Question

A sample of ${}_{53}^{131}\text{I}$, as iodine ion, was administered to a patient in a carrier consisting of 0.10 mg of stable iodide ion. After 4.00 days, 67.7% of the initial radioactivity was detected in the thyroid gland of the patient. What mass of the stable iodide ion had migrated to the thyroid gland? ($t_{1/2}=8days.$)

• A. 0.0958 mg
• B. 0.0158 mg
• C. 0.192 mg
• D. None of these

Answer 1

The correct option is A 0.0958 mg

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

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

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

Hence, $70.7$ % of initial activity is present. $67.7$ % activity is migrated to thyroid gland.

Weight of iodine migrated to the thyroid gland is $\frac{67.7}{70.7}\times 100=95.75$
which is $0.1\times \frac{95.75}{100}=0.0958mg$