`.^(90)Sr` decays to `.^(90)Y` by `beta` decay with a half-life of `28` years. `.^(90)Y` decays by `beta`-to `.^(90)Zr` with a half-life of `64h`. A pure sample of `.^(90)Sr` is allowed to decay. What is the valued of `(N_(Sr))/(N_(y))` after (a) `1h` (b) `10` years ?

Explanation

`N_(sr)=N_(Sr)^(0)r^((-lambda_(sr)t))` ....(1)
`N_(y)=(lambda_(sr)N_(sr)^(0))/(lambda_(y)-lambda_(sr))[e^((lambda_(sr)t))-e^((-lambda_yt))]` .......(2)
Dividing the two equations
`(N_(y))/(N_(sr))(lambda_(sr))/(lambda_(y)-lambda_(sr))[1-e^((-lambdat))(lambda_(sr)-lambda_(y))t]`
`lambda_(sr)=0.693//(28xx365xx24)=2.825xx10^(-6)h^(-1)`
`lambda_(y)=0.693//64=0.0108 h^(-1)`
(a) For `t=1h` and using the values for the decay constant `N_(sr)//N_(y)=3.56xx10^(5)`
(b) For `t=10 "year", N_(sr)//N_(y)=3823`