A sample of `._(53)I^(131)`, as `I^(ɵ)` ion, was administered to a patient in a carrier conissting `1.0 mg` of stable `I^(ɵ)` ion. After `4.0` days, `60%` of the initial radioactivity was detected in the thyroid gland of the patient. What mass of the stable `I^(ɵ)` ion had migrated to the thyroid gland? (Given: `t_(1//2)` of `I^(131) = 8` days)

Options

A. `0.65 mg`
B. `0.75 mg`
C. `0.85 mg`
D. `0.95 mg`

Answer

C

Explanation

`k = (2.303)/(t)log[(N_(0))/(N)]`
`(0.693)/(t_(1//2)) = (2.303)/(4 days)log((N_(0))/(N))`
`(0.693)/(8 days) = (2.303)/(4 days) log((N_(0))/(N))`
`:. (N)/(N_(0)) ~~ 0.7 rArr 70%` of the initial activity is present.
Given that `60%` activity is migrated to thyroid gland. Weight of `I^(ɵ)` ion migrated to thyroid gland is:
`(60)/(70) xx 100 = 85.7%`
i.e., `1.0 mg xx (85.7)/(100) = 0.857 mg`