Question

A sample of ${}_{53}{I}^{131}$ as iodide ion was adminstered to a patient in a carrier consisting of $0.10mg$ of stable iodide ion. After $4$ days $67.7\%$ of initial radioactivity was detected in the thyroid gland of the patient. What mass of stable iodide ion had migrated to thyroid gland. $t_{1/2}$ for iodide ion $=8day$.

Answer 1

Then half lif period is 8 days. $k=\frac{0.693}{t_{1/2}}$

$Ift=4day,K=\frac{0.693}{8}$, then

$t=\frac{2.303}{K}\log \frac{r_0}{r}$

$4=\frac{2.303\times 8}{0.693}\log \frac{r_0}{r}$

$r=0.707r_0$

Thus, iodide ion left is $0.707$ part of initially injected sample, however the rate decreases only 67.7 or 0.677 in 4 day. Thus, if 0.707 is left then iodide ion migrated to thyroid $=1$

Thus, 0.677 is left then iodide ion migrated to thyroid
$=\frac{1\times 0.677}{0.707}=0.958$
or $95.8$% of the iodide ion is migrated to gland.

Therefore the answer is 1.