Question 19.PS.4: Half-Life Iodine-131, used to treat hyperthyroidism, has a h......
Half-Life
Iodine-131, used to treat hyperthyroidism, has a half-life of 8.04 days.
^{131}_{~53}I → ^{131}_{~54}Xe + ^{\ 0}_{-1}e t_{1/2} = 8.04 days
If you have a sample containing 10.0 µg of iodine-131, what mass of the isotope will remain after 32.2 days?
0.0625 µg
Strategy and Explanation First, we find the number of half-lives in the given 32.2-day time period. Since the half-life is 8.04 days, the number of half-lives is
32.2 days × \frac{1 half-life}{8.04 days} = 4.00 half-lives
This means that the initial quantity of 10.0 µg is reduced by half four times.
10.0 µg × 1/2 × 1/2 × 1/2 × 1/2 = 10.0 µg × 1/16 = 0.0625 µg
After 32.2 days, only one sixteenth of the original ^{131}I remains.
Reasonable Answer Check After the passage of four half-lives, the remaining ^{131}I should be a small fraction of the starting amount, and it is.