Potassium-40 is radioactive and decays into Argon-40. The half-life of Potassium-40 is 1.3 billion years. You measure the # of atom of each isotope and find 75 atoms of Potassium-40 and 525 atoms of Argon-40. How many half-lives have passed since the rock formed?

3 half-lives have passed since the rock formed.

Explanation:

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

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

b)

number of half lives =

Thus 3 half-lives have passed since the rock formed.