When a particular rock formed it contained 12mg of radioactive isotope of potassium-40. The rock now contains 3mg of potassium-40. The half life of potassium-40 is 1.3 billion years. The approximate age of the rock is billion years

Answer : The age of the rock is, 2.60 billion years

Explanation :

Half-life = 1.3 billion years

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = time passed by the sample  = ?

a = initial amount of the reactant  = 12 mg

a - x = amount left after decay process = 3 mg

Now put all the given values in above equation, we get

Therefore, the age of the rock is, 2.60 billion years