Asample contains 25% parent isotope and 75% daughter isotopes. if the half-life of the parent isotope is 72 years, how old is the sample?

The sample is 144 years old.

Explanation: This is a type of radioactive decay and all radioactive decays follow first order kinetics.

We are given half life which is 72 years.  

To calculate the rate constant, we use the formula:

Also 25 % of parent isotope is left, that means 75 % has been decomposed

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

where,

k = rate constant

t = time taken for decay process

a = initial amount of the reactant  = parent isotope= 100

a - x = amount left after decay process  = 25

Putting values in above equation, we get: