Isotope decay

The experimentally measured rates of decay of radioactive atoms show that the decay is first order, where the number of atoms decomposing in a unit of time is proportional to the number present—this can be expressed in the following equation dN/dt = —X N. Another term used for characterizing rate of decay is half-life (t 1/2), the time required for half of the initial number of atoms to decay. Isotopes are considered to be in secular equilibrium, when the rate of decay of the parent is equal to that of its daughter. 

All the possible mass numbers between 142 and 150 are already taken by neod)Tnium (Z = 60) and samarium (Z = 62), so that no stable isotope is expected for element 61. They would all be radioactive, just as in the case of technetium (Z = 43). The Mattauch rule however was not capable of ascribing these radioactive isotopes a certain half-life. A number of uranium and thorium isotopes are also radioactive, but their half-lives are great enough so that one can still find them in nature. During that same year, in 1934, the American physicist and future Noble Prize winner, Willard Libby (1908-1980), discovered that neodymium is a (3 emitter (Libby, 1934). According to Soddy s displacement laws, this should imply that when neodymium decays, isotopes of element 61 should be formed. 

Hazard Flammable and explosive in powder form. Dusts of thorium have very low ignition points and may ignite at room temperature. Radioactive decay isotopes are dangerous when ingested. 

Radioactive decay is first order in the decaying isotope. For example, strontium-90 contained in fallout from nuclear explosions decays to yttrium-90 and a beta particle. Write the rate law for the decay of strontium-90. 

The lower energy and short penetration ability of beta particles requires a scintillator in direct contact with the decaying isotope. This is accomplished by dissolving or suspending the sample in a liquid fluor. Counters which use this technique are called beta counters or liquid scintillation counters. 

The mass number of the product must be 214 because its mass number plus that of the alpha particle must equal 218, the mass number of the decaying polonium-218 isotope. The atomic number of the product must be 82 because its atomic number plus that of the alpha particle must equal 84, the atomic number of the decaying isotope. Inasmuch as the element with an atomic number of 82 is lead, the product is g Pb. 

This inherent inefficiency in decay counting requires large doses of isotope for effective quantitative tracing of labeled compounds, including therapeutic drug candidates. The fundamental description of radioactive decay is that the decay rate (the measured quantity) is proportional to the number of the decaying isotopes present, with the proportionality constant being the mean isotopic lifetime [t = ti/2 In (2)] ... 

Gamma ray spectrometry is widely used in safeguards laboratories to measure the isotopic abundance of various U and Pu isotopes but also their concentration, as well as the concentration of alternative nuclear elements (see Sect. 14.4.4.8) fission and decay isotopes (Parus and Raab 1996 Parus et al. 1987). Laboratory applications make use of the developments of NDA technology mentioned in Sect. 63.3.1, but are usually part of DA procedures. 

All elements of atomic number greater than 83 exhibit radioactive decay K, Rb, Ir and a few other light elements emit p particles. The heavy elements decay through various isotopes until a stable nucleus is reached. Known half-lives range from seconds to 10 years. 

Gr. aktis, aktinos, beam or ray). Discovered by Andre Debierne in 1899 and independently by F. Giesel in 1902. Occurs naturally in association with uranium minerals. Actinium-227, a decay product of uranium-235, is a beta emitter with a 21.6-year half-life. Its principal decay products are thorium-227 (18.5-day half-life), radium-223 (11.4-day half-life), and a number of short-lived products including radon, bismuth, polonium, and lead isotopes. In equilibrium with its decay products, it is a powerful source of alpha rays. Actinium metal has been prepared by the reduction of actinium fluoride with lithium vapor at about 1100 to 1300-degrees G. The chemical behavior of actinium is similar to that of the rare earths, particularly lanthanum. Purified actinium comes into equilibrium with its decay products at the end of 185 days, and then decays according to its 21.6-year half-life. It is about 150 times as active as radium, making it of value in the production of neutrons. 

In 1964, workers at the Joint Nuclear Research Institute at Dubna (U.S.S.R.) bombarded plutonium with accelerated 113 to 115 MeV neon ions. By measuring fission tracks in a special glass with a microscope, they detected an isotope that decays by spontaneous fission. They suggested that this isotope, which had a half-life of 0.3 +/- 0.1 s might be 260-104, produced by the following reaction 242Pu + 22Ne —> 104 +4n. 

Element 259-104 is formed by the merging of a 13C nuclei with 249Cf, followed by emission of three neutrons. This isotope has a half-life of 3 to 4 s, and decays by emitting an alpha particle into 255No, which has a half-life of 185 s. 

Fm and heavier isotopes can be produced by intense neutron irradiation of lower elements, such as plutonium, using a process of successive neutron capture interspersed with beta decays until these mass numbers and atomic numbers are reached. 

Sixteen isotopes of fermium are known to exist. 257Fm, with a half-life of about 100.5 days, is the longest lived. 250Fm, with a half-life of 30 minutes, has been shown to be a decay product of element 254-102. Chemical identification of 250Fm confirmed the production of element 102 (nobelium). 

Ernest O. Lawrence, inventor of the cyclotron) This member of the 5f transition elements (actinide series) was discovered in March 1961 by A. Ghiorso, T. Sikkeland, A.E. Larsh, and R.M. Latimer. A 3-Mg californium target, consisting of a mixture of isotopes of mass number 249, 250, 251, and 252, was bombarded with either lOB or IIB. The electrically charged transmutation nuclei recoiled with an atmosphere of helium and were collected on a thin copper conveyor tape which was then moved to place collected atoms in front of a series of solid-state detectors. The isotope of element 103 produced in this way decayed by emitting an 8.6 MeV alpha particle with a half-life of 8 s. 

Monna and co-workers studied the use of radioactive isotopes as a means of dating sediments collected from the bottom of lakes and estuaries. To verify this method they analyzed a 208po standard known to have an activity of 77.5 decays/min, obtaining the following results... 

The rate of decay, or activity, for a radioactive isotope follows first-order kinetics... 

Neutron Activation Analysis Few samples of interest are naturally radioactive. For many elements, however, radioactivity may be induced by irradiating the sample with neutrons in a process called neutron activation analysis (NAA). The radioactive element formed by neutron activation decays to a stable isotope by emitting gamma rays and, if necessary, other nuclear particles. The rate of gamma-ray emission is proportional to the analyte s initial concentration in the sample. For example, when a sample containing nonradioactive 13AI is placed in a nuclear reactor and irradiated with neutrons, the following nuclear reaction results. 

The radioactive isotope of 13AI has a characteristic decay process that includes the release of a beta particle and a gamma ray. 

Isotope Dilution Another important quantitative radiochemical method is isotope dilution. In this method of analysis a sample of analyte, called a tracer, is prepared in a radioactive form with a known activity. Ax, for its radioactive decay. A measured mass of the tracer, Wf, is added to a sample containing an unknown mass, w, of a nonradioactive analyte, and the material is homogenized. The sample is then processed to isolate wa grams of purified analyte, containing both radioactive and nonradioactive materials. The activity of the isolated sample, A, is measured. If all the analyte, both radioactive and nonradioactive, is recovered, then A and Ax will be equal. Normally, some of the analyte is lost during isolation and purification. In this case A is less than Ax, and... 

One example of a characterization application is the determination of a sample s age based on the kinetics for the decay of a radioactive isotope present in the sample. The most common example is carbon-14 dating, which is used to determine the age of natural organic materials. 

Other isotopes can be used to determine the age of samples. The age of rocks, for example, has been determined from the ratio of the number of radioactive atoms to the number of stable gfPb atoms produced by radioactive decay. For rocks that do not contain uranium, dating is accomplished by comparing the ratio of radioactive fgK to the stable fgAr. Another example is the dating of sediments collected from lakes by measuring the amount of g Pb present. 

Radiochemical methods of analysis take advantage of the decay of radioactive isotopes. A direct measurement of the rate at which a radioactive isotope decays may be used to determine its concentration in a sample. For analytes that are not naturally radioactive, neutron activation often can be used to induce radioactivity. Isotope dilution, in which a radioactively labeled form of an analyte is spiked into the sample, can be used as an internal standard for quantitative work. 

Table 13.1 provides a list of several isotopes commonly used as tracers. The half-lives for these isotopes also are listed. What is the rate constant for the radioactive decay of each isotope ... 

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