A sample of ._(131)^(53) I is iodide ion was admistered to a patient in a carrier consisting of 0.10 mg of stable iiodide ion. After 4 day 67.7% of initial radioactivity was detected in the throidgland of the patient. What mass of stable iodide ion hadmigrated to thyroid glad? (t_(1//2) for iodide ion = 8 day)

A sample of ._(131)^(53) I is iodide ion was admistered to a patient i

1.	A sample of ._(131)^(53) I is iodide ion was admistered to a patient in a carrier consisting of 0.10 mg of stable iiodide ion. After 4 day 67.7% of initial radioactivity was detected in the throidgland of the patient. What mass of stable iodide ion hadmigrated to thyroid glad? (t_(1//2) for iodide ion = 8 day)
Answer» Solution :If `t = 4`day, `lambda = (0.693)/(8)`, then since `r_(0) prop N_(0)` and `r prop N` `:. (r_(0))/(r) = (N_(0))/(N)` `:. t = (2.303)/(lambda) log (r_(0))/(r)` `4 = (2.303xx8)/(0.693) log (1)/(0.693) log(r_(0))/(r)` `r = 0.707 r_(0)` Thus iodide ION left is `0.707` part of intially injected sample, HOWEVER the RATE decreases only `67.7%` or `0.688` in 4 days, thus If `0.707` is left then iodidie ion migrated to thryorid `=1` Thus `0.677`is left than iodide ion migrated to thyroid `= (1xx0677)/(0.707) = 0.958` or `95.8%` of the iodide ion is migrated to gland.