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

Answer:

$t = 2.52 billion \:years$

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

$\lambda = \frac{ln2}{1.26 \times 10^6 yrs}$

$t = 1.26\times 10^6\times \frac{ln4}{ln2}$

$t = 2.52 billion \:years$