A sample of , as iodide ion, was administered to a patient in a carrier consisting of mg of iodide i — Nuclear Chemistry and Radioactivity Chemistry Question
Question
A sample of ${}^{131}_{53}\text{I}$, as iodide ion, was administered to a patient in a carrier consisting of $10\sqrt{2}$ mg of iodide ion. After 4.0 days, 10% of the initial radioactivity was detected in the thyroid gland of the patient. What mass (in mg) of the iodide ion had migrated to the thyroid gland? Half-life of ${}^{131}_{53}\text{I}$ is 8.0 days.
💡 Solution & Explanation
Let fraction $f$ of the total iodine migrate to the thyroid. The initial activity $A_0 \propto N_0$. The radioactive iodine that migrates is $f N_0$. After 4.0 days (0.5 half-lives), its activity decays to $(f N_0 / \sqrt{2}) \lambda$. This is given as 10% of the initial total radioactivity ($0.10 \lambda N_0$). Equating them: $f / \sqrt{2} = 0.10 \implies f = 0.10\sqrt{2}$. Since the carrier and radioactive isotope migrate together, the total mass migrated is $f \times \text{Total Mass} = 0.10\sqrt{2} \times 10\sqrt{2} = 2 \text{ mg}$. Therefore, correct answer is 0002.