210 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1965 



is SO, the present average isotopic composition of lead, uranium, and 

 thorium in the earth's crust indicates an age of 4,500 million years 

 (18, 19), in remarkable agreement with a similarly determined age of 

 stony meteorites (20). This would be the time elapsed since the 

 separation of the iron from the silicate phase, which may have taken 

 place in a diffuse state of matter and may have preceded the forma- 

 tion of the planets. 



THE AGE OF THE ELEMENTS 



Time intervals can be calculated only for radioactive elements with 

 a known rate of decay. According to the well-known laws of radio- 

 active decay, the amount of these elements decreases exponentially 

 with time; calculating their amounts for distant epochs in the past, 

 one inevitably arrives at time limits beyond which the calculated 

 abundances of radioactive isotopes become mireasonably large — 

 greater than those of the presently observed end products, or even 

 greater than the total amount of matter in the universe. Clearly, 

 the radioactive elements can only be of finite age. Now, the rate of 

 decay of radioactive elements is not influenced by external conditions 

 if the temperature remains below 1,000 million degrees and the density 

 below, say, one million times that of water. Neither in the interior 

 of normal (dwarf or "main-sequence") stars, nor in interstellar clouds 

 from which suns and planetary systems are believed to have sprung, 

 do such extreme conditions exist. We may well say that the state 

 of matter in the observable universe requires radioactive decay to 

 proceed relentlessly. As this could happen only for a finite interval 

 of time, it would mean that the observable agglomerates of matter in 

 the universe could also have existed for only a limited time. 



Thus, at a remote epoch a building up of the radioactive isotopes 

 must have taken place, in addition to their spontaneous or forced 

 decay. Now, conditions leading to the formation of the heavy radio- 

 active isotopes will throw the rest of the lighter elements into a melt- 

 ing pot, too — will cause their rapid building up and disintegration; 

 this is a trivial consequence of the theory of nuclear structure. The 

 age of the radioactive isotopes is thus almost synonymous with the 

 age of the elements. 



According to a method proposed by Kussell (21), a maximum age 

 for the elements can be derived from the relative terrestrial abun- 

 dances of a radioactive isotope and its end product. It yields a 

 maximum age, because some of the end product must have been created 

 nonradiogenically in the initial "melting pot," when all the elements 

 came into being under extreme conditions of temperature and density. 

 Of the different isotopes, that leading to the lowest estimate of age is to 

 be taken. The upper limit of age of the terrestrial elements thus found 



