Notice that short half lives go with large decay constants. The fraction of the original activity remaining after succeeding half-lives is:Īctivity after 1 half-life = ½ of the originalĪctivity after 2 half-lives = ½ x ½ = ¼ of the originalĪctivity after 3 half-lives = ½ x ½ x ½ = (½) 3 = 1/8 of the originalĪctivity after 4 half-lives = (½) 4 = 1/16 of the originalĪctivity after 5 half-lives = (½) 5 = 1/32 of the originalĪctivity after 6 half-lives = (½) 6 = 1/64 of the originalĪctivity after 7 half-lives = (½) 7 = 1/128 of the original The number of atoms existing after 5 to 7 half-lives can usually be assumed to be negligible.
After seven half-lives, only 1/128, or 0.78%, of the atoms remains. After five half-lives have elapsed, only 1/32, or 3.1%, of the original number of atoms remains. 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). In 14 more days, half of that remaining half will decay, and so on. If a radioisotope has a half-life of 14 days, half of its atoms will have decayed within 14 days. Each radionuclide has its own particular half-life that never changes, regardless of the quantity or form of the material (i.e., solid, liquid, gas, element or compound) or its past history. Therefore, the rate of nuclear decay can be also measured in terms of half-lives. Thus, the probability of its breaking down does not increase with time, but stays constant no matter how long the nucleus has existed. A nucleus does not “age” with the passage of time. In other words, a nucleus of a radionuclide has no “memory”. As was written, radioactive decay is a random process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay.
The half-life is defined as the amount of time it takes for a given isotope to lose half of its radioactivity. One of the most useful terms for estimating how quickly a nuclide will decay is the radioactive half-life ( t 1/2).
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