Question

If K 40 has a half-life of 1.4 x 100 years and only 10% of the original K 40 remains, how old is the earth?

Answer 1

Answer:

t = 465.16 years

Explanation:

Given that:

Half life = 1.4 x 100 years = 140 years

$t_{1/2}=\frac {ln\ 2}{k}$

Where, k is rate constant

So,  

$k=\frac {ln\ 2}{t_{1/2}}$

$k=\frac {ln\ 2}{140}\ year^{-1}$

The rate constant, k = 0.00495 year⁻¹

Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

$[A_0]$ is the initial concentration

As 10% of the initial remains, so:

$\frac {[A_t]}{[A_0]}=0.1$

So,  

$0.1=e^{-0.00495\times t}$

t = 465.16 years