During nuclear explosion, one of the products is `""^(90)Sr` with half`-` life of `28.1` years. If `1 mug` of `""^(90)Sr` was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.

Explanation

`t_(1//2) = 28.1 Y: k = (0.693)/(t_(1//2))= 0.693/28.1 Y^(-1)`
All radioactive explosions follow first order kinetics.
`t= (2.303)/k log a/(a-x)`
Ist case, a=1 mug, t= 10 Y, `k=0.693/28.1 Y^(-1)`
`10Y = 2.303/(0.693//28.1 Y^(-1)) log a/(a-x)`
`loga/(a-x) = (10Y)xx(0.693//28.1Y^(-1))/(2.303) = 0.107`
`a/(a-x)` = Antilog 0.107 = 1.279
`(a-x) = a/1.279=(1"mug")/(1.279)=0.7819` mug
IInd case, a=1mug, t=60Y, `k=0.693//28.1 Y^(-1)`
60 Y `= (2.303)/(0.693//28.1Y^(-1))= log a/(a-x)`
`loga/(a-x) = (60Y) xx (0.693//28.1Y^(-1))/(2.303) = 0.642`
`a/(a-x)`= Antilog 0.642 = 4.385
`(a-x) = a/4.385 = (1"mug")/(4.385) = 0.2280` mug