Radioactive decay, of isotopes

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. 

The decay of radioactive isotopes created in the earth s atmosphere by the interaction of cosmic rays with atomic nuclei of atmospheric constituents. After such nuclei (e.g., 3H as 3HH0 or 14C as 14C02) are removed from the atmosphere, e.g., fed into a groundwater system (3H) or built into a living organism (14C), their number decreases according to the law of radioactive decay. 

The temperature in the core of the Earth—due to the decay of radioactive isotopes—is on the order of 4,000°C, the temperature of the lava of volcanoes is about 1,200°C, and the temperature of thermal springs can reach 350°C. If the groundwater temperature exceeds 150°C, flash steam power plants can be built, and if it is between 100 and 150°C, binary cycle power plants can be operated. 

Like the s isotopes, the r isotopes are produced by neutron irradiation, but the flux must be sufficiently intense that the neutron captures would be rapid compared to the beta-decay lifetimes of the radioactive isotopes. For the s-process path through stable isotopes these beta-decay times are typically minutes to hours but on very neutron-rich paths encountered in the r-process, the corresponding times may be but tiny fractions of a second. In s-process circumstances (10 to loo years between captures), decay of radioactive isotopes will occur first and the r-process isotopes are... 

Energy released from impacts, together with heat from the decay of radioactive isotopes, led to differentiation in planetary embryos, once these objects became partially molten (Tonks and Melosh, 1992). Iron and siderophile elements (e.g., platinum, palladium, and gold) preferentially sank to the center to form a core, while the lighter silicates and lithophile elements formed a mantle. Differentiation was probably a continuous process rather than a single event, so that large planets like Earth accreted from embryos that were already partially or wholly differentiated. 

The stable isotopes have nuclei that do not decay to other isotopes on geologic timescales, but may themselves be produced by the decay of radioactive isotopes. Radioactive (unstable) isotopes have nuclei that spontaneously decay over time to form other isotopes. For example, C, a radioisotope of carbon, is produced in the atmosphere by the interaction of cosmic-ray neutrons with stable... 

The decay of radioactive isotopes is a simple exponential (first-order) process. 

An example of a nearly pure first-order irreversible reaction is the decay of radioactive isotopes. These reactions depend on instabilities within the nucleus rather than the electronic configuration of the atom and are thus totally uninfluenced by the surroundings. The reaction rate is dependent on the concentration of the isotope and the probability of spontaneous decay. An important example in aquatic systems is the decay of carbon-14 (Fig. 9.5), which is formed in the upper atmosphere by interaction between cosmic ray particles and nitrogen atoms. is then mixed into the lower atmosphere and... 

The data discussed above are for present-day abundances in the photosphere and meteorites. However, two processes affected the solar abundances over time. The first is element settling from the solar photosphere into the Sun s interior the second is decay of radioactive isotopes that contribute to the overall atomic abundance of an element. The first, discussed in the following, is more important for the sun and large-scale modeling the changes in isotopic compositions and their effects on abundances are comparably minor but important for radiometric dating. The isotopic effects are considered in the solar system abundance table in this section, but are not described at length here. 

A chemist proposes a research project to discover a catalyst that will speed up the decay of radioactive isotopes that are waste products of a medical laboratory. Such a discovery would be a potential solution to the problem of nuclear waste disposal. Critique this proposal. 

An example of the exponential function is in the decay of radioactive isotopes. If No is the number of atoms of the isotope at time t = 0, the number at any other time, t, is given by... 

The decay of radioactive isotopes via electron emission, so-called beta decay, is a well-known phenomenon, hi this mode imstable nuclei that have an excessive number of neutrons, for example can emit fast electrons, particles, in order to attain a stable nuclear configuration. Nuclei with insufficient neutrons, such as can obtain stability by emitting fast positrons, particles (the anti-matter equivalents of electrons). Both processes are classified as radioactive f) decay. In each case, the mass munber of the nucleus remains constant but the atomic number changes. There exist several positron emitting isotopes, of which and in particular... 

The arrangement can also be used as a power source (Figure 15.15b). If one plate is continuously maintained hotter than the other, a current will flow in the circuit, and power is generated. In this format, these devices are used in space probes that operate too far from the sun for photoelectricity to be used for power supplies. In such cases, heat is generated by the slow decay of radioactive isotopes. 

It s important to realize that the halMife decay of radioactive isotopes is not linear. For example, you can t find the remaining amount of an isotope as 7.5 half-lives by finding the midpoint between 7 and 8 half-lives. This decay is an example of an exponential decay, shown in Figure 5-2. 

When the assemblies are discharged from the Reactor Tank, they are moved to the D E canal m the Process Room, placed in the D E conveyor, and transferred to the Disassembly Basin side of the D E canals The D E canal is a water ed canal located under die diieldtng wall that separates the Disassembly Area from the Process Room. In the IKsassembly Basin, the assemblies are transferred to hangers suspended from overhead monoids diat are used to store and transport the irradiated asseihblies throughout the Disassembfy Area 2>4, Section 9.1.2). The assemblies are initial stored in the VTS basin for a specified period of time to allow for decay of radioactive isotopes. This time varies with the types of material, since each material yvitt decay at a different rate. 

Decay of radioactive isotopes is affected by the stability of an element at a certain energy level. Bismuth (Bi), at atomic number 83, is the heaviest element in the Periodic Table with a minimum of one stable isotope. All other heavier elements are radioactive. 

Another aspect of time is the decay of radioactive isotopes. The half-life is the time it takes for the isotope to drop to half the radioactive intensity. This can be microseconds to hundreds of thousands of years. Some isotopes used in medicine have half-lives of fom hours. Plutonium (a synthetic radioactive element) has a half-life of 24110 years ( Pu) or 370 000 years ( Pu). It is regularly shipped from East Asia to Europe and back agaiir... 

An example of the exponential function is in the decay of radioactive isotopes. If Nit) represents the number at time t. 

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