Nuclides ratios

Table 6.1 shows some other best-fit parameters to Solar-System s-process abundances. The seed nucleus is basically 56Fe light nuclei have low cross-sections (but can act as neutron poisons , e.g. 14N for the 13C(a, n) neutron source), whereas heavier nuclei are not abundant enough to have a major influence. Certain nuclidic ratios, e.g. 37Cl/36Ar and 41K/40Ca, indicate that under 1 per cent of Solar-System material has been s-processed. 

Example Problem In a rock, one finds a nuclidic ratio of 206Pb to 238U of 0.60. 

Figure 16.7 Relative error of total activity estimates based on nuclide ratio and the Pb x 10 estimate as a function of time...

Apart from the activity ratios of the radon-222 decay product radionuclides, the residence time of tropospheric aerosols can be derived from the activity ratios of the fission product radionuclides released into the atmosphere during the explosions from nuclear weapons testing or nuclear reactor accidents, such as Sr/ Sr and " Ba/ Sr. These nuclide ratios are considered as nuclear clocks. The applicability of the radionuclide ratios depends on whether steady-state conditions hold at the time and place of measurement and on the kind of sample, whether surface air or precipitation (rain or snow), used for the radioisotope activity determination. 

The equation describes the manner in which the nuclear magnetization, M, at position r and time t processes about the magnetic flux density, B, in which it is found. The constant y is the magnetogyric ratio of the nuclides under study. The precessional frequency, co, is given by the Lannor equation. 

Our present views on the electronic structure of atoms are based on a variety of experimental results and theoretical models which are fully discussed in many elementary texts. In summary, an atom comprises a central, massive, positively charged nucleus surrounded by a more tenuous envelope of negative electrons. The nucleus is composed of neutrons ( n) and protons ([p, i.e. H ) of approximately equal mass tightly bound by the force field of mesons. The number of protons (2) is called the atomic number and this, together with the number of neutrons (A ), gives the atomic mass number of the nuclide (A = N + Z). An element consists of atoms all of which have the same number of protons (2) and this number determines the position of the element in the periodic table (H. G. J. Moseley, 191.3). Isotopes of an element all have the same value of 2 but differ in the number of neutrons in their nuclei. The charge on the electron (e ) is equal in size but opposite in sign to that of the proton and the ratio of their masses is 1/1836.1527. 

We can use Fig. 17.13 to predict the type of disintegration that a radioactive nuclide is likely to undergo. Nuclei that lie above the band of stability are neutron rich they have a high proportion of neutrons. These nuclei tend to decay in such a way that the final n/p ratio is closer to that found in the band of stability. For example, a l4C nucleus can reach a more stable state by ejecting a (3 particle, which reduces the n/p ratio as a result of the conversion of a neutron into a proton (Fig. 17.15) ... 

Nuclides that lie below the belt of stability have low neutron-proton ratios and must reduce their nuclear charges to become stable. These nuclides can convert protons into neutrons by positron emission. Positrons (symbolized jS ) are particles with the same mass as electrons but with a charge of -Ft instead of-1. Here are three examples ... 

A nuclide with a low neutron-proton ratio can also reduce its nuclear charge by capturing one of its 1 S orbital... 

Neutrons readily induce nuclear reactions, but they always produce nuclides on the high neutron-proton side of the belt of stability. Protons must be added to the nucleus to produce an unstable nuclide with a low neutron-proton ratio. Because protons have positive charges, this means that the bombarding particle must have a positive charge. Nuclear reactions with positively charged particles require projectile particles that possess enough kinetic energy to overcome the electrical repulsion between two positive particles. 

Eission products often are radioactive. This is because the fissioning nucleus has an // Z ratio of 1.54, so its products have a similar N Z ratio, hi contrast, stable nuclides in the = 77 to 157 range have ratios of around 1.3, so the products of fission have excess neutrons, making them unstable. 

C22-0034. Determine Z, A, and N for each of the following nuclides (a) the nuclide of neon that contains the same number of protons and neutrons (b) the nuclide of lead that contains 1.5 times as many neutrons as protons and (c) the nuclide of zirconium whose neutron-proton ratio is 1.25. 

This situation, when the activity of the higher atomic number nuclide, the parent, is equal to the activity in the next step in the chain, the daughter, is known as radioactive equilibrium (also referred to as secular equilibrium). Thus, secular equilibrium between a parent and a daughter implies an activity ratio of 1. 

Processes that fractionate nuclides within a chain produce parent-daughter disequilibrium the return to equilibrium then allows quantification of time. Because of the prescribed decay behavior, U-series disequilibria can be used for geochronology or for examining the rates and time scales of any dynamic processes which induces fractionation. In many cases, the direction of disequilibrium (activity ratios above or below one) provides a powerful means of tracing specific processes. 

One of the behaviors of the system not easy to grasp is why the return to equilibrium is mostly controlled by the half-life of the daughter nuclide This can be investigated by considering the Ra/ °Th system ( °Th decays to form Ra with a half-life of 1599 years). If fractionation by some process results in an activity ratio greater than 1 at time t = 0, the equation describing the return to equilibrium, as shown above, is ... 

Figure 3. Parent daughter disequilibrium will return to equilibrium over a known time scale related to the half-life of the daughter nuclide. To return to within 5% of an activity ratio of 1 requires a time period equal to five times the half-life of the daughter nuclide. Because of the wide variety of half-lives within the U-decay-series, these systems can be used to constrain the time scales of processes from single years up to 1 Ma.

Secular equilibrium materials. For materials that have remained a closed system for sufficient time that secular equilibrium has been achieved, the half-lives of nuclides within the decay chain can be calculated from the relationship A,pP = A,dD. If the atom ratio P/D is measured, and one of the decay constants is well known, then the other can be readily calculated. Limitations on this approach are the ability to measure the atom ratios to sufficient precision, and finding samples that have remained closed systems for a sufficient length of time. This approach has been used to derive the present recommended half lives for °Th and (Cheng et al. 2000 Ludwig et al. 1992). 

N2)q and (N2/Ni)q represent the initial activity and activity ratio, respectively, just after the fractionation between parenf and daughter nuclides. 

Figure 1. (a) Schematic representation of the evolution by radioactive decay of the daughter-parent (N2/N1) activity ratio as a function of time t after an initial fractionation at time 0. The initial (N2/Ni)o activity ratio is arbitrarily set at 2. Time t is reported as t/T2, where T2 is the half-life of the daughter nuclide. Radioactive equilibrium is nearly reached after about 5 T2. (b) Evolution of (N2/N1) activity ratios for various parent-daughter pairs as a function of time since fractionation (after Williams 1987). Note that the different shape of the curves in (a) and (b) is a consequence of the logarithmic scale on the x axis in (b). 

T = [(N2) - (N2)] / X2 [(N2) - (Ni)] or T = [(N2/Ni) -(N2/Ni)] / X2 [(N2/N1) - 1], where parentheses denote activities or activity ratios (note that (Ni) = (Ni) because of the long half-life of the parent nuclide and the absence of crystal fractionation). If the (N2/N1) ratio is known, then the residence time can be calculated from the measurement of the (N2/N1) ratio in lavas erupted from the central conduit. An eccentric eruption, whose magma has bypassed the reservoir, may provide a value for the (N2/N1) ratio. 

Measurement of U-series disequilibria in MORB presents a considerable analytical challenge. Typical concentrations of normal MORB (NMORB) are variable but are generally in the 50-150 ppb U range and 100-400 ppb Th range. Some depleted MORB have concentrations as low as 8-20 ppb U and Th. The concentrations of °Th, Pa, and Ra in secular equilibrium with these U contents are exceedingly low. For instance, the atomic ratio of U to Ra in secular equilibrium is 2.5 x 10 with a quick rule of thumb being that 50 ng of U corresponds to 20 fg of Ra and 15 fg of Pa. Thus, dissolution of a gram of MORB still requires measurement of fg quantities of these nuclides by any mass spectrometric techniques. 

The initial U activity in the mantle wedge (Uw) is set to an arbitrary value of 1 and all the other nuclides are scaled relative to Uw The initial U activity in the oceanic crust is twice the activity in the mantle wedge. The Th/U ratios of the mantle wedge and the slab are both equal to 2.5. This value is relevant for modeling the higher ( Th/ Th) observed in some arc lavas. Fluid is added to a portion of mantle wedge, and the mass fraction of fluid (f) and the composition of the mixture at time step i is given by (same equation for all the nuclides) ... 

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