Question

A radioactive isotope has a life of T years. How long will it take the activity to reduce to (a) `3.125% (b) 1%` of its original activity?

Answer 1

(a) Here, `N/(N_0)=3.125/100=1/32` form `N/(N_0)=(1/2)^n=1/32=(1/2)^(5) :. n=5`
form `t=nT=5T`
(b) Here, `N/(N_0)=1/100 form N/(N_0)=e^(-lambdat)=1/100`
`-lambdat=log1-log_e 100=0-2.303 log_(10)100=-2.303xx2=-4.606`
`t=4.606/lambda=4.606/(0.693//T)=6.65T`