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 its will remain after 10 years and 60 years if it is not lost metabolically.

Explanation

As radioactive disintegrations follow first order kinetics,
Decay constant of `""^(90)"Sr "(k)=(0.693)/(t_(1//2))=(0.693)/(28.1" y")=2.466xx10^(-2)y^(-1)`
To calculate the amount left after 10 years.
`a=1 mug,t=10" years,"k=2.466xx10^(-2)y^(-1),(a-x)=?`
`k=(2.303)/(t)log""(a)/(a-x)`
`2.466xx10^(-2)=(2.303)/(10)log""(1)/((a-x))" or "log(a-x)=-0.1071`
or `(a-x)=" Antilog "=1.8929=0.7814 mug`
To Calculate the amount left after 60 years.
`2.466xx10^(-2)=(2.303)/(60)log""(1)/(a-x)" or "log(a-x)=-0.6425`
or `(a-x)=" Antilog T"*3575=0.2278" "mug.`