Predicting Nuclear Stability Using the Periodic Table Harvey F. Blanck Austin Peay State University, Clarksville, TN 37044 Althoueh t h e oeriodic table has long been an extremely useful guide to many atomic characteristics. it is not used to predict the stability of atomic nuclei. Several empirical rules will he develoned in this article to use with the oeriodic table ~-~ as an aid t o recalling those nuclides that are st'able. Most zeneral chemistw textbooks have a chapter on nuclear chemistry contaiuGg a graph of the stableisotopes of all the elements showine the relationshio between N, the number of neutrons in ;he nucleus, and 2,the number of maoh orotons in the nucleus. A .. . of A, the mass number, and Z for the stable nuclides much more clearly reveals patternsof nuclear stabilitv (see figure). No consecutive elements have the same A v&es and oily a few A values are absent. Not all sources commonly available quite agree upon which nuclides are stable. The reference used here for nuclear stability is the 1986 Table of Radioactive Isotopes by Browne and Firestone.' Nuclear stability patterns may be largely summarized by three rules. ~
.~ ~
~~
I. 1 .. For - .elements ~ - thmueh I each haa two stable isotones with consecutive A values exrept Be ('Be decomposes into two alpha particles).The A values are from 1 through 15, omitting 5 and 8. Thua the stable nuclides are 'H,AH: 'He, 4He; %i, -Li; 9He:'OH. ~~~
I1B;
'%,
IsC;
~
and '4N,S 'N
2. For elements with an oddZ such that 8 < Z 5 83 there are one or
two atahle isotopes for each element, all of which have odd A values. The A values may, with few exceptions, be determined by rounding the molar mass to the nearest whole number. If the result is odd, that is its only stable isotope. If the result is even, there are two stahle isotopes having A values immediately above and below the even number. This method fails to predict the existence of"Cl,"K, and 'I3In because their relative abundances are low (248, I%, and 4%). It also incorrectly predicts the existence of and I151n, which, although unstable, have natural abundances of 63%and 9670, respectively. Te and Pm have no stable isotopes, which is indicated on most periodic tables by enelmure of molar masses within parentheses. 3. Ty@cally elements with an even Z such that 8 5 Z < 83 have stableiwtopesat every A not present between the lowest A of the next lower Z element and the highest A of the next higher 5: element. In other words, stable nuclides of elements with an even Z fill in the "boles" left by the two adjacent odd Z elements. Using this procedure, 147 of the 196 stable nuclides with an even Z of 8 or more mav be listed with only - two,. lS2Gdand '860s, incorrectly predietkd as stahle. As perhaps might be anticioated. there are some oroblems with elements adjacent the two odd Z elemenis, T c and Pm, since they hive no stahle isotopes. Both Mo and Ru have stahle nuclides with A equal to 98, which is the most stable isotope of T C . ~
tb
Resented in part at the 97th meeting of me Tennessee Academy of Science at Jackson State Community College, Jackson, Tennessee. November 1987. and at the 40th ACS Southeast Regional Meeting. Atlanta, Georgia, November 1988. Browne. E.; Firestone. R. B. TableofRadioactivelsotopes;Wiley: New York, 1986. 2 tH 4BCa 9 6 2 112Cg 1&5Nd,l l 8 ~ ~ , i49Sm, 15BDy, and 208gi , , r, are listed by Browne and Firestone as being unstable, but with no mode of decay indicated. All have half-lives in excess of 10" years Of these, 'Hand 209Biare listed as stable in the figure. The most stable isotope of Tc may be listed on some periodic tables as 97 or 99 rather than 98.
'
Circles Plot of -5 number versus atomic number for stable indicate stable isotopes not predicted by rule 3 fa elements with an even atomic number. Stable isotopes of Nd and Sm, which are the elements adjacent to Pm, have an irregular pattern and are difficult to predict. Some even Z elements also have one or two even A stable isotopes immediately above andlor below those already mentioned. There are 42 such nuclides. These nuclides are circled in the figure. Examples: Periodic Table Ammlc weight rounds to 75. Wd; one nuclide.
Stable Isotopes 7sAs
74.92
Fill In missing A valm b & m
7
adjacent elements. 78.96
Ammlc welgm rounds to 80. Even: two nudldes. 79.90 Volume 66
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AU follow the rules mentioned above except T4Se. The above rules result in successful prediction of 206 of the 255 stable nuclides, with errors nearly always being errors of omission. While the periodic table cannot, of course, replace extensive stability and decay tables, it is nevertheless almost always readily available. Therefore, coupled with just three rather simple stability rules the periodic table
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Journal of Chemical Education
becomes a handy guide to nuclide stability when discussing topics such as stellar nucleosynthesis, elemental abundances, radioactive dating, and related topi~s.4,~ Ryberg, J.; Choppin, G. R. J. Chem. Educ. 1977, 54, 742-744. Rowe, M. W. J. Chem. ~ d u c1986,63,300-303.
