Radioactive manganese-52 decays with a half-life of 5.6 days. A chemist obtains a fresh sample of manganese-52 and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below 25% of the initial measured value. How long does she have to perform the experiment?

11.2 days

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) for completion of 75% of reaction

The time for which she has to perform the experiment is 11.2 days

the answer is option a.