Question

A rock formed with 1,000 atoms of a radioactive parent element, but only contains 250 radioactive parent atoms today. If the half-life is 1,000,000 years, how old is the rock?

Answer 1

Answer:

age of rock is 2 million years

Explanation:

$M_{R}=\frac{M_{O} }{2^{n} }$

Where $M_{R}$ is mass remaining

            $M_{R}$ is original mass

         n= t/t(1/2) , which is the ratio of time to half life

$M_{O}$ = 1000atoms

$M_{R}$ =250 atoms

$250 =\frac{1000}{2^{n} }$

$2^{n} = \frac{1000}{250}\\ 2^{n} =4\\2^{n} = 2^{2}\\ n=2$

$n =\frac{t}{t\frac{1}{2} }$

t =t(1/2) *n

t(1/2) =1000000 years

t=1000000 *2

t=2,000,000 years