Question

In a old rock ratio of nuclei of uranium and lead is 1:1. Half life of uranium is 4.5 *10^9 years. Let initially it contains only uranium nuclei. How old is the rock?​

Answer 1

The ratio of the amounts of U 238 and Pb 206 in a rock sample enables the age of the rock to be estimated using the technique of radiometric dating.

U 238 forms a decay chain in which it undergoes a sequence of 8  

α  and 6  β  decays:

 

It moves back in the periodic table until the isotope falls in the band of stability at Pb 206.

Each step has its own individual half - life but the first decay to Th 234 is about 20,000 times slower than the other decay steps.

Those of you who are familiar with chemical kinetics will know that it is the slowest step in a mechanism which determines the overall rate of reaction, the so - called "rate determining step".

This is the case here in the conversion of U 238 to Pb 206.