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

`K = (2.303)/(t) "log" (N_(0))/(N_(i))` `(K = (0.693)/(t_(1//2)))`
`(0.693)/(8) = (2.303)/(4) "log" (N_(0))/(N_(t))`
`(N_(0))/(N_(t)) = 1.141` or `(N_(t))/(N_(0)) = 0.707 = 70.7%`
Practical % left in thyroid gland `= 67.7%`
Theoretical % left of the initial conc `= 70.7%`
Diagnostic value `= (67.7)/(70.7) xx 100 = 95.8%`
Amont left `= ((1)/(2))^(1//2) xx a_(0)`
`= 0.707 xx 0.1 mg`
`= 0.0707 mg "of" I^(ɵ)`
Amount decomposed of `I^(ɵ) = 0.1 - 0.0707`
`= 0.029 mg`
Diagnostic value `= (0.029 xx 95.8)/(100) = 0.02778 mg`