We’re being asked to determine the percentage of the initial activity of cesium-130 will be present after 75 minutes, assuming radioactive decay occurs by a first-order rate mechanism.
Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:
[N]t = concentration at time t
k = decay constant
t = time
[N]0 = initial concentration.
Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half.
The half-life of a first-order reaction is given by:
The half-life of cesium-130 is 15 minutes. What percentage of the initial activity will be present after 75 minutes, assuming radioactive decay occurs by a first order rate mechanism?