# Half-life

Isotopes have an interesting property; they decay to form other more stable isotopes. The rate of decay is expressed by the isotopes’ half-lives. A half-life is the time in which the concentration of an isotope decays to one half of its original concentration. The rate of emission from a radiation source reduces to 1/2 in one half-life, to ¼ in two half-lives, to 1/8 in three half-lives, and to 1/2n in n half-lives. Half-lives of some of the isotopes of interest to us are uranium-235 (about 0.7 billion years), plutonium-239 (24,360 years), cesium-137 (30 years), and strontium-90 (28.8 years). Iodine-131 has a half-life of only 8.04 days.

Example: A radiation leak released cesium-137 radionuclide. How long would it take until the radioactivity of cesium drops to 1/1000 of its initial value? The half-life of 137Cs is 30 years. (Hint: 210 = 1024)

Solution: About ten half-lives or 300 years.

In energy, we derived the equation for the doubling-time of a quantity that grows exponentially with time. Examples given were population growth, interest accumulating on a savings account, and energy consumption. The same equation can be shown to apply for the radioactive decay of isotopes, except decay rate (negative growth rate) and half-life are used instead of growth rate and doubling time. Following the approach, we can write:

T1/2 = 70/Percentage Rate of Decay

Example: Using data from the previous example, calculate the rate of decay for cesium-137?

Solution: Rate of decay is 70/30 = 2.33% per year.

## References

(1) Toossi Reza, "Energy and the Environment:Sources, technologies, and impacts", Verve Publishers, 2005

Bodansky, Nuclear Energy Principles, Practices, and Prospects, Second Ed., Springer, 2004.

Seaborg, G., T., Peaceful Uses of Nuclear Energy, University Press of the Pacific, 2005.

International Journal of Nuclear Engineering and Design, Direct Science Elsevier Publishing Company, devoted to the Thermal, Mechanical, Material and Structural Aspects of Nuclear Fission.

Journal of Fusion Energy, Springer Netherlands. It features articles pertinent to development of thermonuclear fusion.

Federation of American Scientists (http://www.fas.org/nuke/intro/nuke/index.html).

International Atomic Energy Agency (http://www.iaea.org).

DoE Office of Nuclear Energy, Science & Technology (http://www.ne.doe.gov).

American Nuclear Society, (http://www.ans.org).

World Association of Nuclear Operator (WANO) (http://www.wano.org.uk).