A Method of Teaching the Electronic Structure of the Atom . '
I.
Elementary Presentation DON DEVAULT
Civilian Public Service Camp No. 135, Germfask, Michigan Z a n y of the results of modern quantum mechanics can be taught to &dents who have had no previous knowledge of atomic strucfure. Pictures of atomic orbifah and simpl~xedenergy level d i a g r a m are us&l visual aidr. There are here described: the phenomenon of stationary sfafes of the atom arising out ofthe wavelike character ofthe electron; fhe energy contents of these states and how the shapes of diferent types of orbitah afect their energies i n mulfi-electron atom; the periodicity i n valence elecfron sfructure as it is defermined by the nature of the energy leveh and by the P a u l i exclusion principle; fhe correlation of many 'chemical properties with an energy level diagram covering the whole periodic fable.
HE putpose of this and the following paper is to offer some suggestions for the teaching of modern ideas of atomic structure in the light of the new quantum mechanics wbich originated around 1925. The hope is that a way can be found to teach the modern ideas as early in a student's training as the old-fashioned concepts are now taught. This idea has been expressed by a number of other authors recently (I, 2 ) . Such an accomplishment would immediately open to the student wider possibilities for understanding the periodic table, for correlating chemical facts, and for pursuing further the subject of atomic structure and chemical binding itself. It would spare him the anguish of later unlearning most of what was previously taught to him. Among the difficulties which, according to the author's own experience, beset the student when taught incomplete and outworn ideas are the following: 1. The usual explanations in terms of atomic structure for the existence of the periodic table stop before, or falter in tackling, the long periods, and practically never mention the rare earths. Furthermore, the rare earths seem entirely out of place or freakish on almost any common arrangement of the periodic table. This can be disturbina- to the interested student. 2. Why the all-important "octet"? That a group of eight electrons should just fit around an atom a t the corners of a cube seems reasonable to the beginning student. But then why 18 next? Sometimes the student is told that the nth shell can hold 2na electrons, giving 2, 8, 18, 32, 50 for successive shells. But the periodic table shows 2, 8, 8, 18, 18, 32. The best that can ordinarily be done for the student who wants to know more is to give .the partially accurate explanation that there are subshells whose energy levels place them in such an order as to give the. observed sequence [see ref. (3), page 26, or ref. (I),page 24, for example].
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3. The exact relationship between the terms "shell," "quantum number," and "energy level" may be hard to grasp. The modem quantum mechanical concept of the atom contains so much that is contrary to ordinary daily experience that visual methods of teaching can be most helpful with all of these problems.' The figures presented here have an authenticity which is a help to the properly skeptical student. The pictures of Figure 1 were carefully calculated directly from the modern quantum mechanics. The diagrams of this and the following paper were put together from actual experimental data. The present paper deals only with very elementary problems. Besides presenting the figures i t will attempt to outline a method by which their meaning may be explained in the classroom. The following paper will present a more exact, more complicated energy level chart, a discussion of more advanced topics, and finally a completely technical description of the construction of the charts. Mentioning first how i t is impossible to see an atom because the wave length of the light is thousands of times longer than the diameter of the atom, the teacher can explain that investigating the atom with any tools we have available--x-rays, electron bombardment, spectroscopy-is like probing a fine watch with a pickax and crowbar, and that any picture we can get must, therefore, be the combined impressions that we infer from the results of a large number of different kinds of experiments. The atom consists of a small, heavy, positively charged nucleus, with light, negatively charged elec1 A clever application of the visual aid method is the use of marginal flip pictures by M a x Born (4) in his hook on general ohvsics.
trons surrounding it. This much of atomic theory has stood firm since its proposal by Rutherford. The early and useful idea of Bohr that the electrons raced around the nucleus in orbits, like the planets around the sun,%has had to be abandoned. One reason is the impossibility of perceiving the electron in any definite orbit with the use of our "sledge-hammer" tools. The other is the discovery of the wavelike behavior of electron^.^ One can well imagine that it is not easy to describe something that is supposed to be both a wave and a particle of matter. In fact it is not certain that anyone knows exactly what is meant. All we,know is that the experiments force us to believe that electrons do have wavelike properties. First, the idea of "standing waves" may be made more familiar to the student by pointing out and illustrating them in vibrating strings, on the surface of water standing in a dish on a table vibrated by a motor, and perhaps even inside a block of jelly. The ability of these things to vibrate in distinctly different modes should be shown, too, by causing the string to vibrate in different numbers of sections or by changing the frequency of vibration or the shape of the boundary walls of the dish of water. Born ( 4 ) gives a clear description of standing waves. The vibrations which an electron undergoes in the space around the nucleus of an atom must be similar to these standing waves, but in s p a c e a s in a block of jelly. The electron is held close to the nucleus by electrical attraction, and the boundaries limiting the vibration are determined by the distance from the nucleus that the electron can go against the nuclear attraction. If the electron is moving with greater energy it can go farther from the nucleus. The houndaries may he expected to be less definite, however, than in the illustrations of standing waves mentioned above. Figure 1 illustrates some of the patterns which the standing waves of an electron may make in the space around the nucleus. The nucleus may he thought of as a tiny dot a t the center of each of the pictures. The cloudy-looking pictures are cross sections or slices taken through the center of the atom, and the density of the cloud a t a given point shows how much vibration goes on a t that point. The smaller "solid" drawings in the corner of each picture show the arrangement in space. The globes, doughnuts, etc., enclose vibrations are taking the points where the most place. ~~~h picture of ~i~~~~1 representsan entirely dif. ferent state of the atom. Thus the picture labeled "Is" (at the bottom of Figure 1) shows the simplest (The significance of the labels type of is explained later.) The motion is greatest a t the and fades off gradually in all directions equally, needs less energy to execute this vibraAS is still taught in elementary chemistry, pictured in Life (5). etc. a These reasons are embodied in the "Uncertainty Principle" of Heisenberg.
tion than for any of the others and a hydrogen atom is normally found in this state. If someone gives the electron more energy it can start vibrating according to the pattern labeled "2s" (for example), just as one may by proper manipulation cause a string that is vibrating in one section to start vihrating in two sections instead. In general the electron keeps vibrating according to one single pattern until some disturbance from the outside causes a transition to another state, and often the addition or subtraction of energy is necessary to make the change. It is not easy to interpret these electron "vibrations" or "standing waves." They are the physical pictures of the mathematical equations of quantum mechanics which have succeeded in explaining many puzzling things, even in other fields than atomic structure and are confirmed indirectly by many observations. Perhaps one may think of the electron itself as spread out over all of the space and undergoing the vibrations like a block of jelly, or of the vibrations as being the electron. The more widely accepted explanation is that the waves are merely ghosts of some sort, perhaps just mathematical apparitions, something like the earth's equator, but that they in some way determine where the electron can go and what speeds it can have. The electron goes mostly where the wave "vibrates" most. We assume this explanation in the rest of the paper. The electron, then, jumps around, taking unknown paths in the space about the nucleus, hut yet in such a way that it spends most of the time in the regions that appear dark in the pictures of Figure 1. If we could imagine ourselves being able to photograph the electron and if we should take a long time-exposure of it jumping around while in one of the states illustrated in Figure 1, SO that the pictures of the paths it has taken pile up on top of each other and give finally just a blur, the developed plate would look something like the corresponding picture given there.4 We say, then, that the cloud.pictures of Figure 1 give the probability of finding the electron a t any given point in the space around the nucleus a t a given i n ~ t a n t . ~ The "electron clouds" of Figure 1 are the modern substitute for the electron orbits of the old theory. The clouds are, therefore, called orbitals for convenience. There are also orbitals corresponding to the labels 4s, 49,4d, 4f,5s, and so on ad infiniturn. For a reason not well understood, called the exclusion principle of Pauli, only two electrons can get into the , E x c e p t for the fact that Figure 1 shows cross rections while our imaginary camera would probably see the full depth. 'The number of dots put into the cloud pictures of Figure 1 per unit of area corresponding to one square angstrem was calculated according to the arbitrary formula: 165 Iog,&*J.a.C X 10' - I), where J. is the wave function as found an page 138, ref. (6),with Z = 1 (e. p.. J.,. = ao-a/nr-l/ae-.- where a. is the radius of the Bohr orbit in normal hydrogen and ir is equal to the distance from the nucleus in units of 00). The corresponding probabilities are also shown in the scale of densities in the legend to the figure. However, difficulties in making the dots of uniform size have reduced the accuracy. Engraving in half-tone has completely obliterated the dot structure present in the original. Smoother though less accurate pictures have been presented by White (7).
same ~ r b i t a l . ~If, then, the atom has many electrons Pauli exclusion principle, two is all that any one orbital they will be found, usually in pairs, in different orbitals. can hold. We express the fact that the 1s orbital is The pictures in Figure 1 show the different possible orbitals when the atom has only one electron. The Te presence of other electrons would alter the shapes of these orbitals somewhat but the general picture would remain the same. No two orbitals in. one atom will have both the same location in space and the same shape and size. Consequently the resulting picture of a multi-electron atom would be much more of a blur than those in Figure 1 and would be more spherical in shape. It would be hard to distinguish the different orbitals. Sometimes we would see one or more orbitals sticking out further than the majority and if such an orbital should have only one electron in it, it might become a "hook" by which that atom could attach itself to other atoms in forming a molecule, but this will be discussed more fully in the following paper. This is about as accurately as one can describe what an atom "looks" l i k e a small, heavy, positively charged nucleus a t the center, surrounded by a cloud of light, dancing, negatively charged electrons, the cloud being made up of "orbitals" which have various shapes and sizes and which contain one or two electrons each. ENERGY LEVELS
The chemical properties of atoms are determined largely by the shapes and sizes of the orbitals which its electrons occupy and by the energy thut the electrons must have to be in the different orbitals. If the class has not yet been introduced to the concept of energy and to its importance in determining the course of chemical reactions, the teacher should do so a t this point. To explain the energies of the electrons in their orbitals, the idea of a stone on a series of shelves of different heights makes a good analogy. For, although an orbital may be cloudy in space, the energy of an electron in it is as definite as the position of a shelf. The gravitational energy that the stone has is greater the higher the shelf, and i t may be released as heat and sound by letting the stone fall to a lower shelf. Thus, on paper we place horizontal lines a t different heights to represent the amounts of energy the electron will have in different orbitals, the highest corresponding to the most. We may call these lines "energy levels," and will often use the term almost synonymously with "orbital." The energy levels of the diierent orbitals of a tellurium atom, for example, are arranged in order in Figure 2. BUILDING AN ATOM
Telhuium has 52 positive charges on the nucleus. Because of its fundamental importance we shall outline in some detail how 52 electrons are added to make a normal neutral atom. The orbital with the smallest amount of energy is the Is. Into i t will go two electrons. As expressed in the And then only on condition that they are spinning in apposite directions.
52 AT NO. TELLURIUM ATOM. Different types of lines are used to indicate different types of orbitals to which the energy levels refer. The shell structure is also shown and the normal number of electrons in each shell.
full by covering it with cross-hatching in our diagram (Figure 2). The next lowest orbital is the 2s. Into it go two more electrons.
The next energy level indicated is labeled 2p. There are, however, three different orbitals having the same energy. We may call them the 2p,, Zp,, and 2p, orbitals.' Two of them are pictured in Figure 1 and the third, the 2pv, is the same as the 2p, except that it is rotated horizontally 90". Therefore we may put six electrons into the 29 energy level. In general s levels have one orbital, p levels three, d levels five,f levels seven, and so on. The next lowest level shown in Figure 2 is the one labeled 3s. Accordingly two electrons go into it, and then six into the 39 level and ten into the 3d level. Three of the five 3d orbitals are shown in Figure 1. Of the two not shown, one, the 3d+,, is like the 3dd, except for being rotated 90" horizontally, and the other, the 3&,, is like the 3 d , except that it is rotated horizontally 45'. Eighteen more electrons fill the 4s, 4p, and 4d levels. These are all indicated as filled in Figure 2 by cross-hatching, into which a number is inserted to show how many electrons are present. So far we have placed 46 electrons in their normal "positions" about the nucleus of a tellurium atom. Six more remain to go in. Figure 2 shows the 5s and 5 p levels as the stablest ones available to them. Accordingly two go into the 5s and four into the 5p. The stippling indicates partial filling. We have already mentioned how the 2p,, Zp,, and 2p, orbitals, for example, form a group of th:ee orbitals which have the same energy content. A glance a t Figure 2 shows that there are also larger groupings of orbitals. Specifically, the 1s forms a group by itself, the 2s and 2p form another group, the 3s, 39, and 3d another, and the 4s, @, and 4d another. These larger groups are called shells. The lowest shell is usually called the K shell, the next the L, the next the M , and so on. The numbers 1, 2, 3, etc., in front of the designations i s , 2s, 2p, etc., were assigned with the same idea in mind; 1 for K shell, and so on. The letters s, p, d, f, etc., designate the smaller groupings which are called subshells. The orbitals in the tellurium atom will not look exactly like those shown for hydrogen in Figure 1 even though the naming is the same. This is because the forces from the other electrons will distort them somewhat and the greater nuclear charge will draw most of them closer to the nucleus. However, the main features will remain the same. As might be guessed from the appearance of the hydrogen orbitals in Figure 1, the orbitals of a given subshell will fit together to form a completely spherical shell-like cloud8 and all the orbitals of a given shell will have their outermost maxima of density a t roughly the same distance from the nucleus, but a t a different distance from those of other shells. An actual shell structure does exist, therefore, but it is quite vague. Individual orbitals can penetrate many shells a t the same time. The numbers designating specific shells; subshells, Variations of these arrangements of orbitals within a given subshell are mentioned in the next paper. Unsdd's theorem (8 and page 150 of 6 ) . -
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orbitals, and the state of the atom in general are called "quantum numbers." These are discussed more fully in the following paper, together with reasons for the fact that the K shell can contain only an s orbital, the L shell only s and p orbitals, etc. The energy levels are also called "quantum levels." Above the filled and partially filled levels Figure 2 shows many empty energy levels. The normal tellurium atom does not have enough electrons to fill these. However, one of the electrons from the 51, orbitals or even from the 5s can be temporarily "excited" up into one of these normally empty levels by some outside influence as the high temperature of a flame or by an electrical discharge. It is like raising the stone from a lower to a higher shelf. When eventually the electron falls back to a lower level the energy it loses appears as light. The characteristic lines in the spectrum of an element are each made up of light from atoms of that element undergoing transitions from a particular high energy state to a particular lower energy state. For example, the yellow light of sodium results from the outermost electrons in its atoms jumping down from the 39 level to the 3s. THE PERIODIC TABLE
In Figure 3 we have done to 92 elements the same thing that Figure 2 does for tellurium. They are arranged in the order of their atomic numbers, which is the order of the number of charges on their nuclei. This arrangement brings out some interesting regnlarities. For one thing, corresponding energy levels are seen to become stabler (lower) with increasing atomic number. This is because the increased charge on the nucleus attracts the electron in a given orbital more strongly. The distribution of the orbital itself in space becomes smaller, closer to the nucleus. One notices further that the increase of stability depends upon the type of orbital. The s and p orbitals sink steadily with increasing atomic number while the d and f orbitals remain a t the same level of energy for relatively long periods before starting to sink. The reason is this: d and f orbitals are shielded fairly completely from the attraction of the nucleus by electrons in inner shells which form a negatively charged screen about the nucleus and counteract the nuclear charge. A look a t the s and p orbitals in Figure 1 shows that they, however, are denser very near the center of the atom than the d orbitals. This means that the s and p orbitals of outer shells penetrate the inner shells and are not so well shielded from the attraction of the nucleus as are the nonpenetrating d and f orbitals. Therefore, the increasing nuclear charge has more effect on s and p orbitals. After a sufficiently large number of electrons haye been added so that the atom has been built out to a large enough size to include part of a d or f orbital then the d or f orbital has something to penetrate and the level of its energy begins to drop also. The outermost groups of electrons, those in incompletely filled subshells covered by stippling in
Figure 3, are especially interesting. These electrons are the ones most easily removed from the atom (as evidenced by their hizher position in the fig-ure). Their orbitals alsoreach oui further than any others and bear the brunt of collisions between atoms. They form the honds hv . .-- -. -,which atoms are aioined to build UD molecules, and in general they determine the main features of the atom's chemical properties. They are, therefore, called the ezectrons. Of the under the valence electrons together with the nucleus make what is called the kernel. ~~~~~~~din the order of atomic number, each atom electron than the preceding atom, has One more except that whenever the valence subshells become filled new subshells must be started. This process of filling up and starting over again produces a repetition or periodicity in the valence electron configurations. This results in a periodicity of chemical properties and makes possible the periodic table. A study of Figure 3 will make these points clearer than can be described in words. ~~~~
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CORRELATION OF CHEMICAL PROPERTIES
The relations between valence electron configurations and the groups of the periodic table are best brought out by such questions as the following:
Find
Xe, and Rn in Figure and te,l the elements N e , A , what C O ~ ~ Ofeatures , their electron structure has. If an atom or ion bas a "comdeted octet" in its valence shell. what sort of valence electron configuration (numbers of electrons
an~~~,",~~~O~,"~~~~I~~~~,"~~htS having a single electron
and no other valence electrons. What group of the periodic table do they form and what are their chemical properties? Subgroup VI-A of the periodic table is made up of the elements 0,S, Se, Te, and Po. What is the characteristic feature of the valence electron stmcture of these elements? Of Subgroup VI-B consists of Cr, Mo,W, lJ? Compare with Subgraup v1.h. \\'hat features of the valence clcrrrun structmrs disting~~i\h the 1r.luiilion elcmentr (i.e.. clerncnts21-21,. 39-4;. and 71-79)' The rare earths?
To further emphasize that the types of orbitals are as important as the number of electrons in the valence shell i t may be asked: P. V, and As each have 5 valence electrons. Which two of these three would you expect to be most nearly alike chemically?
Positive ions are formed by loss of electrons, since The student must have some knowledge of the chemical properties of a sufficiently large number of this leaves some of the positive charge of the nucleus elements before he can effectively correlate them with un-neutralized. Naturally such ions are formed more atomic structure. Such correlation is ideally carried easily in elements whose valence electrons occupy energy on throughout the chemistry course and aids in organ- levels that are placed high in Figure 3, because such are izing and memorizing chemical behavior as fast as it is more easily removed. The energy required to remove learned. It is good practice for the student to observe one electron from the normal valence shell is called and discover the correlations himself, as much as the ionization potential. A graph of ionization potenpossible. We shall suggest a few leading questions tials against atomic numbers is given in Figure 4 or may be taken directly from Figure 3. that should help in such studies. Some appropriate questions : Valence is a term that has become rather ambiguous but is generally related to the number of one kind of Lookingnt the row of ckmrnt. frorrl Li t a Ne (in either Figure3 atom that can join to one of another kind. Recently a or Figure 1), w l n d ~of these do you thirtlr would most easily form number of new terms have been coined to avoid am- positive ions? Of the group of elements, Be, Mg, Ca, Sr. Ba, and Ra, which biguities. In compounds which are held together by electro- elements will most easily form positive ions? static attraction between ions the charee on the ions is In forming positive ions in'solution or under many called the electroualence. other common chemical conditions it usually becomes In compounds in which the principal binding is by most convenient for the atom to lose all of its valence the sharing of electron pairs the number of such bonds electrons, if it doesn't have too many, probably bewhich an atom forms is called its covalence. Mixtures cause i t can then combine with more molecules of the of electrovalence and covalence are also possible. solvent. Ions in solution are generally "solvated." An arbitrary but very useful assignment of valence On this basis predict how many electrons would be lost by the is the oxidation number. The oxidation number of an elements Li, Ra, Al, etc., in forming positive ions. What excepelement is arrived a t by assigning free ions the charge tions can you find to this rule? they actually have and then arbitrarily distributing Negative ions are formed by adding extra electrons charges among the other atoms within a molecule or to an atom. Not all atoms will show attraction for ion so that each oxygen atom always has two negative extra electrons. The most favorable condition is that charges (except in peroxides), each hydrogen always the valence shell should contain one or more very stable one charge (positive except in metallic hydrides), unfilled orbitals. This means that the valence energy and the remainder so as to produce the total charge on levels should be found relatively low in Figure 3, and the molecule or ion. The oxidation number is often there should be room for at least one more electron in equal to the sum of electrovalence and covalence, except them. for signs. In Figure 4 the conventional oxidation See how this rule agrees with the facts that the halogens farm numbers of the elements are plotted. A careful study negative ions more readily than any other group in the periodic will reveal correlations with the periodic table, or with table, and that, of the haloaens. fluorine does it more readily than the others. the electronic structure chart of Figure 3.
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Electron-pair or covalent bonds are formed between atoms when an orbital having only a single electron in it reaches out into the space between the atoms and
valence electrons and the numbers and types of orbitals available in the valence shell for the formation of such bonds.
FIGURE ~.--CO~~~AFLISON OF PERIODIC TRENDS OF SEVERAL CHEMICAL AND PHYSICAL PnoPmTIes os THE ELEMENTS
Source of data: ionization potentials: from data and figure of following paper. Atomic radii: Van der Waals radii for inert gases are from viscosity measurements (9). others are from Pauling (3). Electronegativities are determined from heats of reaction (3). Oxidation numbers: Deming ( l o ) , Latimer and Hildebrand ( 1 1 ) . Compressibilities: data of Richards obtained from Ephraim (12).
overlaps in that space an orbital with a single electron in it from the other atom. The result is that a pair of electrons share two orbitals, one from each atom, between them. They both spend part of their time on one atom and part of their time on the other. It is not necessary for the electrons to come originally from both atoms, as the same result can be obtained by two electrons in one orbital of one atom sharing it with a completely empty overlapping orbital from the other atom. The latter case is sometimes known as "coordinate covalence," but the distinction is hardly significant. Covalent bonds form when neither of the atoms has a strong enough attraction to monopolize completely both electrons and must instead share them. Figure 3 can be helpful in showing the' numbers of
More complete discussion is left for the following paper, however, and a real treatise is found in Pauling's "Nature of the Chemical Bond" (3). Figure 4 shows electronegativities according to the scale proposed by Pauling (3). Electronegativity means electron-grasping tendency. Elements whose electronegativities are not far apart form covalent bonds with each other. If their electronegativities are very different they form ionic bonds, that is, the less electronegative atom loses electrons to the more electronegative one, thus becoming a positive ion and making a negative ion of the other. The electrical attraction between the positive and negative charges then holds them together. Na+Cl- (electronegativities 0.9 and 3.0) is an example of the latter while CS2
(electronegativities 2.5 and 2.5) is an example of the former. Heats of reaction may be estimated roughly from this scale of electronegativities. Pauling (3) gives the following approximate rule for finding the number of large calories of heat evolved when one mole of a compound is formed from its elements, the elements being in the states in which they are usually found when pure: For each bond in a molecule of the compound determine the difference between the electronegativities of the two atoms joined by the bond, square the differences, add them all together, multiply by 23, and subtract 55 for each nitrogen atom and 24 for each oxygen atom in the molecule. This does not apply to compounds with double bonds. Electronegativities influence not only the character of the bonds which an atom fonns but also determine whether the element will tend to form acids or bases -whether i t will be nonmetallic or metallic. The reason is this: Most bases and acids, except the hydrogen halides, are fonnedfrom the element in question by having one or more oxygen atoms attached to it and a hydrogen atom attached to the oxygen. Whether the result is an acid or base depends upon whether it is easier to pull the hydrogen atom off (as an ion) or the whole OH group (as an ion). If the element is highly electronegative i t will strongly attract electrons, of which oxygen has an abundance in its valence shell, and will not attract positive charges like the hydrogen ion so strongly. An acid results. Less electronegative elements will hold the oxygen less firmly and the hydrogen more so. It is interestine to notice that a horizontalline drawn across Figure 3 a t a level corresponding to 8 or 9 electron volts approximately separates the acidic elements (having no valence energy levels above the line) from the basic elements (having valence energy levels above the line). The size of an atom or ion is very important, for this often determines the number of other atoms which can fit around it, and therefore the nature of the compounds which can be formed. More important, the smaller the atoms the more intense the forces between them and therefore the more stable will their compounds be. Hildebrand (13) explains in detail the effectof atomic size on chemical properties. A plot of atomic and ionic radii against atomic number is included in Figure 4. Figure 3 will serve roughly the same purpose, because in a rough way the higher an energy level appears in Figure 3, the larger will be the corresponding orbital. The size of the atom is about the size of its outermost orbitals. The correlations between the energy levels of Figure 3 and many other chemical properties, such as some of those plotted in Figure 4, are shown in the schematic plot next to the bottom of Figure 4. So many prop-
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erties follow the trends marked there that it is a scheme worth remembering.
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What in the discussion of enerw emlains -.levels in this DaDer . the dip of the "row-trends"? What is the reason for the rising "group-trends"?
The last diagram in Figure 4 shows a more complicated property which, although periodic, does not follow the same trends as the other properties discussed. ACKNOWLEDGMENTS
The author is indebted to all of his former teachers and professors for ideas which have entered here. The original inspiration for this work came from Professor D. M. Yost's clear explanations of energy levels in his course on inorganic chemistty a t the California Institute of Technology. Professor J. H. Hildebrand of the University of California gave encouragement in the early stages and his successful methods of using the periodic table and atomic structure to correlate chemical properties have entered directly into some of the foregoing. Professor C. D. Coryell has made some classroom use of the energy level chart at the University of California a t Los Angeles (in the more complicated fonn given in the following paper), and has given continual encouragement and much valuable criticism. Professor P. A. Leighton, Stanford University, snggested the simplified diagram(Figure 3) with simplified treatment. Mr. R. P. DeVault did much of the work of preparing the figures. The small "solid" drawings in Figure 1 were adapted from somewhat similar drawings by Mr. Lawrence Andrews of the University of California a t Los Angeles. Miss Nancy J. Cross, Stanford University, gave the manuscript valuable criticism. LITERATURE CITED
LUDER, J. CHEM.EDUC..20,21 (1943). WERE,ibid., 20;479 (1943). SISLERAND VANDER PAWLING. "Nature of the Chemical Bond," 2nd ed., Cornell University Press, Ithaca, New York. 1940. BORN. "The Restless Universe," Harper and Brothers, London. 1936. Life,11,76-7 (Oct.20,1941). P A P L ~ AND ~ ~ GWILSON,"Introduction to Quantum Mechan~ c s , McGraw-Hill Book Company, Inc., New York, 1935. 38, 513 (1931), and "Introduction to WHITE,Phys. RLUS., Atomic Spectra," McGraw-Hill Book Company, Inc., New York. 1934. Ann. UNS~LD , d. phys., 82, 355 (1927). "International Critical Tables," McGraw-Hill Book Campany, Inc., New York, 1929, Vol. 6, page350. DEMING,"General Chemistry," 4th ed., John Wiley and Sons, Inc., New York, 1935, page 326. LaTlrruK AS" HILUFRKAKI), 'Rcfcrencc nook of Inorganic Clwtnistry." The hlacmillan Company. S c w York. 1940. AS" \VARD. ''f:r~tz linhrnitn. lnareanic Chrmistrv." THOKSE 3rd English ed., ~ n r n e ya i d Jackson. ind don, 1939, page
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(13) HILDEBRAND, "Principles of Chemistry," The Macmillan Company. New York, 1940.
