SECT. 3] AGE DETERMINATION IN SEDIMENTS BY NATURAL RADIOACTIVITY 



819 



Fig. 3. Age determination using the ratio of two elements from radioactive series for the 

 case when the decay constant of the parent element is much larger than the decay 

 constant of the daughter element. The ordinate gives the ratio of the two radio- 

 isotopes. The abscissa gives the time scale in non-dimensional imits as multiples of 

 mean lifetime. 



same equation is applicable when the production of lead is used in age deter- 

 mination by the use of the natural radioactive series. 



B. Theoretical Method of Age Determination, Type 2 



When two isotopes of the same element are radioactive and each forms a new 

 radioactive element, the ratio of the radio-isotopes produced can be used for 

 age determination. A condition is that the ratio of the two isotopes of the parent 

 element is constant in nature. This is nearly always true of elements with a 

 high atomic weight. The decay equation of each of the isotopes is 



iV«2 = :^iVi(l_e-M) 

 A2 



and iV<4 = ^iV3(l 



-A,( 



). 



(8) 



By taking the ratio of these two, we obtain 



iV^ _ AiA4iVi (l-e-^2«) 



(9) 



When the ratio of the parent isotopes is constant, when concentrations are given 

 in units of per cent-equivalent, and when the precipitation is faster than 1000 

 years, we obtain an equation for the age: 



t = 



X2 — A^ 



In 



A2 Nt^ 



(10) 



