Answer :
Answer: Thus 3 half lives have taken place.
Explanation:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
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.
[tex]t_{\frac{1}{2}}=\frac{2.303}{k}\log\frac{100}{50}[/tex]
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
Number of half lives =[tex]\frac{\text {total time}}{\text {half life}}=\frac{36million}{12million}=3[/tex]
Thus 3 half lives have taken place.