After 200 million years, only 1/16 of the original amount of a particular radioactive waste will remain. the half-life of this radioactive waste is how many million years?

Answer : The half-life of this radioactive waste is,

Explanation :

First we have to calculate the rate constant.

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

where,

k = rate constant  = ?

t = time passed by the sample  = 200 million years

a = let initial amount of the reactant  = X

a - x = amount left after decay process =

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

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

Therefore, the half-life of this radioactive waste is,