Question

Radiocontrast dyes are considered safe because the isotopes have short half-lives and the isotopes coat the gastrointestinal tract and are not absorbed by normal tissue. If a patient ingests 10.0 mg of iodine, how long until the iodine-134 is 99% out of the patient's system if the half-life of iodine-134 is 52.6 minutes?

Answer 1

the answer is D.6.14hr.

Answer 2

Time till the 99% of the iodine is out of the system is 5.82 hours.

Step-by-step explanation:

Initial amount of Iodine-134 =
`N_o=10.0 mg`

Final amount of iodine-134 left = N =
`(100\%-99\%) of 10.0 mg = 1\% of 10 mg=0.1 mg`

Half life of iodine-134 =
`t_{(1)/(2)}=52.6 min`

Time till the 99% of the iodine is out of the system = t

Decay constant =
`\lambda`

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(52.6 min)=0.0131749 min^(-1)`

`\log N=\log N_o-(\lambda t)/(2.303)`

`\log(N)/(N_o)=(-\lambda t)/(2.303)`

`\log(0.1 mg)/(10 mg)=-(0.0131749 min ^(-1)t)/(2.303)`

t = 349.60417 min =5.8267 hours

(1 hour = 60 min)

Time till the 99% of the iodine is out of the system is 5.82 hours.