with. Let me explain.

Consider: if the energy of the next state up (i.e., the first unoccupied state) in an atom of one element is relatively low compared to (i.e., more negative than) the energy of the last occupied state of the atom of a second element, then the first atom will tend to be reactive in trying to acquire the outermost electron of the second. That is because in transferring from the second atom to the first, the electron “drops down” to a lower energy, and nature loves an overall lower-energy state. This type of reactivity for acquisition is typical of atoms of the nonmetals, which are represented at the lower right in Table D.1 and darkly shaded and represented to the lower right in our periodic tables IV and B.2. (That is, typical with the exception of the noble gas elements in the last column, which I describe further on from here.) One such atom, for example, the fluorine atom, is so acquisitive as a constituent of hydrofluoric acid that it will rip silicon from its (SiO₂) bond with oxygen to etch glass.

Conversely, if the energy of an atom's present outermost occupied state is relatively high (less negative) compared to the (unoccupied) next higher-energy state of the atom of another element, the first atom will tend to be reactive in letting its outermost electron “drop to a lower energy” and go to the second atom. This type of reactivity is more and more typical of the metals as one looks more and more to the upper left in Table D.1 and the upper left in the two periodic tables mentioned above. For example, the single outer 1s electron of the sodium atom has such a small negative energy that, if a chunk of this metal is dropped in water, oxygen atoms, which are very acquisitive with much-more-negative energy states available, will shove aside their previously bonded hydrogen atoms to latch onto that higher energy (less negative energy) sodium electron. The event produces hydrogen gas, which can combine to burn with the oxygen in the air, releasing heat and light (and, if sufficient quantities are involved, explosion).

If the electron is transferred completely from one atom to another in either of the above cases, then the atom that acquires the electron acquires a net negative charge and thus becomes an anion. The atom that loses the electron is left with a net positive charge and thus becomes a cation. The two oppositely charged ions attract each other electrostatically and tend to stick together in what is called an ionic bond. For example, sodium and chlorine form an ionic bond, making NaCl, common table salt.

If the outer states and next higher-energy unoccupied states of two atoms tend to be comparable in acquisitiveness, they may still lower the overall energy of their electrons by sharing their outer electrons (in a way that distorts the states of both atoms to lower energy) in what is call a covalent bond. In this bond, the energy of the overall molecule is lower than that of the two atoms separately. Note that all bonds are some combination of ionic and covalent bonds. (Specific bonds and bond types are described a bit more in Chapter 15.)

Atoms whose outermost electrons occupy states of completely filled shells (therefore states of relatively low energy) tend not to have that electron stripped away. And if their next higher in energy (unoccupied) state is not very strongly negative in energy, they won't tend to acquire an electron into that state either. They simply tend not react with other atoms either to lose or to gain an electron. These are the “aloof” Group VIIIA noble gas elements, represented in the rightmost column of Table D.1 and our periodic tables IV and B.2. Note: another way to describe the propensity to bond is to say that the atom of each element tends to gain or lose electrons so as to more closely approach the just-filled occupancy of a shell displayed by the atom of the nearest (in atomic number) noble gas element.

MORE ABOUT THE SIZES OF ATOMS AND IONS

The decrease in atomic size from left to right in Table D.1 is counterintuitive. As we move from left to right in the table, we successively consider elements whose atoms have more and more electrons, that is, atoms of higher and higher atomic number. And wouldn't we expect that more electrons make for larger (rather than smaller) atoms?

From the physics described in Chapter 14 and earlier in this appendix, we know that the answer is no. More electrons surrounding the nucleus means an equally greater number of positively charged protons in the nucleus. This results in a greater attraction of each electron to all of the protons, mitigated to some extent by the screening of the protons by the negative charges of the other electrons that surround the nucleus. The net effect is that (as we consider atoms having more and more electrons across a given row of the table) every additional electron (except for those in column/Group VIA, as noted earlier) sees a greater attraction to the nucleus, with a corresponding reduction in the size of all of the electron states, that is, a smaller atom with more electrons. But this works only within each row until the last p state for that row, that approximate energy level, is filled.

The atoms of elements in Column IA have one electron more than completely fills a shell (except, of course, for hydrogen, which has only one electron). And (except for hydrogen) this one electron occupies a higher (less negative) energy s state (as compared to the energy of the states in the preceding completely filled shell of states). In every case, the lone outer electron is largely screened from all but one positive unit of charge in the nucleus because of the tightly bound, spherically symmetric, completely filled shells of the rest of the electrons within. And so this last electron is not strongly attracted to the nucleus, and its s state is substantially larger than the states of the filled shell of electrons in the atom of the noble gas in the row before. It's really a little bit like having that electron in a higher-n (less negative energy) state of hydrogen—one electron around a core that has (as seen by the outer electron) a screened net approximately single positive charge, as it would appear in an atom with Z = 1 (hydrogen). Thus atoms of each successive element up column/Group IA is larger in size and less negative in binding energy. Each of these atoms, followed by atoms successively having one more electron than the atom of its predecessor element, starts the progression across a row again toward smaller-size, completely filled, compact shells, and finally the leap to a still larger, less tightly bound s state for the atom of the element listed first in the following row.

The largest atom shown in Table D.1 is the cesium atom—symbol Cs, atomic number Z = 55, at the top-left of the table. It has a diameter of nearly one-half of one-millionth of a millimeter. That is, 2 × (Cs radius of 2.35 units) × (one unit = 0.1 × one-millionth of a millimeter) = 0.470 millionths of a millimeter. And, since one millimeter is about the thickness of a dime, and atoms of higher atomic number don't get to be much larger, we can say that the spatial extent of most atoms is less than half of one-millionth of the thickness of a dime.

Note that the radius of the cesium atom, atomic number 55 with just two more electrons than the iodine atom, is nearly 1.6 times the radius of the iodine atom. This illustrates the huge jump in size that takes place as electrons are added beyond a completely filled (or nearly completely filled) shell into the next, much-larger-in-size, s state. And the radius of the iodine atom with its 53 electrons is only 3.6 times the radius of the one-electron hydrogen atom, illustrating the degree to which the filled inner shells and nearly filled outer shell of states in the iodine atom are drawn down to a relatively small size.

Note also the relatively large drop in the sizes of the atoms of the elements in Column IIA as compared to the sizes of the atoms of elements in their same row in Column IA. This can be explained by the unusually large decrease in the outer occupied state energies (reflecting the correspondingly tighter binding of the outer electrons) that results from the just filling of the s-state subshells in the atoms of the elements in Column IIA. (Refer to the corresponding s-block subshell of states shown in Table III, which shows only the atomic number, Z, identifying each element. (Those atoms with just completed subshells feel a bit of the kind of tight binding that comes with having electrons that just complete the population of a full shell.)

VALENCE-SUBSHELL IONS

Remember that an ion is created when an atom either is stripped of one or more of its electrons, or acquires one or more extra electrons. (Ions may also consist of combined atoms that collectively are either stripped of or acquire electrons, as for example the hydroxide ion which is created when water, H₂O, is dissociated into a hydroxide ion, OH^–, and a hydrogen ion, H⁺, stripping an electron from H as it is acquired by OH.) And remember that the number of electrons that an atom of an element tends to gain or lose is called its valence. When electrons are stripped away, (+) valence cations are produced, because there are more protons than electrons and a net positive charge. When electrons are acquired, (–) valence anions are produced, because there are then more electrons than protons and a net negative charge. The valences of the ions explain much of the way that atoms of the elements toward the upper left and lower right of Table D.1 (and our two periodic tables) tend to combine to form compounds; plus-valence atoms (of elements to the upper left) tend to lose electrons in combination with minus-valence atoms (of elements to the lower right) that tend to acquire them.

(+) valence-subshell ions are produced when the outermost electrons of an atom are all stripped away, leaving only the completely filled 1s state valence subshell in Row 2 or a completely filled p state valence subshell in subsequent rows, with any inner subshells also entirely filled. (–) valence-subshell ions are produced when enough extra outer electrons are acquired by an atom to form the next completely filled valence subshell of states.

Dashed circles within the spheres in Table D.1 show the relative measured sizes of the valence-subshell cations that are produced when one, two, or three electrons are removed from atoms, respectively symbolized by the superscript (+), (2+), or (3+). Note for example, lithium, Li, and its valence-subshell cation, Li⁺, shown respectively by the sphere and the dashed circle in the second row on the far left in Column IA after hydrogen. (Note also that there is no dashed circle for the hydrogen ion. When the hydrogen atom loses its one electron, all that is left is the lone proton, ten thousand times smaller than the sphere shown for the hydrogen atom and not visible at the scale shown in Table D.1.) Dashed circles surrounding the spheres show the relative sizes of the valence-subshell anions that are created when one, two, or three extra electrons are acquired by atoms, situations respectively symbolized by the superscript (–), (2–), or (3–). Note, for example, nitrogen, N, and its valence-subshell anion, N^3–, shown as N/N^3– in the second row of Column VA.

ELEMENTS OF THE TRANSITION METAL B-TYPE GROUPS AND THEIR PROPERTIES

We next consider the properties of the “B” group transition metal elements, the fifty-nine B-type elements across the middle and top of the periodic tables IV in Chapter 13 and B.2 in Appendix B, those elements whose atomic numbers mark their place in the d block of Table III in Chapter 13.⁴ The properties of ten of these transition metals, those found in the first transition metal series in the middle of the fourth row of Tables III and IV, are shown inset as a block in Table D.1. Note the relatively small variation in both atom size and outer-electron energy across most of the set of ten elements. And yet these elements have different chemical and physical properties. Atomic size and outer-electron energies serve to explain the gross features of the atoms of the elements and consequently the tables, and the smaller differences in energies should help to explain other less dramatic variations in properties.

The transition metals include some of the most commonly known elements, including some of the first of the elements to be found or isolated in their pure elemental form. With reference also to Tables IV and B.2, I note particularly now some of the more familiar of these elements (in italics below). For the elements in the first transition metal series of the fourth row, starting with scandium, atomic number Z = 21, followed by titanium, vanadium, chromium, and manganese, we have iron, cobalt, nickel, copper, and zinc. And, below the last three of these, in the fifth row (second transition metal series) we have palladium, silver, and cadmium; while in the sixth row (third series), we have platinum, gold, and mercury.

What holds metals together as solids, what produces their electrical properties, and what accounts for their magnetic properties, is presented briefly, along with a similarly brief description of some aspects of their practical use and related inventions, in Chapter 16. We'll not go into detail here regarding their chemical properties. To dig deeper, I would recommend that you read a good text, like Fine and Beall, Chemistry for Engineers and Scientists, Reference E, or Housecroft and Sharpe, Inorganic Chemistry, Reference H.

THE RARE EARTH AND HEAVIER ELEMENTS (NOT SHOWN IN TABLE D.1)

In contrast to the d states, the f states have little influence on an element's properties. And so it is that the filling of the 4f states in the rare earth 4f block of elements, atomic numbers Z = 58 through Z= 71, causes little change in element properties from those displayed by their predecessor lanthanum, atomic number Z = 57. That is why these elements are often referred to as the lanthanide (or lanthanoid) series. Similarly, the filling of the 5f states of the 5f block of elements, atomic numbers Z = 91 through Z = 103, causes little change in element properties from those displayed by their predecessor actinium, atomic number Z = 89. And so these elements are often referred to as the actinide (or actinoid) series. The filling of d states in atoms of the elements following the lanthanide series, starting with atoms of the element hafnium, atomic number Z = 72, is once again accompanied by significant differences in properties element to successive element, except, as already noted, in regard to atomic size.