Question

A sample of $I_{51}^{131}$ as iodine ion was administered to a patient in a carrier consisting of $\text{0.10} \, mg$ of stable iodine ion. After $4$ days $67.7\%$ of initial radioactivity was detected in the thyroid gland of the patient. The percentage of stable iodine ion that had migrated to the thyroid gland, if $t_{1/2}$ for iodide ion is $8$ days is

• A. $65.8\%$
• B. $95.7\%$
• C. $85.8\%$
• D. $75.8\%$

Answer 1

Answer: (B)

Let us take $xmg$ iodine migrated to thyroid gland.
if $A$ is activity of complete sample of mass $m$ . Then activity of $x$ is given by
$A_{x}=\frac{A}{m}x$
$A_{x}$ is $\text{67.7}\%$ of initial total sample at $t=4$ days.
$A_{x}=\left(\frac{\text{67.7}}{100}\right)A_{0} \, \&A=\frac{A_{0}}{2^{t / T}}$
$T=$ half life time
So using above equation,
$\frac{\text{67.7}}{100}A_{0}=\frac{A_{0}}{2^{4 / 8}} \, \left(\frac{x}{m}\right)$
$\frac{x}{m}\times 100=\text{67.7}\times \sqrt{2}=\text{95.7}\%$