Calculations of the decay of radioactive nuclei are relatively straightforward, owing to the fact that there is only one fundamental law governing all decay process. This law states that the probability per unit time that a nucleus will decay is a constant, independent of time. This constant is called the decay constant and is denoted by λ, “lambda”. The radioactive decay of certain number of atoms (mass) is exponential in time.
Radioactive decay law: N = N.e-λt
The rate of nuclear decay is also measured in terms of half-lives. The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. If a radioisotope has a half-life of 14 days, half of its atoms will have decayed within 14 days. In 14 more days, half of that remaining half will decay, and so on. Half lives range from millionths of a second for highly radioactive fission products to billions of years for long-lived materials (such as naturally occurring uranium). Notice that short half lives go with large decay constants. Radioactive material with a short half life is much more radioactive (at the time of production) but will obviously lose its radioactivity rapidly. No matter how long or short the half life is, after seven half lives have passed, there is less than 1 percent of the initial activity remaining.
The radioactive decay law can be derived also for activity calculations or mass of radioactive material calculations:
(Number of nuclei) N = N.e-λt (Activity) A = A.e-λt (Mass) m = m.e-λt
, where N (number of particles) is the total number of particles in the sample, A (total activity) is the number of decays per unit time of a radioactive sample, m is the mass of remaining radioactive material.
Table of examples of half lives and decay constants. Notice that short half lives go with large decay constants. Radioactive material with a short half life is much more radioactive but will obviously lose its radioactivity rapidly.