Half-Life Practice Problem ANSWERS
1. Barium-122 has a half-life of 2 minutes. A fresh sample weighing 80 g was obtained. If it takes 10 minutes to set up an experiment using barium-122, how much barium-122 will be left when the experiment begins? a. At the end of 10 minutes (5 half-lives) only 2.5 g are left, the rest has decayed.
2. If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days. a. Since the half-life is 8 days, 24 days corresponds to 3 half-lives. After one half-life 5 mg are left; after two half-lives, 2.5 mg; and after 3 half-lives 1.25 mg remains.
3. Iodine-131 is used to destroy thyroid tissue in the treatment of an overactive thyroid. The half-life of iodine-
131 is 8 days. If a hospital receives a shipment of 200 g of iodine-131, how much I-131 would remain after
32 days? a. 12.5 g
4. Mercury -197 is used for kidney scans and has a half-life of 3 days. If the amount of mercury-197 needed for a study is 1.0 gram and the time allowed for shipment is 15 days, how much mercury-197 will need to be ordered? a. 32 g
5. The half-life of Zn-71 is 2.4 minutes. If you had 100.0 g at the beginning, how many grams would be left after
7.2 minutes has elapsed? a. 12.5 g remaining
6. Os-182 has a half-life of 21.5 hours. How many grams of a 10.0 gram sample would have decayed after exactly three half-lives? a. 8.75 g have decayed
7. How much time will be required for a sample of H-3 to lose 75% of its radioactivity? The half-life of tritium is
12.26 years. a. 24.52 years
8. What is the half-life of a 100.0 g sample of nitrogen-16 that decays to 12.5 g of nitrogen-16 in 21.6 seconds? a. 7.2 seconds
9. All isotopes of technetium are radioactive, but they have widely varying half-lives. If an 800.0 g sample of technetium-99 decays to 50.0 g of technetium-99 in 639,000 years, what is its half-life? a. 2,556,000 years
10. A 208 g sample of sodium-24 decays to 13.0 g of sodium-24 within 60.0 hours. What is the half-life of this radioactive isotope? a. 15 hours
11. After 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remain. What is the half-life of the sample? a. 4.00 days
12. How long will it take for a 40.0 gram sample of I-131 (half-life = 8.040 days) to decay to more than 1/100 its original mass? a. 56.28 days
13. Fermium-253 has a half-life of 0.334 seconds. A radioactive sample is considered to be completely decayed after 10 half-lives. How much time will elapse for this sample to be considered gone? a. 3.34 seconds
14. 100.0 grams of an isotope with a half-life of 36.0 hours is present at time zero. How much time will have elapsed when less than 5.00 grams remains? a. 180 hours