818 



KOCZY 



[CHAP. 30 



(a) If Ai is much smaller than A2, Nq^ — ^ N^ and the equation can be approxi- 

 mated as follows: 



i\r2 = mi^{l-e-'2(), 

 A2 



(4) 



which gives the formula for age as 



1 



a;'" ' 



^2A2\ 



(5) 



where Nq^ is the initial amount of the decaying nuclide and N^ the nuclide 

 produced. This method is applicable when one of the long-lived nuclides, such as 

 uranium or thorium, is incorporated without daughter products in a mineral. 



0.5 1.0 



2.0 2.5 3.0 3.5 4.0 



Ag/. 



Fig. 2. Age determination with the aid of the ratio of two radioactive elements from the 

 same series where the decay constant of the daughter product is large compared with 

 the decay constant of the parent element. The ordinate gives the ratio of activities 

 of the two radio-elements. The abscissa gives the time scale in non-dimensional units 

 as multiples of mean lifetime. 



The produced nuchdes with half life large enough to be used for the purposes of 

 marine geology are, in that case, ionium (230Th), protactinium (23iPa) and 

 radium (228R,a, 226^^). 



(b) In the case where Ai is much larger than A2 the equilibrium equation is 

 approximately 



N'^ 



NoHl 



-^,f 



), 



but as No'^^Nh^i', we obtain as a formula for the age 



iV2\ 



t 



i-i 



1 + 



NK 



(6) 



(7) 



where the same notation is used as above. 



This equation is used when a radio-nuchde produces a stable isotope, such as 

 potassium-40 giving argon-40, and rubidium-87 producing strontium-87. The 



