Answers to Chem-Team Half-Life Problems (part 1)
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 20.0 days?
20.0 / 3.6 = 5.56 half-lives
(1/2)5.56 = 0.0213 (the decimal fraction remaining after 5.56 half-lives)
(6.02 x 1023) (0.0213) = 1.28 x 1022 atoms remain
4) After 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remain. What is the half-life of
the sample?
2.00 mg / 128.0 mg = 0.015625
How many half-lives must have elaspsed to get to 0.015625 remaining?
(1/2)n = 0.015625
n log 0.5 = log 0.015625
n = log 0.5 / log 0.015625
n=6
24 days / 6 half-lives = 4.00 days (the length of the half-life)
6) How long will it take for a 40.0 gram sample of I-131 (half-life = 8.040 days) to decay to 1/100 its
original mass?
(1/2)n = 0.01 (see #2 for the solution technique, 0.01 comes from 1/100 in the problem)
n = 6.64
6.64 x 8.040 days = 53.4 days
7) 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?
0.334 x 10 = 3.34 seconds
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 5.00 grams remains?
5.00 / 100.0 = 0.05 (decimal fraction remaining)
(1/2)n = 0.05 (see #2 for the solution technique)
n = 4.32 half-lives
36.0 hours x 4.32 = 155.6 hours