One of the hazards of nuclear explosion is the generation of `.^(90)Sr` and its subsequent incorporation in bones. This nuclide has a half-life of `28.1` year. Suppose one micro-gram was absorbed by a new-born child, how much `Sr^(90)` will remain in his bones after 20 year?

Explanation

Initial amount of `Sr^(90)(N_(0))=1 mug`
Amount of `Sr^(90)` after `20 "year" (N_(t))=[?]`
Used time `(t)=20` years
Half`-` life period of `Sr^(90)(t_(t//2))=28.1 year^(-1)`
Decay constant `(lambda)=(0.693)/(t_(1//2))=(0.693)/(28.1)year^(-1)`
For `Sr^(90)`.
`(` Because all radioactive decays are the examples of first `-` order reaction `)`
`=(0.693)/(28.1)=(2.303)/(20)"log"(N_(0))/(N_(t))`
On solving,
`"log"_(10) (N_(0))/(N_(t))=0.2141`
or `"log"_(10) (N_(t))/(N_(0))=-0.2141`
or `(N_(t))/(N_(0))=0.6102`
or `N_(t)=0.6102xxN_(0)`
`:. N_(t)=0.61.02xx1 mug`
`=0.6102mug`