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

there is none because earth is stationary and flat.