Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock is found to contain 83.9% of the amount of uranium-238 that it contained when it was formed. (The amount that the rock contained when it was formed can be deduced from the presence of the decay products of U-238.) How old is the Rock?

years

Explanation:

For a first order reaction constant is given as :

where t = 4.5 billion years

             =   years

Therefore,

   =

Now,

where, C = concentration at present time

            = initial amount

Here,

Therefore,

  years

Thus, the age of the rock is years.

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