Question

During the nuclear explosion, one of the products is ${}^{90}Sr$ with half of $6.93years$. If $1\mu g$ of ${}^{90}Sr$ was absorbed in the bones of a newly born baby in place of $Ca$, how much time, in years, is required to reduce it by $90\%$ if it is not lost metabolically

Answer 1

Step 1. Given data

The half-life of ${}^{90}Sr$, $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$=6.93years$

Step 2. Finding the decay constant, $\lambda$

By using the formula of the Half-life,

$t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{0.693}{\lambda }$

$\lambda =\frac{0.693}{6.93}$

$\lambda =0.1y^{-1}$

Step 3. Finding the time, $t$

By using the formula of time,

$t_{x\%}=\frac{2.303}{\lambda }\log \frac{100}{100-x}$ [Where, $x=90$]

$t_{90\%}=\frac{2.303}{0.1}\log \frac{100}{100-90}$

$t_{90\%}=23.03years$

Therefore, $23.03years$ required to reduce by $90\%$.