Radioactive disintegration constant

Decay Constant (A,)—The fraction of the number of atoms of a radioactive nuclide which decay in unit time (see Disintegration Constant). 

Calculate the rate constant for the radioactive disintegration of an isotope that has a half-life of 6930 years. 

Half-life is defined as the time required for a radioisotope to reduce its initial radioactivity (disintegration rate) to one-half (or 50%). The half-life is represented by the symbol, t a, and it is unique for a given radioisotope. The useful lifetimes of radiopharmaceuticals are usually determined by radioactive decay, which constantly decreases the amount of radioactivity present. The half-life is related to decay constant, X of a radioisotope (discussed in the subsequent section), as follows ... 

Elementary reactions (also termed monomolecular reactions) that involve only a single entity in the formation of an activated complex. Unimolecular rate constants, k, are concentration-independent and are typically expressed in units of sUnimolecular reactions are expected to be first order (i.e., -dc/dt = kc where c is the concentration and t is time). Examples of unimolecular processes include radioactive disintegrations, isomeriza-tions, disassociations, and decompositions. Reactions in solution are unimolecular only if the solvent is not covalently incorporated into the product(s). 

Half-life period of a given radioactive substance is independent of the amount of substance present initially. It depends only on disintegration constant of the element. 

A reaction of this type is said to follow first-order kinetics because the rate is proportional to the concentration of a single species raised to the first power (fig. 7.2). An example is the decay of a radioactive isotope such as 14C. The rate of decay at any time (the number of radioactive disintegrations per second) is simply proportional to the amount of l4C present. The rate constant for this extremely slow nuclear reaction is 8 x 10-12 s l. Another example is the initial electron-transfer reaction that occurs when photosyn-... 

The unit of the velocity constant k is sec-1. Many reactions follow first order kinetics or pseudo-first order kinetics over certain ranges of experimental conditions. Examples are the cracking of butane, many pyrolysis reactions, the decomposition of nitrogen pentoxide (N205), and the radioactive disintegration of unstable nuclei. Instead of the velocity constant, a quantity referred to as the half-life t1/2 is often used. The half-life is the time required for the concentration of the reactant to drop to one-half of its initial value. Substitution of the appropriate numerical values into Equation 3-33 gives... 

The series of Radioactive disintegrations the uranium-radium series, the uranium-actinium series, the thorium series, and the neptunium series. The age of the earth. The fundamental particles electron, proton, positron, neutron, positive, negative, and neutral mesons, neutrino. The photon (light quantum) the energy of a photon, hv. Planck s constant. The wave-particle duality of light and of matter. The wavelengths of electrons. 

Standard Oxidation-reduction Potentials and Equilibrium Constants 655 Constants of Radioactive Disintegration 665-8... 

At the beginning of the twentieth century, research turned to the newly discovered radioactive substances. Ramsay and Soddy (1903) showed that helium was derived by radioactive disintegration of radium, the ftrst demonstration that one element was derived from another. Once the decay constant of radium had been determined, the door was open for the ftrst application of the noble gases geochronology (Strutt, 1908), a methodology that has been pursued ever since. 

The decay of a radionuclide is a statistical process in the sense that it is not possible to predict exactly when a particular nucleus will disintegrate. One may, however, ascribe a probability that a nucleus will decay in unit time. This probability is known as the radioactive decay constant (transformation constant), X, of the radionuclide. The number of atoms of a radioactive substance disintegrating per unit time, 6N/dt, which is referred to as the activity of the substance, is proportional to the total number, N, of radioactive atoms present at time t, the constant of proportionality being X. 

The decay constant is sometimes also called the disintegration constant. The half-life and the decay constant give the same information, so either may be used to characterize decay. Another useful concept in radioactive decay is the average lifetime. Average lifetime is the reciprocal of decay constant. 

The disintegration of an unstable nucleus is an event so completely unpredictable and random that the only thing which can be said is that an imstable nucleus will decay within a given period of time. For a particular isotope, the proportion of nuclei that decay in a given time is a constant known as its disintegration constant. If the decline in activity of a radioactive isotope is plotted against time (Figure 13.2) a typical exponential form is obtained. 

This constant k is immutable for radioactive disintegrations (hence its application to the measurement of time by atomic clocks ), but depends essentially on temperature for chemical reactions, qualified for this reason as thermal reactions. 

Atoms with the same number of protons but a different number of neutrons are called isotopes. To identify an isotope we use the symbol E, where E is the element s atomic symbol, Z is the element s atomic number (which is the number of protons), and A is the element s atomic mass number (which is the sum of the number of protons and neutrons). Although isotopes of a given element have the same chemical properties, their nuclear properties are different. The most important difference between isotopes is their stability. The nuclear configuration of a stable isotope remains constant with time. Unstable isotopes, however, spontaneously disintegrate, emitting radioactive particles as they transform into a more stable form. 

Since the half-life is independent of the number of radioactive atoms, it remains constant throughout the decay process. Thus, 50% of the radioactive atoms disintegrate in one half-life, 75% in two half-lives, and 87.5% in three half-lives. 

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... 

Chemical forms with at least one radioactive atomic nucleus are radioactive substances. The capability of atomic nuclei to undergo spontaneous nuclear transformation is called radioactivity. Nuclear transformations are accompanied by emission of nuclear radiation (Severa and Bar 1991). The average number of nuclei that disintegrate per unit time (= activity) is directly proportional to the total number of radioactive nuclei. The time for 50% of the original nuclei to disintegrate (= half-life or Tb 1/2) is equal to In 2/decay constant for that element (Kiefer 1990). Radiations... 

With respect to an enzyme, the rate of substrate-to-product conversion catalyzed by an enzyme under a given set of conditions, either measured by the amount of substance (e.g., micromoles) converted per unit time or by concentration change (e.g., millimolarity) per unit time. See Specific Activity Turnover Number. 2. Referring to the measure of a property of a biomolecule, pharmaceutical, procedure, eta, with respect to the response that substance or procedure produces. 3. See Optical Activity. 4. The amount of radioactive substance (or number of atoms) that disintegrates per unit time. See Specific Activity. 5. A unitless thermodynamic parameter which is used in place of concentration to correct for nonideality of gases or of solutions. The absolute activity of a substance B, symbolized by Ab, is related to the chemical potential of B (symbolized by /jlb) by the relationship yu,B = RTln Ab where R is the universal gas constant and Tis the absolute temperature. The ratio of the absolute activity of some substance B to some absolute activity for some reference state, A , is referred to as the relative activity (usually simply called activity ). The relative activity is symbolized by a and is defined by the relationship b = Ab/A = If... 

Relation between half-life and decay constant Suppose, after time ty2 half of the atoms of the radioactive substance have disintegrated, that is... 

A sample of 100 mg of a radioactive nuclide decay to 81.85 mg of the same in exactly 7 days. The decay constant for this disintegration and the half life of the nuclide. Calculated ... 

A problem not mentioned in Chapter 15 is one that is very special for radioactive decay when the elapsed time given in the problem is insignificant in comparison with the half-life. Under such circumstances, Equation 26-2 is totally inappropriate, and the proper equation to use is Equation 26-1. In this case, consider —dN to be the number of atoms that disintegrate in a finite period of time df, which is negligible compared to q consider also that A remains constant during this same period of time. The following problem shows this application of Equation 26-1. 

---