DISCOVERY 



97 



tim?, an atom m.iy exist unchanged for any time from 

 zero to infinity. There is, however, for each radio- 

 element an " average hfe " of so long and this in 

 years, days, hours, etc., is numerically equal to 

 the reciprocal of the fraction that disintegrates per 

 year, per day, per hour, etc. The second is that for 

 each radio-element there is a constant interval of time 

 at the end of which the number of atoms, at its begin- 

 ning, has fallen (through disintegration) to half. This 

 is called the half-value period, and is the unit in which 

 the life of a radio-element is most often expressed. 

 Between the fraction disintegrating, the " average life," 

 and the half-value period are simple numerical rela- 

 tions ; the reciprocal of the fraction disintegrating is 

 the " average hfe," and that multiplied by the factor 

 0-693 is the half-value period. In the example above 

 the fraction disintegrating is j\5th per day (lo per 

 cent.). The " average life " of the atoms is 10 days ; 

 the half-value period 6-93 days. In this last period 

 the million atoms become 500,000, in 13-86 days 

 250,000, in 20-79 days 125,000, and so on. The fraction 

 for radium is jjVf P^^ year ; the " average life " of 

 radium atoms is 2.309 years, the half-value period 

 1,600 years. If an ounce of radium had been sepa- 

 rated from its ore about 1279 B.C. it would have weighed 

 half an ounce in 322 A.D., and a quarter of an ounce 

 to-day, and this weight will fall regularly by half every 

 r,6oo years so long as the universe continues. 



Thorium has the longest half-value period of all, 

 C5, 000, 000, 000 years ; uranium comes next with a 

 third of this amount. These are enormous and almost 

 unthinkable periods of time. Three bodies have 

 periods reckoned in hundreds of thousands of year?. 

 Next comes radium, with a period of a thousand years 

 or so, and next actinium, with twenty years — the only 

 radio-element whose period approximates to the life 

 of man. Most radio-elements have periods less than 

 a year, and some are very short indeed ; that of the 

 element known as thorium A is -14 of a second, so that 

 in seven times that period (a second approximately) 

 the amount of this element falls in the ratio of 128 

 to I. Thorium A consequently has a short life, 

 but, no doubt, a merry one. Yet it is long compared 

 with that of the element thorium C, whose period is 

 ■ooooooooooi of a second. It is only right to add that 

 this short period has not been measured directly ; it 

 is calculated, however, from trustworthy evidence. 

 The shortest period directly measured is that of 

 actinium A, a mere five-hundredth of a second ! 



It may well be asked how it is, if the world be old 

 and the half-value periods of most radio-elements 

 short, that these bodies exist at the present day at all. 

 To this, in short space, it is not easy to make reply. 

 Consider, first of all, the long-lived primary elements, 

 thorium and uranium. They are rare elements, be- 



coming as time goes on still rarer. For, although 

 the process of disintegration is exceedingly slow, there 

 is no evidence of the existence of a compensating 

 influence on the earth by which these elements, by 

 being built up from others, might be maintained at 

 their present amount. Yet the periods are so very 

 great that it is not to be wondered that these elements 

 have persisted on earth so long. Compared with the 

 lifetime of a man they may be almost exactly de- 

 scribed as not changing at all. 



Consider next uranium and its product, the body 

 known as uranium X. The latter is easily separated 

 from the former by simple chemical means. Let us 



100 



75 



50 



t 

 25 





30 



60 90 120 150 180 



-THE DECAY-CUR\^ OF URANIUM X. 



consider a preparation of uranium from which the 

 whole of the uranium X has recently been separated. 

 Uranium disintegrates, and for every atom which dis- 

 integrates an atom of uranium X is produced. It 

 is clear that, if uranium X were not radio-active, it must 

 accumulate with time in the preparation of uranium. 

 Actually, however, it is radio-active, disintegrating to 

 fonn a third body ; consequently it does not accumu- 

 Lite beyond a certain point, for there comes a time 

 when the number of atoms of uranium X produced by 

 the atoms of uranium is exactly that which disintegrates 

 to form the third body. After that time has been 

 reached the quantity of uranium X remains constant. 

 The quantity remains constant, but the atoms com- 

 prising the material do not remain unchanged, for two 

 things are happening. Some atoms are disintegrating 

 to form the third body and as many others are taking 

 their place from the disintegration of uranium. When 

 this occurs uranium X is said to be in equilibrium with 

 its parent uranium. 



