The half-life for the radioactive decay of ce−141 is 32.5 days. if a sample has an activity of 3.8 μci after 162.5 d have elapsed, what was the initial activity, in microcuries, of the sample?

Answer : The initial activity, in microcuries, of the sample was, 120.9 μci

Explanation :

Half-life = 32.5 days

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

Now we have to calculate the time passed.

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

where,

k = rate constant  =

t = time passed by the sample  = 162.5 days

a = initial amount of the reactant  = ?

a - x = amount left after decay process = 3.8 μci

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

Therefore, the initial activity, in microcuries, of the sample was, 120.9 μci

the correct answer is c