Question

During the nuclear explosion, one of the products is ${}^{90}Sr$ with half life of 6.93 years. 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 (nearest integer), is required to reduced it by 90% if it is not lost metabolically

• A. 23.00
• B. 23
• C. 23.0

Answer 1

Answer: (A), (B), (C)

Since half life is in the unit of time, so it is a first order reaction.
Decay constant or rate constant is denoted by $\lambda$
For a first order reaction:

$\text{Decay constant}\left(\lambda \right)=\frac{ln2}{\left(t_{1/2}\right)}=\frac{0.693}{6.93}$

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


$\lambda t=\ln \left(\frac{C_0}{C}\right)$
$C_0$ and $C$ being the intial concentration and final concentration at time t respectively
$\text{Now}\lambda$ $\left(t_{90\%}\right)=\text{ln}\left(\frac{100}{10}\right)$
$t_{90\%}=10\ln 10$

$t_{90\%}=10\times 2.303$

$t_{90\%}=23.03yr\approx 23\left(\text{Nearest integer}\right)$