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

t = 465.16 years

Step-by-step 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* t)`

t = 465.16 years