Untitled - Kelly Walsh High School

296 CHEMISTRY FOR THE UTTERLY CONFUSED
20-3 Half-Lives (t 1/2)
A radioactive isotope may be unstable, but it is impossible to predict when a
certain atom will decay. However, if we have a statistically large enough sample,
some trends become obvious. The radioactive decay follows first-order kinetics
(see Chapter 13 for a more in-depth discussion of first-order reactions). If we
monitor the number of radioactive atoms in a sample, we observe that it takes
a certain amount of time for half the sample to decay; it takes the same amount
of time for half the remaining sample to decay, and so on. The amount of time
it takes for half the sample to decay is the half-life of the isotope and has the
symbol t 1/2. The table below shows the percentage of the radioactive isotope
remaining versus half-life.
Half-lives may be very short, 4.2 10 6 seconds for Po-213, or very long, 4.5
10 9 years for U-238.
If only multiples of half-lives are considered, the calculations are very straightforward.
Iodine-131 is useful in the treatment of thyroid cancer and has a t 1/2 of 8 days.
How long would it take to decay to 25% of its original amount?
Solution:
Half-life, t 1/2
Percent Radioactive
Isotope Remaining
0 100.000
1 50.000
2 25.000
3 12.500
4 6.250
5 3.125
6 1.562
7 0.781
8 0.391
9 0.195
10 0.098
Looking at the chart, you can see that 25% would be at 2 half-lives or 16 days.
Since radioactive decay is not a linear process, you cannot use the chart to predict
how much would still be radioactive at the end of some time (or amount)