Fluorine-18, which has a half-life of 110 min, is used in PET scans.

a. If 100. mg of fluorine-18 is shipped at 8:00 a. m., how many milligrams of the radioisotope are still active after 110 min?

b. If 100. mg of fluorine-18 is shipped at 8:00 a. m., how many milligrams of the radioisotope are still active when the sample arrives at the radiology laboratory at 1:30 p. m.?

Part a. 50.0 mg

Part b. 12.5 mg

Explanation:

For every hal-life time the amount of the radioisotope (fluorine-18) will be cut to half.

Part a.

Since the half-life of fluorine-18 is 110 min, ater this very time, half of the fluorine-18 is still alive, i. e 100. mg / 2 = 50.0 mg. ← answer

Part b.

Compute the time elapsed from 8:00 am, when the fluorine-18 is shipped, to 1:30 pm, when the sample arrives at teh radiology laboratory.

1:30 pm - 8:00 am = 5 hours and 30 minutes

Convert to minutes + 5*60 + 30 = 330 min

Compute the number of half-lives in 330 min:

330 min / 110 min per half-life = 3 half-lives.

Conclusion:

the radiosotope has been reduced to half 3 times

100.0 mg * (1/2) * (1/2) * (1/2) = 100.0 mg * (1/2) ³ = 100.0 mg / 8 = 12.5 mg

Hence, 12.5 mg of the radioisotope are still alive ← answer