Half-life problems
1) What happens to the half-life of a radioactive substance as it decays? 1) ______
A) It increases. B) It remains constant.
C) It decreases. D) It could do any of these.
2) If the half-life of a material is 45 years, how much will be left after 100 years? 2) ______
A) less than 1/4 B) less than 1/2
C) more than 1/2 D) more than 1/4
3) If 4.0 × 1018 atoms decay with a half-life of 2.3 years, how many are remaining after 3.7 years? 3) ______
A) 1.3 × 1018 B) 1.7 × 1018 C) 2.5 × 1018 D) 1.1 ×1018
4) A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min? 4) ______
A) 1/4 B) 1/16 C) 1/8 D) 1/2
5) How long would it take 4.0 × 1020 atoms to decay to 1.0 × 1019 atoms if their half-life was 14.7 years? 5) ______
A) 29.4 years B) 58.8 years C) 147 years D) 78.2 years
Rates of nuclear decay
6. The half-life of Pa-234 is 6.75 hr. How much (what fraction) of a sample of this
isotope remains after 20.25 hr?
7. The half-life of Rn-222 is 3.823 day. What was the original mass of a sample of this
isotope if 0.0500 g remains after 7.646 day?
8. The half-life of Th-227 is 18.2 day. How many days are required for 0.75 of a given
sample to decay?
9. An object taken from a cave has a carbon-14 fraction which is 0.03125 of the amount in a living organism. How old is the object? (half-life for C-14 is 5730 yr)
Radioactive Decay and Half-Life Practice Problems
1. Determine the fraction of the isotope that is remaining.
2. Use the remaining fraction of the isotope, to determine how many half-lives have passed? Ie. If there is 1/8 of a sample left then: ½ X ½ X ½ = 1/8 - 3 half-lives have passed.
3. Multiply the number of half-lives that have passed by the half-life. Ie. 3 X 200 years.
1. The half-life of iodine-131 is 8.1 days. How long will it take for three-fourths of a sample of iodine-131 to decay?
2. Radon-222 is a radioactive gas with a half-life of 3.82 days. How long would it take for fifteen-sixteenths of a sample of radon-222 to decay?
3. Uranium-238 decays very slowly, with a half-life of 4.47 billion years. What percentage of a sample of uranium-238 would remain after 13.4 billion years?
4. A sample of Strontium-90 is found to have decayed to one-eighth of its original amount after 87.3 years. What is the half-life of strontium-90?
5. A sample of Francium-212 will decay to one-sixteenth its original amount after 80 minutes. What is the half-life of francium-212?
6. The ratio of carbon-14 to carbon-12 is a prehistoric wooden artifact is measured to be one-eighth of the ratio measured in a fresh sample of wood from the same region. The half-life of carbon-14 is 5,715 years. Determine its age.
7. Health officials are concerned about radon levels in homes. The half-life of radon-222 is 3.82 days. If a sample of gas contains 4.38 micrograms of radon-222, how much will remain in the sample after 15.2 days?
Answers:
1. B
2. A
3. A
4. B
5. D
6. 1/8
7. 0.2 g
8. 36.4 days
9. 2.865X104 years
1. 16.2 days
2. 15.3 days
3. 29.1 years
4. 20 min
5. 11,150 years
6. 0.274 µg