Half-life

James Richard Fromm


It has been determined experimentally for large aggregates of radioactive atoms that the number of atoms which disintegrate in a unit of time is proportional to the number of atoms present. The percentage of atoms which disintegrate in any given period of time is constant for a given isotope. In order to compare the activity of various radioactive species, the length of time it takes for one-half of the atoms to disintegrate has been chosen as a standard, and is called the half-life.

Selected Radioisotopes and Their Half-Life
Astatine-218 - 2.0 sec. Iodine-129 - 1.7 x 107 yrs. Radium-226 - 1,620 yrs.
Barium-131 - 12.0 days Iodine-131 - 8.14 days Radon-222 - 3.82 days
Bismuth-210 - 5.0 days Iron-59 - 46.3 days Sodium-24 - 15.0 hrs.
Bismuth-212 - 60.5 min. Lead-210 - 19.4 yrs. Strontium-90 - 19.9-28 yrs.
Bismuth-214 - 19.7 min. Lead-214 - 26.8 min. Sulfur-35 - 87.1 days
Bromine-82 - 35.5 hrs. Phosphorus-32 - 14.3 days Thallium-206 - 4.20 days
Calcium-45 - 152-165 days Plutonium-239 - 2.44 x104 yrs. Thallium-210 - 1.32 min.
Carbon-14 - 5,760 yrs. Polonium-210 - 138.4 days Thorium-230 - 8.0 x 104 yrs.
Cesium-137 - 30 yrs. Polonium-214 - 1.64 x 10-4 days Thorium-234 - 24.1 days
Chlorine-36 - 3.1 x 105 yrs. Polonium-215 - 0.0018 sec. Uranium-234 - 2.48 x 106 yrs.
Cobalt-60 - 5.26 yrs. Polonium-216 - 0.16 sec. Uranium-235 - 7.1 x 108 yrs.
Fluorine-20 - 11.4 sec. Polonium-218 - 3.05 min. Uranium-238 - 4.51 x 109 yrs
Gold-198 - 2.69 days Potassium-40 - 1.28 x 109 yrs. Uranium-239 - 23.5 min.
Hydrogen-3 - 12.3 yrs. Protactinium-234 - 1.18 min. .

Knowledge of the half-life of an isotope is useful in almost all calculations involving tracer isotopes. It also leads to an interesting use for naturally occurring isotopes: dating of ancient objects. In the upper atmosphere, radioactive CO2 (C-14) is formed as a result of bombardment of the upper atmosphere by cosmic rays. Through mixing by winds, the distribution of this form of carbon dioxide in the atmosphere remains virtually uniform. Since carbon dioxide is constantly being removed from the air by plants and created by cosmic rays, we can assume that the percentage of carbon dioxide in the air has been approximately the same for several hundred million years. All plants have a constant concentration of C-14 in their composition, because they use the radioactive C-14 in photosynthesis. When the plant is alive, C-14 is continually disintegrating, but it is continually being replaced by photosynthesis. However, when the plant dies, no more CO2 containing C-14 is replaced by photosynthesis. Now, only disintegration is occurring and the C-14 concentration in the plant begins to decrease. By measuring the C-14 level in the plant, it is possible to tell how long the plant has been dead. If an archaeologist unearths logs in an excavation of an ancient city, radiocarbon dating of the timbers will indicate approximately when the trees were cut down.

By employing various isotopes in a somewhat similar fashion, geologists have been able to date the formation of many ancient rocks and even to roughly date the formation of the earth. In uranium-bearing rocks, the radioactive uranium decomposes through a series of steps. The final product of this decay is lead. In the process, eight alpha particles are given off for each atom of uranium converted to lead. By measuring entrapped He to U and Pb to U ratios, it is possible to date the rocks. The half-life of uranium must, of course, be known for the calculation.

Some other uses for various radioisotopes
Calcium-45 Studying plant nutrition.
Carbon-14 Treating brain tumors, measuring age of ancient objects.
Cobalt-60 Treating cancer, irradiating food, inducing mutations.
Iodine-131 Studying and treating the thyroid gland, finding leaks in water pipes.
Iron-59 Studying the blood.
Phosphorus-32 Studying plants' use of fertilizer.
Sodium-24 Diagnosing circulatory disease.
Strontium-90 Treating small lesions.
Sulfur-35 Studying the body's use of certain amino acids.

Copyright 1997 James R. Fromm