ISAAC ASIMOV Boston University School of Medicine, Boston, Massachusetts
IT
IS generally realieed that such radioactive elements as technetium, promethium, and those with atomic numbers over 92 do not occur naturally on earth b e cause the half-lives of their isotopes are so short that any which existed a t the time of the formation of the planet have long since decayed. The radioactive elements, uranium and thorium, as well as a few radioactive isotopes of simpler elements are, however, found in nature because of their unusually long half-lives. So far as the author knows, no quantitative treatment of this matter has as yet appeared in the literature, although it is fairly simple to calculate the degree t o which any isotope has decayed during the lifetime of the earth, provided the isotope's half-life is known. Thus, the percentage of the original quantity of a given radioactive isotope still surviving today can be represented by the following equation:
S = 2-Ely,
x
100
where s is the percentage of the isotope surviving today, E is the age of Earth, and r1/,is the half-life. ~f the age of the earth is set at 3.35 x 108 then equation (1) becomes:
s
=
antilog (2
- 1.0008
Y1/1
lo?
(2)
Sullivan's chart of isotopes2lists ten long-lived radioactive isotopes upon which equation (2) may he used profitably. Using Sullivan's values for half-lives of all these isotopes except La" (for which he gives none) and using the value given by Pringle, st u Z . , ~ in the case of that isotope, the accompanying table can be prepared. It is interesting t o note that the one element that has altered its isotopic composition considerably over the geologic ages has been uranium. I n the beginning, 5.5 per cent of the uranium atoms were the now famous UZa5. Today, the corresponding figure is only 0.71 per cent. How short may a half-life be to allow significant survival? We may answer this question by taking an extreme example. The mass of the earth is about 6.0 X lo2' g. If we were to imagine this entire mass t o have been originally composed of neptunium's most longlived isotope, NpZ3', the number of neptunium atoms existing would have been 1.5 X 1040. From equation (2) it can he calculated that if NpZ8' had a half-life HOLMES, A., Nature, 163,453(1949). SULLIVAN, W. H., "Trilinear Chart of Nuclear Species," John Wiley & Sons, Inc., New York, 1949. AND K. I, ROULSTON, Phy8iOl, 8PRINGLE, R, W,, S, Rev., 78,303 (1950). 3
Survival of Long-lived Radioactive Isotopes Isotope
K'o Rba?
La"
Nd"@
Srn'62
Lu"' Re'8' Th'8' Um UP'
Half-life, years
1.4 x 6.3 X 1.2 X 5 x 2 x 2.4 X 4 X 1.4 x 8 x 4 .. 59 X
lo0 1Ol0 10" 10'0 10'1 10'0 loB2 1O1O lo8 loe
Per cent of isotope surviving today 19.1 96.4 98.1 95.5 98.9 90.8 99.92 84.7 7.38 59.7
of 20 million years, that colossal number of atoms would, nevertheless, have decayed in the over three billion years of the earth's existence to such an extent that today only one such atom would exist. Since NpZ3' has, in actual fact, a half-life of only 2.2 million years, it is not surprising that it does not occur naturally on the earth. Since the isotopes listed in the table (plus, perhaps, the one or two doubtful cases such as In1", concerning whose radioactivity there is yet some question) are the only ones with half-lives greater than 20 million years, they are the only radioactive isotopes whose atoms may be said to have existed continuously since the formation of the earth. Isotopes of half-life lower than 20 million years are found on earth in what may be called "micro-quantities," their atoms having been formed in one of the three following ways long after the earth's origin: (1) Through the decay of a long-lived precursor. Sullivan's chart lists 39 isotopes of the elements thallium, lead, bismuth, polonium, astatine, radon, francium, radium, actinium, thorium, protactinium, and uranium as "naturally occurring," due to their places UZa5,and U238. in the radioactive decay chains of ThZaZ, Their mass numbers vary from 206 to 234, and their half-lives vary from 230,000 years in the case of UZa4 to 2.6 X lo-' seconds in the case of Po212. The most famous of this group is the radium isotope, Razz', with a half-life of just over 1600 years. (2) Through the natural transmutative processes continually occurring on earth. For instance, the carbon isotope, CL4,with a half-life of only 5700 years, nevertheless exists in measurable quantities because of its formation from N14by cosmic ray bombardment. (3) Through controlled nuclear reactions in the lahoratory. The most famous case of this is the plutonium isotope, PuZ3',with a half-life of only 24,000 years, which now exists in quantities sufficient for the critical mass to have been exceeded many times.
398
