Question

A rock has 25 percent of its original amount of potassium-40 remaining in it; potassium-40 has a half-life of 1.25 billion years. How long ago was the rock formed? 1.25 billion years ago 2.50 billion years ago 5.00 billion years ago 6.25 billion years ago

Answer 1

For rock dating, the kinetics used is first-order with the equation

ln(initial conc./final conc.) = kt

First, we determine k, which is the reaction constant. With the given half-life, this means that the final conc. is half of the initial conc. Hence,

ln 2 = k (1.25 x10^7)
k =5.55 x 10^-8

Then we use this to predict the time elapsed.

ln (1/0.25) = (5.55x10^-8)(t)
t = 2.5 x 10^7 or 2.5 billion years

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