A radioactive sample consists of two isotopes one of then decays by `alpha-` emission with a half life of `tau_(1)=405s` and the other one decays by `beta` emission with half life of `tau_(1)`=1620s`. At time t=0, probabilities of getting `alpha` and `beta` particles from the sample are equal.
(a) If a particle coming out of the sample is detected at t=1620s, what is the probability that it is `alpha` particle?
(b) Find the time when total number of surviving nuclei is half the initial quantity.
Given If `x^(4)+4x-2.5=0` then `x=0.59`
`"log"_(10)2=0.301, "log"_(10)5.9=0.774`

Answer

(a) `(1)/(9)` (b) 1215s