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  • During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1μg of 90Sr 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.

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

best_answer

Given,
half life = 21.8 years
\begin{aligned} \therefore k & =0.693 / t_{1 / 2} \\ & =0.693 / 21.8\end{aligned}
           

and, t=\frac{2.303}{k} \log \frac{[R]_0}{[R]}

by putting the value we get,

\begin{gathered}10=\frac{2.303}{0.693 / 21.8} \log \frac{1}{[R]} \\ \log [R]=-\frac{10 \times 0.693}{2.303 \times 21.8}\end{gathered}


taking antilog on both sides,
[R] = antilog(-0.1071)
      = 0.781 \mu g

Thus 0.781 \mu g$ of $S r^{90} will remain after 10 years.

Again, 

t=\frac{2.303}{k} \log \frac{[\mathrm{R}]_0}{[\mathrm{R}]}

\begin{aligned} & \Rightarrow 60=\frac{2.303}{\frac{0.693}{28.1}} \log \frac{1}{[R]} \\ & \Rightarrow \log [R]=-\frac{60 \times 0.693}{2.303 \times 28.1}\end{aligned}

\begin{aligned} \Rightarrow[R] & =\operatorname{antilog}(-0.6425) \\ & =\operatorname{antilog}(\overline{1} .3575) \\ & =0.2278 \mu \mathrm{~g}\end{aligned}


Thus 0.2278 \mu g_{\text {of }} S r^{90} will remain after 60 years.
              

Posted by

manish

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