Question

During nuclear explosion, one of the products is ${}^{90}Sr$ with half life of $28.1yr$. 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 $10$ year and $60$ year if it is not lost metabolically.

Answer 1

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{28.1}=0.0247/year$

(i) After 10 years, let $x\mu$ be the concentration of ${}^{90}Sr$.
$k=\frac{2.303}{t}log\frac{[A{]}_0}{\left[A\right]}$

$0.0247=\frac{2.303}{10years}log\left(\frac{1}{x}\right)$

$x=0.782\mu g$

(ii) After 60 years, let $y\mu$ be the concentration of ${}^{90}Sr$.
$k=\frac{2.303}{t}log\frac{[A{]}_0}{\left[A\right]}$

$0.0247=\frac{2.303}{60years}log\left(\frac{1}{y}\right)$

$y=0.228\mu g$