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.

Answer

After 10 years `=>0.7814 mug` 0.2278 mug`

Explanation

Radioactive disintegrations are of first order. Thus,
Decay constant `.^(90)Sr(k)=(0.693)/(t_(1//2))=(0.693)/(28.1years).`
`=2.466xx10^(-2)year^(-1)`
`a.` Amount left after 10 years `:`
`a=mug,t=10 years , (a-x)=?`
`k=2.466xx10^(-2)year^(-1)`
`:.k=(2.303)/(t)log``(a)/(a-x)`
`2.466xx10^(-2)=(2.303)/(10)log``(1mug)/((a-x))`
`or log(a-x)=-0.1071+1-1=bar(1).8929`
or(a-x)=Antilog `bar(1).8929`
`=0.7814 mug`
b. Amount left after 60 years :
`2.466xx10^(-2)=(2.303)/(60)log (1mug)/((a-x))`
`log(a-x)=-0.6425`
`=0.2278mu g `