Half-Life of a Radioisotope

The half-life of a radioisotope is the amount of time it takes for one-half of a sample to decay. For example, 53 has a half-life of 8.0 days. As 53 decays, it produces the nonra-dioactive isotope iiXe and a beta particle. 

Given the half-life of a radioisotope, calculate the amount of radioisotope remaining after one or more half-lives. 

Suppose we have a sample that initially contains 20. mg of 53I. In 8.0 days, one-half (10. mg) of all the 1-131 nuclei in the sample will decay, which leaves 10. mg of 1-131. After 16 days (two half-lives), 5.0 mg of the remaining 1-131 decays, which leaves 5.0 mg of 1-131. After 24 days, (three half-lives), 2.5 mg of the remaining 1-131 decays, which leaves 2.5 mg of 1-131 nuclei still capable of producing radiation. 

FIGURE 16.4 The decay curve for iodine-131 show/s that one-half of the radioactive sample decays and one-half remains radioactive after each half-life of 8.0 days. 

Q How many milligrams of the 20.-mg sample remain radioactive after 2 half-lives  

Phosphorus-32, a radioisotope used in the treatment of leukania, has a half-life of 14.3 days. If a sample contains 8.0 mg of phosphorus-32, how many milligrams of phosphorus-32 remain after 42.9 days  

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The biological half-life of a radioisotope is the time required for the body to excrete half of the radioisotope. The effective half-life is the time required for the amount of a radioisotope in the body to be reduced to half its original amount, as a result of both the decay of the radioisotope and its excretion. Sulfur-35 (tu2 = 87.4 d) is used in cancer research. The biological half-life of sulfur-35 in the human body is 90. d. What is the effective half-life of sulfur-35 ... 

If the half-life of a radioisotope is 13.3 hours, calculate the mean life of the isotope. 

What is the half-life of a radioisotope that takes 15 min to decay to 90% of its original activity ... 

The word radioactive sounds scciry, but science and medicine are stuffed with useful, friendly applications for radioisotopes. Many of these applications are centered on the predictable decay rates of various radioisotopes. These predictable rates are characterized by half-lives. The half-life of a radioisotope is simply the amount of time it tcikes for exactly half of a sample of that isotope to decay into daughter nuclei. For excimple, if a scientist knows that a sample originally contained 42 mg of a certain radioisotope and measures 21 mg of that isotope in the sample four days later, then the half-life of that radioisotope is four days. The half-lives of radioisotopes range from seconds to billions of yecirs. 

The relation between the half life of a radioisotope (ordinate) and the characteristic time scale for marine processes (abscissa). The shaded area indicates the range where the two life times are a good match. 

Radioisotopes Useful in Biological Research Hundreds of biological compounds (e.g., amino acids, nucleosides, and numerous metabolic intermediates) labeled with various radioisotopes are commercially available. These preparations vary considerably in their specific activity, which is the amount of radioactivity per unit of material, measured in disintegrations per minute (dpm) per millimole. The specific activity of a labeled compound depends on the probability of decay of the radioisotope, indicated by its half-life, which is the time required for half the atoms to undergo radioactive decay. In general, the shorter the half-life of a radioisotope, the higher its specific activity (Table 3-3). 

So far, our discussion has been mainly qualitative. We now consider the topic of half-lives from a more quantitative point of view. This approach enables us to determine the half-life of a radioisotope or the age of an object. 

The half-life of a radioisotope is the amount of time it takes for one-half of a sample to decay. 

Once a radioactive chemical is introduced into the body, little can be done to speed its removal. Some removal will eventually occur as a result of excretion (urine, feces, perspiration, or expired air) and the activity will diminish as a result of radioactive decay. The effective half-life of a radioisotope depends upon both its physical half-life (radioactive decay) and its biological half-life (biological... 

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