Posted by Anonymous on .
Suppose 32000 radioactive nuclei are in a sample. About how many remain after two days if the half-life is 22 hrs? What is the initial activity of the sample in decays per minute?
Two days is 48 hours or 2.18 half-lives. The original number of radioactive nuclei, 2 days earlier, is higher by a factor 2^2.18 = 4.53, so there were N0 = 145,000 radioactive nuclei then.
There is a formula that relates activity per molecule (k) to half life (T). It is k = ln2/T = 0.693/T
T = 22 hours = 1320 min
The initial activity is
A = N0*k = (145,000)(0.693)/1320
= 76 decays/min