Question

A nuclear explosion leads to formation of radio nuclei of ${}^{131}\text{I}$ and ${}^{90}\text{Sr}$. Calculate the time required for the activity of these radio nuclide to fall to 1.0% of its initial value. Which isotope will produce more serious long term effect? Radio iodine and radio strontium affect the thyroid and bones respectively if they are accumulated in respective glands during ingestion in mammals. Given $t_{1/2}$ for ${}^{131}\text{I}$ and ${}^{90}\text{Sr}$ are 8 and 20 days respectively.

• A. ${}^{131}\text{I}$
• B. ${}^{90}\text{Sr}$
• C. Both ${}^{131}\text{I}and{}^{90}\text{Sr}$ take same time
• D. Cannot be determined

Answer 1

The correct option is B ${}^{90}\text{Sr}$

$t=\frac{1}{k}ln\left(\frac{a_0}{a}\right)t_{\frac{1}{2}}=\frac{ln2}{k}ForIodine,t=\frac{t_{\frac{1}{2}}}{ln2}ln\left(\frac{100}{1}\right)t=\frac{8}{ln2}ln\left(\frac{100}{1}\right)=53.17daysForSr,t=\frac{20}{ln2}ln\left(\frac{100}{1}\right)=133days$

${}^{131}\text{I}:53.17;{}^{90}\text{Sr}:132.9day;{}^{90}\text{Sr}$ will take longer time to reduce its activity to 1% and will provide more long term effect.