98 



DISCOVERY 



These facts have an interesting consequence. If 

 uranium X be completely separated from uranium it 

 will disintegrate away according to the law that has 

 been described above, but as fast as it disappears, when 

 alone, it is grown from its parent uranium, the growth 

 continuing until equilibrium is again reached. A few 

 figures may make this clearer. Suppose loo to repre- 

 sent the weight of uranium X in equilibrium with a 

 given quantity of uranium. Then at the moment of 

 sep.iration of the former from the latter, which we 

 shall call zero-time, the former preparation contains 

 100 units of uranium X, the latter none. The amounts 

 found experimentally at subsequent times are set out 

 in the table below : 



Note that there are always 100 units of uranium X 

 in existence ; whatever part is lost by disintegration 

 of uranium X is made up by disintegration of uranium. 



The curves obtained by plotting these two sets of 

 results against the time are shown in Fig. 2, and are 

 called decay- and rise-curves respectively. 



A radio-element, therefore, appears to have a life 

 only when it is away from its parent. Separate it 

 from it and no power that is known can arrest or 

 influence its rate of disintegration. But if it be with 

 its parent, and equilibrium has been reached, the 

 amount of it is constant, or it will only vary directly as 

 does the amount of its parent . A product with its parent 

 therefore appears to have the same life as its parent. 



The fraction of the product that disintegrates per 



second has, however, a bearing on the matter. It 



cannot affect the life of the product when it is with 



its parent, but it does affect the weight of the product 



in equilibrium with a given weight of the parent. It 



is found that these weights are to one another in 



the sara: ratio as their half- value periods, and this 



result holds equally whether we consider a parent and 



its product or the parent and its product's product, 



or its product's product's product, etc. This is a very 



important and useful result. For example, the amount 



of uranium X in cquiHbrium with one kilogram of 



24'6 X 1,000 X 1,000 .,,. 



uranmm is ^!^ '—-- milligrams, since 



5,000,000,000 X 365 



2j\'6 days and 5,000,000,000 j^ars are the periods of the 



two b3dies respectively, and since there are 1,000 milli- 



grams in a gram and 1,000 grams in a kilogram. This 

 result when evaluated is 0-000013 milligram. So with 

 radium, which is uranium X's product's product's pro- 

 duct's product. The amount of radium in equilibrium 

 with one kilogram of uranium may likewise be evalu- 

 ated as 0-34 milligram. And so for other bodies. The 

 longer the life of a radio-element the more there is of 

 its weight in a preparation which contains the original 

 parent. And the converse of this holds true also. 

 In a mineral containing uranium and (as the majority 

 of such minerals do) all its successive products, if the 

 amount of pure uranium contained in it be determined, 

 and the amount of radium be separated and deter- 

 mined, then if the period of uranium be known that 

 of radium can be calculated, and vice versa. 



There are about four principal methods of measur- 



lOO 



75 



50 



25 





Fig. 2.- 



30 60 90 120 150 



-THE DECW- .\ND RISE-CURVES OF URANIUJI X. 



ing the life of a radio-element, three of which may 

 be described in outline. The first is to count the 

 actual number of a-particles emitted each second by 

 a known weight of the disintegrating material. Each 

 a- particle that strikes a specially prepared screen 

 gives a flash of light, and the number of flashes may 

 be counted with a microscope by an observer in a dark 

 room. In this way the number disintegrating may 

 be obtained. Now the number of atoms in any given 

 weight of this element is known. Divide the number 

 of atoms that break up per second in a given weight 

 by the total number of atoms in that weight, and the 

 fraction disintegrating per second is obtained. In 

 this way the period of radium may be measured. 



A second method is to separate out and purify (if 

 you can) and weigh the quantity of a radio-element 



