Question

A paleontologist estimates that when a particular rock formed, it contained 12 mg of the radioactive isotope potassium-40, which has a half-life of 1.26 billion years. The rock now contains 3 mg of the isotope. About how old is the rock? Enter in billions of years.

Answer 1

`t = 2.52 billion \:years`

Step-by-step explanation:

As we know by radioactivity law

`N = N_o e^(-\lambda t)`

so here we will have

`N = 3 mg`

`N_o = 12 mg`

now we will have

`3 = 12 e^(-\lambda t)`

`\lambda t = ln 4`

now we also know that

`\lambda = (ln2)/(1.26 * 10^6 yrs)`

`t = 1.26* 10^6* (ln4)/(ln2)`

`t = 2.52 billion \:years`