A radioactive isotope `Cs^(137)` has a half life period of 30 years. Starting with `1 mg` of `Cs^(137)` how much would remain after 120 years?

Explanation

Half-life period of radioactive isotope `Cs^(137) (t_(1//2)) = 30` years
Total time `= 120` years
We know `T = n xx t_(1//2)` `[{:(T = "Total time"),(n = "Number of half lives"):}]`
or `120 = n xx 30`
`n = 4`
`:'` Amount left after `n` half period `(N) = ((1)/(2))^(n) N_(0)`
`[N_(0) =` initial amount of radioactive element]
`:. N = ((1)/(2))^(4) N_(0) = ((1)/(2))^(4) xx 1`
`:. N = (1)/(16) = 0.0625 mg`