Question

One of the hazards of a nuclear explosion is the generation of $S{r}^{90}$ and its subsequent incorporation in bones. This nuclide has a half-life of 28.1 years. Suppose one microgram was absorbed by a newborn child, how much $S{r}^{90}$ will remain in his bones after 20 years?

• A. $6.13\times {10}^{-7}$ g
• B. $6.13\times {10}^6$ g
• C. $61.3\times {10}^{-6}$ g
• D. None of these

Answer 1

The correct option is A $6.13\times {10}^{-7}$ g

All radioactive decays are first-order reactions.

It is given that the nuclide of ${}^{90}Sr$ has a half-life of $28.1$ years.

One microgram of it was absorbed by a newborn child.

$\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{28.1}/yr$

$t=\frac{2.303}{\lambda }log\frac{a}{a-x}$

$20=\frac{2.303}{0.693}\times 28.1\times log\frac{{10}^{-6}}{a-x}$

$0.214=log\frac{{10}^{-6}}{a-x}$

$1.64=\frac{{10}^{-6}}{a-x}$

$a-x=6.1\times {10}^{-7}$ g