A radionuclide consists of two isotopes. One isotope decays by α emission and the other by β emission, with half-lives t1=405s and t2=1620s, respectively. At t=0, the probabilities of obtaining α and β particles from the radionuclide are equal. Calculate their respective probabilities at t=1620s. If the total number of nuclei at t=0 is N0, calculate the time t when the total number of undecayed nuclei equals N0/2. Given log102=0.3010, log105.94=0.7742, and x4+4x−2.5=0 has root x=0.594.
(a) Calculate the respective probabilities of obtaining α and β particles at t=1620s.
(b) Calculate the time at which the total number of undecayed nuclei is N0/2.