Question

A sample of ${}_{53}^{131}I$, 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 ${}_{53}^{131}I$ is $8.0$ days.

Answer 1

$\lambda =\frac{0.693}{t_{1/2}}=\frac{2.303}{t}log\frac{N_0}{N}$

Given $t_{1/2}=8hr$ to find at after 4 days Hence , t = 4

putting the values in above equation , we get:

$\lambda =\frac{0.693}{8}=\frac{2.303}{4}log\frac{N_0}{N}$

$\therefore \frac{N_0}{N}=$ 0.707

Hence, 70.7 % of the initial activity is present. 10.0 % activity is migrated to the thyroid gland.

Weight of iodine migrated to the thyroid gland is $\frac{10.0}{70.7}\times 100$ = 14.14

which is 10$\sqrt{2}\times \frac{14.14}{100}$ = 2 mg