Assuming that the radioactive decay of Ce is a 1st
order reaction, we can use the following formula to look for the rate constant
k.
t1/2 = ln 2 / k
32.5 = ln 2 / k
k = 0.021 day^-1
The integrated rate law for a 1st order reaction
is:
ln A = -k t + ln Ai
Where,
A = final activity = 3.1 ci
Ai = initial activity
t = time that elapsed = 97.5 d
Substituting the given values to the equation:
ln 3.1 = -0.021 * 97.5 + ln Ai
ln Ai = 3.18
Ai = 24.02 ci (ANSWER)
