A Method of Teaching the Electronic Structure of the Atom II.
Advanced Topics DON DEVAULT
Civilian Public Service Camp No. 135, Germfask, Michigan
T
HE preceding paper (1)does not completely bridge the gap between its energy level chart of the periodic table and the experimental data from which the chart was derived. There are also several other topics involving spectroscopy, x-rays, and chemical binding which are interesting to the advanced student and which this paper will try to present in suggestive form. The work of constructing the energy level diagram revealed several minor errors in the spectroscopicliterature, and also some better values for several ionization potentials. These are recorded in the last section of this paper. ACCURATE ENERGY LEVEL DIAGRAM OF NEUTRAL ATOMS
The energy level chart of the periodic table given in the preceding paper (Figure 3) greatly simplified and smoothed out the energy levels, presenting each snbshell as though it had just one energy level. This was necessary to show the important trends without confusion. Actually there are many levels associated with each subshell. Figure 1, this paper, is an energy level chart of the whole periodic table, giving as many of these energy levels as possible, plotted from actual experimental data. In Figure 1 circles are used to represent electrons. They are arranged in groups to correspond to the actual distribution among subshells found in the atoms in their neutral, gaseous, monatomic, normal (most stable) state. The configurations and energies would be changed somewhat by such influences as compound formation or condensation to a solid. A group of circles representing the electrons in a subshell is placed on the chart a t a height indicating roughly the energy necessary to remove one electron from that subshell completely. The energy necessary to remove another electron from the same subshell would be larger and cannot be conveniently shown on the chart. Different types of circles are used for electrons in diierent types of orbitals as explained in the legend to Figure 1. Paired electrons, pfaced side by side, are in the same orbital and spinning in opposite directions. Since the energy of the electron depends upon its relation to all the other electrons in the atom, the energy really belongs to the whole atom and the energy levels really refer to states of the whole atom rather than to
supposed states of a single electron. We take the "energy of an electron" to mean the energy change which the whole atom undergoes when the electron is removed from the atom. One should notice that the energy scale in Figure 1 is not uniform, but logarithmic. One centimeter of height represents much more energy at the bottom than it does a t the top. All levels belonging to the same subshell, or, more exactly, all levels corresponding to atomic states in which there are the same numbers of electrons in each subshell, are tied together into groups on the chart with thick vertical bars. There are two reasons why the energy of removal can have more than one value (giving the multiplicity of levels belonging to a single subshell) : 1. The electron configurations shown in Figure 1 do not completely describe the initial states of the atoms. They show only the distribution of electrons into subshells and amount of pairing and unpairing. There remain differentpossibilities for relative orbital and spin orientations among the valence electrons, each of which will give the atom somewhat different energy. 2. There are similar variations possible in the final state. Thus the energy of removal is the difference in energy contents between a choice of initial and a 'choice of final states. It is impossible to plot on one diagram all of these choices. The levels chosen for plotting are as follows: 1. The lowest level in the group belonging to the highest subshell that normally has any electrons in it indicates the energy obtained when the initial state before removal is the normal state of the neutral atom and the final state is the normal state of the ion formed. This energy is called the ionization 9otential. 2. All levels above the ionization potential (that is, the normally empty levels and those in the same group as the ionization potential) are based on the normal state of the ion. The fine structure comes from the different possibilities for the initial state. 3. All levels below the ionization potential are based upon the normal state of the neutral atom. The fine structure arises from the different possibilities in the final state. Several extra rules are necessary to explain details in the choice of levels : 4. To arrive a t the normal state of the ion in V, Co.
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Ni, and La a second electron must he moved to a lower subshell as indicated by the arrows. 5 . Whenever an electron is moved from a subshell containing both paired and unpaired electrons, it is one of the paired electrons that must be moved. 6. To measure the energies of removal from a subshell which normally has no electrons in it (the empty levels shown a t the top of Figure 1) an electron must first he moved into i t to form the "initial state" and then the energy of removal measured. So far as possible the initial state was made to conform with the normal state of the ion in respect to all the electrons except the ele-
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vated one. (This means that the arrows must be observed in V, Co, Ni, and La even in the initial state.) Different levels result from different orientations of the elevated electron with respect to the other electrons. A few cases in which different arrangements of the other electrons gave lower energies were included also. 7. The number of unpaired electrons is never changed except as results directly from the removal of an electron (or from following the arrows). 8. The different levels indicated for any other occupied suhshell result from different orientations in the final state within that suhshell.
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N U C L E A R
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C H A R G E
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quantum number abbreviated 1, indicates l-he ~t is 0 for all s orbitals, 1for all P orbitah 2 subshell. some of the quantum numbers related to the shells for all d orbitals, 3 for j orbitals, 4 for g, and so on. A and subshells are placed a t the right-hand edge of glance at Figure 1 of the preceding paper shows that the ~i~~~~ 1. These specify exactly the state of one or difference between the value of 1 and the value of n for a more electrons in an atom. One might compare given orbital is equal to the number of maxima of clqud nlrlntumnumbers to a person's street, city, county, density that can be found along any radius centerlag and state address. Obviously, therefore, it is not possible ~h~ prin&fid quantum number, often abbreviated n. at the indicates the shell. l t is the 1, 2, 3, e t c , in the labels for an electron to have an orbital quantum number as -ls,n ~ 2 f i , "3s,,. , ~ etc., which we have already used ex- large as its principal quantum number. This limits tensively. ~h~ pincipal quantum number of an elec- the number of subshells that a shell can contain. ~h~ orbital quantum number shows, through a simple tron in the K shell is 1, in the L shell 2, etc. QUANTUM NUMBEBS
formula,' the amount of orbital angular momentum that the electron has. The angular momentum of an electron is a measure of its revolution about some axis. An electron in an atomic orbital can do a certain amount of revolving about an axis through the nucleus. Thus electrons in s orbitals are considered to oscillate through the nucleus, those in p orbitals to revolve.closely about the nucleus, and in d orbitals to revolve more widely about it. A given subshell may he divided into its orbitals in different ways for different circumstances, but always with the same total number of orhitals resulting. The preceding paper used the division shown in Figure 1, where the different orbitals are distinguished by the letter subscripts, x , y, z, etc. If we are studying effects in a magnetic field the orbitals arrange themselves so that it becomes convenient to describe them by the orbital magnetic quantum numher, m,, which shows how much of the orbital angular momentum is around an axis in the direction of the magnetic field. Thus a value of 0 would mean an orientation of the axis of rotation a t right angles to the magnetic field. Naturally, m, cannot he larger than 1 hut it may have any absolute value equal to or smaller than 1 including zero, and i t may he either or - . Thus the total possible 1. numher of orbitals in a subshell comes out 21 Comparable to mLin its usage is the sein mapetic number m, which indicates the orientation of an electron's spin with respect to a magnetic field. Its value is alwavs either +I./. , - or -I/.. , We may restate the exclusion principle of Pauli by saying that no two electrons in an atom can have the same values for all four quantum numbers, n,I, m,, and m,. If two electrons are in the same orbital they have the same values for n, I, and mi, hut must have opposite values for m,.
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like a top an its own axis, to the extent of d1/z(1/2 1) of a natural quantum mechanical unit of angular momentum. The quantum numher j indicates the total angular momentum of an electron resulting from a combination of its orbital and its spin angular momentum. The quantum number L is used to indicate the resultant orbital angular momentum of all the electrons in an atom. All orbital angular momentum is canceled out in all filled suhshells. Thus only incompletely filled suhshells need he considered in determining L. The quantum numher S indicates the resulting spin angular momentum of all the electrons in a n atom. It is equal to half the numher of unpaired electrons. The quantum numher 3 indicates the total angular momentum of all the electrons in the atom. I t may he regarded as the resultant of L and S , or as the resultant of all the j's of all the individual electranswhichever type of description best fits the atom under consideration. The former type is used more in lighter atoms, the latter in the heavier atoms.
pletes an analogy between matter and radiant energy by observing that light has the properties of particles. A particle or quantum of light is called a photon. The energy of a photon depends upon its wave length according to the formula: (Wave length in Angstroms) - '2~34Q/~En,.,, inpip.tron.inl,s,. Table 1 shows the relations between color and energy of photons in the visible region. TABLE 1 COLOR OW LIGHT
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(dwrrdms) >7000 7000-6470 6470-5850 5850-5150 5750-4910 4910-4240 4240-4000
