Question

One of the hazards of the nuclear explosion is the generation of ${}^{90}\text{Sr}$ and its subsequent incorporation in bones. This nuclide has a half-life of 28.1 years. Suppose one microgram was absorbed by a new-born child, the amount ${}^{90}\text{Sr}$ will remain in his bones after 20 year is :

• A. $6.1\times {10}^{-7}g$
• B. $4.5\times {10}^{-7}g$
• C. $3.2\times {10}^{-7}g$
• D. none of these

Answer 1

Answer: (A)

$6.1\times {10}^{-7}g$

Given, $t_{1/2}=28.1year;N_0={10}^{-6}g$
$t=20year;N=?$
$\because t=\frac{2.303}{\lambda }\log \frac{N_0}{N}$
$\therefore 20=\frac{2.303\times 28.1}{0.693}\log \frac{{10}^{-6}}{N}$
$\therefore N=6.1\times {10}^{-7}g$