Physics 060 Half-life problems
April 1, 2008
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 halflives 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 radon222, how much will remain in the sample after 15.2 days?
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
9.
B
A
A
B
D
1/8
0.2 g
36.4 days
2.865X104 years
1.
2.
3.
4.
5.
6.
16.2 days
15.3 days
29.1 years
20 min
11,150 years
0.274 µg