Half-life radioactive samples

Half-Life (,Radioactive Element). The average time required for one-half of the atoms in a sample of radioactive element to decay The half-lite t is given by... 

Most of the problems on past AP exams that contain half-lives are relatively simple to solve, using either conceptual or mathematical approaches. On the exam, you are not provided with any equations related to nuclear chemistry. Therefore, any calculations you will have to make should be fairly simplistic and easy to solve using a few simple rules. From a conceptual perspective, this that means half-life problems can be solved by repeatedly cutting the starting amount in half. For example, after one half-life, a sample will have 14 the number of radioactive nuclei that it started with. After two half-lives, the sample will have (y)(y),or(y), times the number of radioactive nuclei left. After three half-lives, the sample will have () )( )() ), or (), times the number of radioactive nuclei left. If you haven t already spotted the pattern here, it is that the amount of sample left after time t will be... 

The activity in a 10.00-mL sample of radioactive wastewater containing fgSr was found to be 9.07 X 10 disintegrations/s. What is the molar concentration of 3gSr in the sample The half-life for fgSr is 28.1 years. 

Air Transport. Relatively small quantities of chemicals are transported by air, although availability of such service for the movement of samples, emergency shipments, and radioactive chemicals with a short half-life is important. Both economic and safety considerations impede the development of air carriage as a significant means of transporting a substantial volume of chemicals. 

Bromine-82 has a half-life of 36 hours. A sample containing Br-82 was found to have an activity of 1.2 X 105 disintegrations/min. How many grams of Br-82 were present in the sample Assume that there were no other radioactive nuclides in the sample. 

Carbon-14 (C-14) with a half-life of 5730 years decays to nitrogen-14 (N-14). A sample of carbon dioxide containing carbon in the form of C-14 only is sealed in a vessel at 1.00-atmosphere pressure. Over time, the CO2 becomes NO2 through the radioactive decay process. The following equilibrium is established ... 

All radioactive decay processes follow first-order kinetics. The half-life of the radioactive isotope tritium (3H, or T) is 12.3 years. How much of a 25.0-mg sample of tritium would remain after 10.9 years ... 

FIGURE 17.18 The exponential decay of the activity of a sample shows that the number of radioactive nuclei in the sample also decays exponentially with time. The curve is characterized by the half-life,... 

Half-lives span a very wide range (Table 17.5). Consider strontium-90, for which the half-life is 28 a. This nuclide is present in nuclear fallout, the fine dust that settles from clouds of airborne particles after the explosion of a nuclear bomb, and may also be present in the accidental release of radioactive materials into the air. Because it is chemically very similar to calcium, strontium may accompany that element through the environment and become incorporated into bones once there, it continues to emit radiation for many years. About 10 half-lives (for strontium-90, 280 a) must pass before the activity of a sample has fallen to 1/1000 of its initial value. Iodine-131, which was released in the accidental fire at the Chernobyl nuclear power plant, has a half-life of only 8.05 d, but it accumulates in the thyroid gland. Several cases of thyroid cancer have been linked to iodine-131 exposure from the accident. Plutonium-239 has a half-life of 24 ka (24000 years). Consequently, very long term storage facilities are required for plutonium waste, and land contaminated with plutonium cannot be inhabited again for thousands of years without expensive remediation efforts. 

Predict the amount of a radioactive sample that will remain after a given time period, given the decay constant or half-life of the sample (Example 17.3). 

A 1.40-g sample containing radioactive cobalt was kept for 2.50 a, at which time it was found to contain 0.266 g of 67Co. The half-life of 67Co is 5.27 a. What percentage (by mass) of the original sample was f,Co ... 

A radioactive sample contains 3.25 X 1018 atoms of a nuclide that decays at a rate of 3.4 X 1013 disintegrations per 15 min. (a) What percentage of the nuclide will have decayed after 150 d (b) How many atoms of the nuclide will remain in the sample (c) What is the half-life of the nuclide ... 

It is practically impossible to predict which particular kernel will pop at any given instant, and in this way the popping of corn is a random process, much like radioactive decay. However, the cornpopping process is predictable in the sense that you can say how much time it will take to prepare a batch of popcorn. Similarly, a sample of radioactive material decays within a known time period. This period is called a half-life. 

The half-life of a radioactive species is defined as the time it takes for the activity of the sample to drop by 50%. In this activity, you will investigate the decay of 137Bam, a metastable isotope of barium that undergoes gamma decay with a half-life of several minutes. 

Radioactive decay is a stochastic process that occurs at random in a large number of atoms of an isotope (see Textbox 13). The exact time when any particular atom decayed or will decay can be neither established nor predicted. The average rate of decay of any radioactive isotope is, however, constant and predictable. It is usually expressed in terms of a half-life, the amount of time it takes for half of the atoms in a sample of a radioactive isotope to decay to a stable form. 

FIGURE 61 The decay of radiocarbon. Radiocarbon is a radioactive isotope whose half-life is 5730 + 40 years. This means that half of the original amount of radiocarbon in any carbon-containing sample will have disintegrated after 5730 years. Half of the remaining radiocarbon will have disintegrated after 11,400 years, and so forth. After about 50,000 years the amount of radiocarbon remaining in any sample is so small that older remains cannot be dated reliably. 

EXAMPLE 22.6. Calculate the time required for a radioactive sample to lose one-third of the atoms of its parent isotope. The half-life is 33 min. 

Draw a graph of the mass of the radioactive atoms left in the decomposition of a 1 200-g sample of a radioactive isotope with a half-life of 10.0 days. Extend the graph to allow readings up to 50 days. Use the vertical axis for mass and the horizontal axis for time. 

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