30. AGE DETERMINATION IN SEDIMENTS BY 

 NATURAL RADIOACTIVITY 



F. F. KoczY 



1. Introduction 



The exact method of age determination in geology is based on the decay of 

 radioactive elements. The simple mathematical expression for this process is 

 given by the differential equation stating that the number of atoms of a 

 radioactive isotope disintegrating per time unit is linearly proportional to the 

 existing number of atoms and independent of exterior parameters : 



dN/dt = -XN, (1) 



where N is the number of atoms present and A the decay constant. By integra- 

 tion we obtain the following equation: 



N = iVoe-^«-«o), (2) 



where No is the number of atoms at the time ^o, and N the number of atoms at 

 the time t. 



The radio-nuclides used for the purpose of age determination belong to three 

 categories, as follows: (1) The three natural radioactive series: uranium, prot- 

 actinium and thorium; (2) the natural radioactive elements: potassium-40 

 and rubidium-87; and (3) cosmic-ray -produced radio-nuclides. The elements 

 belonging to the two latter categories generally decay by one step into a stable 

 isotope, but the three natural radioactive series cover all the heavy elements 

 down to lead. 



The time span (t — to), of particular interest in deep-sea research, is the time 

 elapsed since a given sediment layer settled on the ocean floor. Other ages 

 important to know include the time when the sediment entered the ocean, and, 

 of further significance, the age of the formation of rock material found in the 

 sediment on the ocean floor. 



In order to be able to determine an age, it is obvious that two parameters 

 must be known : one connected with the time of formation of the investigated 

 material, the other with the present time representing a reference point. In the 

 most simple cases, these parameters are No, the number of atoms present t 

 years ago, and Ni, the number of atoms present now. The first of these para- 

 meters has to be determined in some way other than by direct measurement, 

 whereas the latter is accessible to precise measurements. One of the problems 

 of age determination is connected with this indirect evaluation, which is 

 usually dependent on certain assumptions that cannot always be established 

 as valid. 



A further problem is encountered through the fact that, in most cases, we can- 

 not determine the number of atoms without relating it to a volume or a mass. 

 Only concentrations of radioactive elements in the sediment, therefore, can be 



[MS received April, 1961] 816 



