4.17   During nuclear explosion, one of the products is ^{90} Sr with half-life of 28.1 years. If 1 \mu g 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.

Answers (1)
M manish

half life = 21.8 years
\therefore\ k=0.693/t_{1/2}
           = 0.693/21.8

and, t = \frac{2.303}{k}\log\frac{[R]_{0}}{[R]}

by putting the value we get,

              10= \frac{2.303}{0.693/21.8}\log\frac{1}{[R]}
            \log[R] = -\frac{10\times 0.693}{2.303\times 21.8}
taking antilog on both sides,
[R] = antilog(-0.1071)
      = 0.781 \mu g

Thus 0.781 \mu g of {Sr}^{90} will remain after given 10 years of time.


Thus 0.2278 \mu g of {Sr}^{90} will remain after 60 years.