Geologists can estimate the age of rocks by their uranium-238 content. The urani

Question

Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then de4cays with first-order kinetics and a half-life of 4.5 billon years. A rock is found to contain 84.3% 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 form the presence of the decay products of U - 238.) How old is the rock? Express your answer using two significant fitgures.

Explanation / Answer

N(t)=Ne^(kt)

First calculate the value for k as follows:

for 1/2 life
1/2 life = 0.693/k

T1/2 = 4.5 billion years

k = 0.693 / 4.5 billon years

k = 0.154 billon years       

0.843N=Ne^(-0.154t)

Divide each side by N: 0.843=e^(-0.154t)

Rewrite as a logarithm: ln(0.843)= -0.154t

t= ln(0.843)/-0.154

= 1.1 billion years.

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