A Rock Dating Calculation: How Old is the Rock?

Understanding Potassium-40 Half-Life

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?

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 x10^9)
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 10^9 or 2.5 billion years

I hope I was able to help you with your question. Have a good day.

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?

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 x10^9) 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 10^9 or 2.5 billion years I hope I was able to help you with your question. Have a good day.