Half-life of radioactive decay

The half-life of radioactive decay or of a chemical reaction is the length of time required for exactly half the material under study to be consumed, e.g. by chemical reaction or radioactive decay. We often give the half-life the symbol t /2, and call it tee half. 

Half-Life of Radioactive Decay Decay rates are also commonly expressed in terms of the fraction of nuclei that decay over a given time interval. The half-life (fi/i) of a nuclide is the time it takes for half the nuclei present in a sample to decay. The number of nuclei remaining is halved after each half-life. Thus, half-life has the same meaning for a nuclear change as for a chemical change (Section 16.4). Figure 23.4 shows the decay of carbon-14, which has a half-life of 5730 years, in terms of number of C nuclei remaining ... 

All radioactive decays occur with first-order kinetics, with the exception of electron capture, which is a two-particle collision. The differential rate law for radioactive decay is given by Equation (2.7). After integration, an alternative and more useful form of the rate law is shown by Equation (2.8). The half-life of radioactive decay is defined as the length of time it takes for the number of unstable nuclides to decrease to exactly one-half of their original value. The half-life, t can be calculated using Equation (2.9), where k is the first-order rate constant... 

The overall mass transfer coefficient is a rate constant, a measure of how fast the process occurs. It is a close parallel to the rate constant of a first-order chemical reaction, or to the half life of radioactive decay. It is different from these chemical rate constants in two important ways. First, K is defined per unit area, and chemical rate constants are normally defined per unit volume. One consequence is that we will sometimes work with Ka, where a is the interfacial area per system volume. The product Ka has the same units of reciprocal time as a first-order chemical rate constant. 

Rutherford, Sir Ernest (1871-1937). First to prove radioactive decay of heavy elements and to carry out a transmutation reaction (1919). Discovered half-life of radioactive elements. Nobel Prize 1908. 

Physical—In the field of radioactive isotopes, the half-life of radioactive carbon, carbon-14, is 5,568 years. In other words, if we start with 1 g of carbon-14, 5,568 years later only 1/2 g of carbon-14 will remain due to the radioactive decay. All radioactive isotopes have a specific half-life which may range from seconds to millions of years. 

Such a product occurs often and is a fixture of many mass transfer correlations. The quantity ka is very similar to the rate constant of a first-order reversible reaction with an equilibrium constant equal to unity. This particular problem is similar to the calculation of a half-life for radioactive decay. 

The C exchanges with C in living organisms, but exchange ceases on death. The radioactive content decays with a half-life of 5730 years. Hence the age of a once living material may be established by determining the amount of C. 

Radon-222 [14859-67-7] Rn, is a naturally occuriing, iaert, radioactive gas formed from the decay of radium-226 [13982-63-3] Ra. Because Ra is a ubiquitous, water-soluble component of the earth s cmst, its daughter product, Rn, is found everywhere. A major health concern is radon s radioactive decay products. Radon has a half-life of 4 days, decayiag to polonium-218 [15422-74-9] Po, with the emission of an a particle. It is Po, an a-emitter having a half-life of 3 min, and polonium-214 [15735-67-8] Po, an a-emitter having a half-life of 1.6 x lO " s, that are of most concern. Polonium-218 decays to lead-214 [15067-28A] a p-emitter haviag = 27 min, which decays to bismuth-214 [14733-03-0], a p-emitter haviag... 

Radiocarbon dating (43) has probably gained the widest general recognition (see Radioisotopes). Developed in the late 1940s, it depends on the formation of the radioactive isotope and its decay, with a half-life of 5730 yr. After forms in the upper stratosphere through nuclear reactions of... 

Tritium is radioactive and decays with a half-life of 12.26 yr. 

Radioactive waste is characterized by volume and activity, defined as the number of disintegrations per second, known as becquerels. Each radionucHde has a unique half-life,, and corresponding decay constant, A = 0.693/tj 2 For a component radionucHde consisting of JS1 atoms, the activity, M, is defined as... 

Decay products of the principal radionuclides used in tracer technology (see Table 1) are not themselves radioactive. Therefore, the primary decomposition events of isotopes in molecules labeled with only one radionuclide / molecule result in unlabeled impurities at a rate proportional to the half-life of the isotope. Eor and H, impurities arising from the decay process are in relatively small amounts. Eor the shorter half-life isotopes the relative amounts of these impurities caused by primary decomposition are larger, but usually not problematic because they are not radioactive and do not interfere with the application of the tracer compounds. Eor multilabeled tritiated compounds the rate of accumulation of labeled impurities owing to tritium decay can be significant. This increases with the number of radioactive atoms per molecule. 

The selective uptake of iodide ion by the thyroid gland is the basis of radioiodine treatment in hyperthyroidism, mainly with although various other radioactive isotopes ate also used (40,41). With a half-life of eight days, the decay of this isotope produces high energy P-particles which cause selective destmction within a 2 mm sphere of their origin. The y-rays also emitted are not absorbed by the thyroid tissue and are employed for external scanning. 

All radioactive isotopes decay with a characteristic half-life. For example, Fe decays with a half-life of 45 days, while Cu decays with a half-life of 12.6 hours. As a result of the decay, signature high-energy photons or y rays are emitted from a given radioisotope. Thus, Fe emits two prominent y rays at 1099 and 1292 keV, " Na emits at 1368 and 2754 keV, and Zn emits at 1115 keV. Compilations of y rays used in NAA can be found in y-ray tables. 

In addition to the 4 stable isotopes sulfur has at least 9 radioactive isotopes, the one with the longest half-life being which decays by activity (Kmax 0.167 MeV, 87.5 d). can be prepared by Cl(n,p), S(n,> ) or S(d,p) and is commercially available as SeicmcQt H2S, SOCb and KSCN. The radiation has a similar energy to that of C ( mav 0.155 MeV) and similar counting techniques can be used (p. 276). The maximum range is 300 min in air and 0.28 mm in water, and effective shielding is provided by a perspex screen 3-10 mm thick. The preparation of many - S-containii compounds has been... 

Although the nucleus of the uranium atom is relatively stable, it is radioactive, and will remain that way for many years. The half-life of U-238 is over 4.5 billion years the half-life of U-235 is over 700 million years. (Half-life refers to the amount of time it takes for one half of the radioactive material to undergo radioactive decay, turning into a more stable atom.) Because of uranium radiation, and to a lesser extent other radioactive elements such as radium and radon, uranium mineral deposits emit a finite quantity of radiation that require precautions to protect workers at the mining site. Gamma radiation is the... 

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 ... 

The constant half-life of a nuclide is used to determine the ages of archaeological artifacts. In isotopic dating, we measure the activity of the radioactive isotopes that they contain. Isotopes used for dating objects include uranium-238, potassium-40, and tritium. However, the most important example is radiocarbon dating, which uses the decay of carbon-14, for which the half-life is 5730 a. 

The law of radioactive decay implies that the number of radioactive nuclei decreases exponentially with time with a characteristic half-life. Radioactive isotopes are used to determine the ages of objects. 

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 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 ... 

A radioactive isotope X with a half-life of 27.4 d decays into another radioactive isotope Y with a half-life of 18.7 d, which decays into the stable isotope Z. Set up and solve the rate laws for the amounts of the three nuclides as a function of time, and plot your results as a graph. 

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