A sample of `._(53)I^(131)`, as iodide 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 radiactivity was detected in the thyroid gland of the patient. What mass of the stable iodide ion had migrated to the thyroid gland? Of what diagnostic value of is such an experiment?
`(t_(1//2) = 8` days)

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understanding the Given Data
- We have a sample of iodine-131 (\( _{53}^{131}I \)) administered to a patient.
- The carrier consists of \( 0.10 \, \text{mg} \) of stable iodide ion.
- After \( 4.00 \) days, \( 67.7\% \) of the initial radioactivity was detected in the thyroid gland.
- The half-life (\( t_{1/2} \)) of iodine-131 is \( 8 \, \text{days} \).

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