HALF-LIFE WORKSHEET
Use the Reference Table to the right to assist you in answering questions 1-3, 5 and 11.
1. How long does it take a 100.00 g sample of As-81 to decay to 12.5 g?
½ life:
As-81 = 33 seconds
2. How long does it take a 180 g sample of C-14 to decay to ⅛ its
original mass?
Au-198 = 2.69 days
C-14 = 5730 years
3. What percent of a sample of As-81 remains un-decayed after 66 seconds?
4. What is the half-life of a radioactive isotope if a 500.0 g sample decays to 62.5 g in 39.3 hours?
5. How old is a bone if it presently contains 0.3125 g of C-14, but it was estimated to have originally
contained 80.000 g of C-14?
6. 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 s?
7. 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 852,000 yr, what is its half-life?
8. Thallium-208 has a half-life of 3.053 min. How long will it take for 120.0 g to decay to 7.50 g?
9. If the half-life of iodine-131 is 8.10 days, how long will it take a 50.00 g sample to decay to 6.25 g?
10. Potassium-42 has a half-life of 12.4 hours. How much of an 848 g sample will be left after 62.0 h?
11. How much of a 144 g sample of carbon-14 will remain after 17,190 yr?
12.
Use the bar graph to the left to answer a-c.
100%
Amount
of
Chromium
-48
a. How long is a half-life for chromium-48?
75%
b. If only 25% of the chromium-48 remains,
how old is the material containing the
chromium-48?
50%
25%
12.5%
0
21.6
43.2
64.8
Time (h)
c. If a sample originally had 120 atoms of
chromium-48, how many atoms will
remain after 64.8 hours?
13. If the half-life of uranium-235 is 7.04 × 108 yr and 12.5 g of uranium-235 remain after 28.16 × 108 yr,
how much of the radioactive isotope was in the original sample?
14. A 208 g sample of sodium-24 decays to 13.0 g of sodium-24 within 60.0 h. What is the half-life of this
radioactive isotope?
HALF-LIFE PROBLEMS
1) The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left
after 7.2 minutes has elapsed?
2) Pd-100 has a half-life of 3.6 days. If one had 6.02 x 1023 atoms at the start, how many atoms would be
present after 18.0 days?
3) Os-182 has a half-life of 21.5 hours. What fraction and how many grams of a 10.0 gram sample would
have decayed after exactly three half-lives?
4) After 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remain. What is the half-life of
the sample?
5) U-238 has a half-life of 4.46 x 109 years. How much U-238 should be present in a sample 8.92 x 109
years old, if 2.00 grams was present initially?
6) How long will it take for a 40.0 gram sample of I-131 (half-life = 8.040 days) to decay to 1/32 its
original mass?
7) Fermium-253 has a half-life of 0.334 seconds. A radioactive sample is considered to be completely
decayed after 5 half-lives. How much time will elapse for this sample to be considered gone?
8) At time zero, there are 10.0 grams of W-187. If the half-life is 24.0 hours, how much will be present at
the end of 4 days (96 hours)?
9) 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 12.5 grams remains?
10) 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.
11) The half life of iodine-131 is 8.040 days. What percentage of an iodine-131 sample will remain after
40.2 days?
12) The half-life of thorium-227 is 18.72 days. How many days are required for three-fourths of a given
amount to decay?
13) If you start with 5.32 x 109 atoms of Cs-137, how much time will pass before the amount remaining is
3.33 x 108 atoms (0.333 x 109 atoms)? The half-life of Cs-137 is 30.17 years.
14) The half-life of the radioactive isotope phosphorus-32 is 14.3 days. How long until a sample loses 50%
of its radioactivity?
ANSWERS
1) 12.5 g
3) ⅛ and 1.25 g
7) 1.67 s
11) 3.125 %
2) 0.188 x 1023 or 1.88 x 1022 atoms
4) 4 days
5) 0.50 g
8) 0.625 g
9) 108.0 h
12) 37.44 days
13) 120.68 yr
6) 48.24 days
10) 24.52 yr
14) 14.3 days