Decay processes

Figure Al.6.18. Liouville space lattice representation in one-to-one correspondence with the diagrams in figure A1.6.17. Interactions of the density matrix with the field from the left (right) is signified by a vertical (liorizontal) step. The advantage to the Liouville lattice representation is that populations are clearly identified as diagonal lattice points, while coherences are off-diagonal points. This allows innnediate identification of the processes subject to population decay processes (adapted from [37]).

K, L, M,. ..), 5 is the energy shift caused by relaxation efiects and cp is the work fimction of tlie spectrometer. The 5 tenn accounts for the relaxation effect involved in the decay process, which leads to a final state consisting of a heavily excited, doubly ionized atom. 

Even if the homogeneous line shape can be extracted, many other processes can contribute. Every decay process contributes to the finite lifetime of an excited species. A, with an individual decay constant k ... 

Lifetimes of 1 ps translate into linewidths of about 5 cm Thus, Ime-shape methods are ideally suited to measure very fast decay processes, in particular predissociation of excited species. An example is the... 

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. 

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

The fluorescence lifetime tp can be measured directly and is the lifetime of the state, taking into account all decay processes. It is related to and by... 

Since is of the order of 1 ns, fluorescence is the dominant decay process for 5i. 

The study of the chemical behavior of concentrated preparations of short-Hved isotopes is compHcated by the rapid production of hydrogen peroxide ia aqueous solutions and the destmction of crystal lattices ia soHd compounds. These effects are brought about by heavy recoils of high energy alpha particles released ia the decay process. 

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. 

During this decay process the number of daughter nuclei, D, is increasing at the same rate that the parent is decaying. So,... 

In this decay process, only one particle is emitted and, because energy is conserved, for each level in the daughter nucleus there is a unique a-particle energy. This means that a measurement of the differences in the energies of the a-particles emitted in a radioactive decay gives expHcidy the differences in the energies of the levels in the daughter nucleus. 

There are two processes where nuclear and atomic contributions are iaterrelated. These are the emission of electrons from the atomic shells as an alternative to the emission of a photon and the emission of bremsstrahlung photons ia the P decay process. 

Scavenging may also be considered as an exponential decay process ... 

Ohmic charge decay processes obey a first order rate law from which the charge Q remaining at any time t can be expressed in terms of the initial charge Qq and relaxation time constant r. Using Eqs. (2-3.4) through (2-3.5) the time constant r can alternatively be expressed as... 

The absorpdon may be monitored via a secondary decay process that is surface-sensitive, such as the emission of Auger electrons, which have a well-defined energy and a short mean ftee path. 

The emission of y rays follows, in the majority of cases, what is known as P decay. In the P-decay process, a radionuclide undergoes transmutation and ejects an electron from inside the nucleus (i.e., not an orbital electron). For the purpose of simplicity, positron and electron capture modes are neglected. The resulting transmutated nucleus ends up in an excited nuclear state, which prompdy relaxes by giving offy rays. This is illustrated in Figure 2. 

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 ... 

The annual cycle depicted in Figure 3 could, therefore, be due to a redox cycle whose kinetics are controlled by pH, decay processes in the sediment, and temperature. 

The fastest reliable PMC transients recorded at electrodes (ZnO single crystals24) were limited by the lifetime of a 10-ns laser flash. It was apparent from the nondeconvoluted signal at shorter time scales that much faster decay processes took place and would be accessible with faster laser pulses. 

How can such problems be counterbalanced Since a large capacitance of a semiconductor/electrolyte junction will not negatively affect the PMC transient measurement, a large area electrode (nanostructured materials) should be selected to decrease the effective excess charge carrier concentration (excess carriers per surface area) in the interface. PMC transient measurements have been performed at a sensitized nanostructured Ti02 liquidjunction solar cell.40 With a 10-ns laser pulse excitation, only the slow decay processes can be studied. The very fast rise time cannot be resolved, but this should be the aim of picosecond studies. Such experiments are being prepared in our laboratory, but using nanostructured... 

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 ... 

Actinium-225 decays by successive emission of three u particles, (a) Write the nuclear equations for the three decay processes, (b) Compare the neutron-to-proton ratio of the final daughter product with that of actinium-225. Which is closer to the band of stability ... 

Example H,0+(aq) + HS"(s) - H2S(g) + H20(1). proton emission A nuclear decay process in which a proton is emitted. In proton emission, the mass and charge numbers of the nucleus both decrease by 1. proton-rich nucleus A nucleus that has a low proportion of neutrons and lies below the band of stability. proton transfer equilibrium The equilibrium involving the transfer of a hydrogen ion between an acid and a base. 

The LIF technique is extremely versatile. The determination of absolute intermediate species concentrations, however, needs either an independent calibration or knowledge of the fluorescence quantum yield, i.e., the ratio of radiative events (detectable fluorescence light) over the sum of all decay processes from the excited quantum state—including predissociation, col-lisional quenching, and energy transfer. This fraction may be quite small (some tenths of a percent, e.g., for the detection of the OH radical in a flame at ambient pressure) and will depend on the local flame composition, pressure, and temperature as well as on the excited electronic state and ro-vibronic level. Short-pulse techniques with picosecond lasers enable direct determination of the quantum yield [14] and permit study of the relevant energy transfer processes [17-20]. 

---