The Periodic Table and Electron Configurations Judith A. Strong Moorhead State University, Moorhead. MN 56560
When electron configurations are taught, many texts use the Uncle Wiggly path or a typographical variation such as that reported recently in THIS JOURNAL'. These systems provide students with a method of writing correct electron configurations, although some of my students who rely on such methods spend an inordinate amount of time when requested t o write electron configurations for heavy elements, such as lead. even after the material has been "covered" and they supposedly have mastered the technique. I have been using a different approach, which is found, in part, in many textbooks2. My students seem to findit a t least as easy, if not easier than the Uncle Wiggly method. I prefer this approach for a number of reasons. Most importantly, i t uses the periodic table as a mnemonic device, and use of the periodic L b l e for prediction is a transferable skill and one widely used by chemists. Also, application is as easy and rapid for heavy elements as for lighter ones. Once learned, the system seems memorable-one glance a t a periodic table and most students can eive an outer electron confieura" tion-without resort to pencil and paper. Some exceptions to the order of filling, especially those for the coinage metals, copper, silver, and gold, as well as those for chromium and molybdenum, are readily incorporated into the presentation. Finally, it is also possible t o use the same techniques in prediction of electron quantum numbers. This application is not commonly found in textbooks, yet i t seems worthwhile in that i t focuses on the fact that quantum numbers and electron configurations are merely different representations of similar information. For prediction of electron configurations I use the following procedure. I usually draw my own diagram of the periodic table on the board and fill in the details as I go along. Alternatively, an overhead transparency of an uncluttered periodic table may be used with a wax pencil or marker to add details. The procedure is best considered in terms of the following three-step process. First, the periodic table is presented in terms of s,p, d, and f blocks, where the label designates the kind of orhital the "most-recently-addeP3 (MRA) electron is filling. The block diagram is shown in Figure 1. Next, the columns within each block are numbered, starting with one, going from left to right. Each number represents the quantity of MRA electrons present in the outermost orbitals of the elements in that column. For example, nitrogen is in column 3 of the D block corresnondin~to a n3 conf~guration.Iff blorks are ikcludrd. the cklunm iumheru arefromone to 14 if lanthanum and dctinlumaro ~nrludedas part of the f block. In this form of the periodic table, 15 columns are present in the f block. However, if lanthanum and actinium are placed in the d block, the f block columns are numbered from two to 14 as shown in Figure 2. An asterisk is placed above the last column in the f block, instead of a number, as this represents a somewhat irregular configuration, d T 4 . If exceptional configurations are to be
included, then column numbers four and nine in the d block and eight in the f block also receive asterisks for later explanation. In step three, the periods, or rows, of the periodic table are numbered from one to seven. This numbering is identical to the period numbers shownon the left side of most versionsof the periodic table. The row number,R, is related to the value of the principal quantum number, n, of electrons being filled within that row. For s and p electrons, the row number is equal ton. For d electrons, filling of electrons corresponding to a particular value of the principal quantum number fol-
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' Carpenter, A. K. J. Chem Educ. 1983, 60, 562.
Mortimer, C. E. "Chemistry: A Conceptual Approach", 4th ed.: Van Nostrand: New York, 1979; p 53. "Outermost" electron implies that of lowest ionization energy; hence, I prefer to avoid the term. Mortimer (see footnote 2) uses the term "differentiatingelectron".
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Journal of Chemical Education
Figure 1. Schematic diagram of the periodic table indicating s, p, d and blocks.
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Figure 2. Schematic diagram of the periodic table indicating row and column numbers and elements of inegular electron configurations. The asterisks above a column and the circles in the table indicate presence of elements with irregular electron configurations that are predicted on the basis of the stability of half-or wholly filledsubsheils.The X values indicate lhe presence of other elements with irregular electron configurations.
lows filling of s electrons in orbitals with nrincinal . auantum . number one unit higher. Onre this occur;, a new row of the periodic table hegins. For this reason one might speak of d electronsas filling one row late, which means that n = R 1. Similarly, for/electrons, filling is two rows late so n = R - 2. Now the diagram should resemble Figure 2 and some regular electron configurationsmay he written. Discussionof irregular electron configurations is hest deferred until prediction of regular configurations is mastered. T o illustrate the method. an element. suchasantimonv. is selected. I t is in column three of the p block and therefore contains three electrons in the outermostp orbitals. Antimony is in row five of the periodic table, so the three electrons are in the 5p orbitals, based upon the fact that the row number, five, equals the principal quantum number for the p block. I t now remains to describe the remaining outer electrons of antimony. I work back across the row from right to left, indicating to my students that it is possible LO use the elements in the table to count electrons because each element has one more electron than its predecessor. When looking a t antimony, three elements, indium, tin, and antimony, are found in t h e p block, representing successive addition of the threep electrons; similarly, there are 10 elements precedingthesein the d block. As the row number is five, and d orbitals fill one row late. there are 10 4d electrons nresent. There are two elements in the s block and, since n R for s orbitals, two 5s electrons are present. Finally the last 36 elements in antimony can be specified by the electron configuration of krypton. The complete electron confieuration is now
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Another example may he useful, this time with platinum. The logic is as follows: Platinum is in column eight of the d block in row six. Thus there are eight electrons in the 5d orbitals. Working backwards, the symbol indicating the presence of the lanthanum series is found. A quick count reveals 14 elements in the f block. The row number is six and f orbitals fill two rows late, so 14 electrons in the 4f orbitals are predicted. Finally, two electrons are present in the 6s orbitals and the remaining 54 electrons may he represented by the symhol, Xe. We have (Xe") 6s24f"5d8
The system will even work to predict regular electron configurations for the f blocks. There are so many irreeular configurations there, as indicated by the X and 6 designations shown in Figure 2, some may find i t undesirable. Because of the d' configurations observed for lanthanum and actinium, some of the regularity is lost in numbering the columns. After introduction to the diagrams and how to interpret them to obtain electron configurations, I finalize my diagram by replacing the asterisks withappropriateconfigurations such as sld" ss'd'U,f d l , and f 'dl and a presentation on thestability of half- and wholly filled suhshells. This is R good place to discus the experimental nature of these electron configurations and the role of s ~ e r t r o s c o ~inv their determination. Students may need a reminder ofihe role of experimentation in the midst of this highly theoretical topic. Once this type of a construct is available, it is reasonably simple to go into an exercise on quantum numbers. I use an approach in which I describe the MRA electron of an element by specification of its four quantum numbers. Of course, this only works for those elements having a regular electron configuration. This interrelation between the quantum numbers and the electron configurations may be shown using the electron configurations themselves, or hv another schematic diagram of the periodic table. The use of the periodic table for &termination is as follows. The principal number. n. is . quantum . readily found, as above, f r o i the row number. Thus inantimony for the third p electron, n = 5, and, because it is a D electron, the azimuthal or subsidiary quantum number, 1, is, by definition, one for a p electron. T o find the mametic orbital quantum number. m,. and the magnetic snin &an~ ~ - ~ - tum number, m., Hund's kui& are applied. Among states of given n and 1values. Hund's first rule states that the state of maximum multiplicity has the lowest energy. Hund's second rule4 specifies that of the possible states of the same multiplicityand electronconfi&ration, thestateofgreatest orhital angular momentum is the most stnble.This turnsout to he the case when the mi value of each electron is maximized subject to the constraints of Hund's first rule. In assienine quantum numbers todesrribeelectronsesadded to fo& th; ground stateofan element, theorbital within asuhshell with the maximum value of mi is used first, and the minimum value last, i.e., f o r d orbitals, +2 is assigned first, then +1,0, -1, and finally -2. Secondly, spin up, or m, = +'IZ, is assigned to the first electron in a given orbital; spin down, or m. = -%,to the second electron added t o a eiven orbital. Not all -~-texts-use this assignment, but I prefe; the consistency of starting with the positive number in both cases and working down. This assignment is also convenient a t the upper level to relate the Russell-Saunders term svmbols for the eround states t o the electron configuration lit turns out &at the value of the total orbital angular momentum, L, of the ground state term can be obtained by summation of the mi values of the electrons present). Now, this information is incorporated into a schematic diagram of the periodic table. T h e n and 1values are given by row numbers and block assignments. Then, each column within a block is labelled with an mr value according to Hund's Rules. For example, the first element in the d block gets +2, the next +1, then 0, then -1, then -2. We are now in the middle of the d block and each of these five d orbitals contains an electron of spin up, as required by Hund's rule of maximum multiplicity. Thus, a hracket may be drawn from column one to c&mn five of the d block to designate m, = +% for all of these; the remaining five columns have m. = -'I2 and have the same sequence of ml values from +2 to -2. Figure 3 shows a completed diagram indicating quantum
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Figure 3. Schematic diagram d lhe periodic table showing lhe far quantum numbers of the most recently added electron for elemems with regular elecWon configurations.Hellum is indicated bath in its normal position and adjacent to hydrogen. The )alteris more appropriate for the present purpose.
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a Bromberg, J. P. "Physical Chemistry", 2nd ed.; Allyn and Bacon:
Boston. 1984: p 583. Volume 63 Number 10 October 1988
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numbers. One might predict +3 t o -3 in the f block, hut most tables place lanthanum and actinium in the d block, so numbering starts with +2 instead of +3. T o reiterate, these are the four quantum numbers of the MRA electron, assuming regular order of filling. I then give my class sets of four quantum numbers, from which they determine the element. For example, given n = 5 , 1 = 2, ml = 1,and m. = -%,it can be seen from the first two values that the element has 5d electrons; given mr = 1and m. = -%the sixth column of the d block is located. The element is iridium, Ir.
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Journal of Chemical Education
Although all these diagrams may seen complex, the logic involved and reliance upon the simple skill of counting simplifies the process. Most of my students can draw diagrams as in Figures 2 or 3 a t will. The major focus is twofold. Students should he able t o ascertain an outer electron confiauration auicklv and accuratelv. Thev should also he exposed to some ofthe marvelous order chat arises from consideration of the periodic table and the relationship between quantum numbers and the elements. I believe my approach allows fulfillment of both of these aoals while keeoine. . rote memorization of rules and diagramsto a minimum.
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