Isotopic estimation

Chromium (atomic mass = 51.9961 amu) has four isotopes. Their masses are 49.94605 amu, 51.94051 amu, 52.94065 amu, and 53.93888 amu. The first two isotopes have a total abundance of87.87%, and the last isotope has an abundance of2365%. What is the abundance of die third isotope Estimate the abundances of die first two isotopes. 

Patel A, Price GD, Mendelssohn MJ (1991) A computer simulation approach to modeling the structure, thermodynamics and oxygen isotope equilibria of silicates. Phys Chem Min 17 690-699 Polyakov VB (1997) Equilibrium fractionation of the iron isotopes estimation from Mossbauer spectroscopy data. Geochim Cosmochim Acta 61 4213-4217... 

Figure 29.2 Schematic overview of the marine nitrogen cycle. A Important species, their oxidation state (vertical axis), and major biological transformations of nitrogen (arrows). B Typical values of the isotopic enrichment factor (e) are shown for reactions that have been characterized isotopically. Estimates of 6 were drawn from the available literature on N2-fixation and the of diazotrophs (Carpenter et al, 1997 Delwiche and Steyn, 1970 Hoering and Ford, 1960 Macko et al., 1987 Montoya et ah, 2002), denitrification (Barford et ah, 1999 Cline and Kaplan, 1975 Delwiche and Steyn, 1970 Mariotti et ah, 1981,1982 McCready et ah, 1983 Miyake and Wada, 1971 Voss et ah, 2001 Wada, 1980 ), nitrification (Delwiche and Steyn, 1970 Mariotti et ah, 1981 Miyake and Wada, 1971 Ybshida, 1988), N03 uptake (Montoya and McCarthy, 1995 Needoba et ah, 2003 Needoba and Harrison, 2004 Pennock et ah, 1996,1998 Wada and Hattori, 1978 Waser et ah, 1998a, 1998b ), NO2 uptake (Wada and Hattori, 1978 Wada, 1980), NH4 uptake (Cifuentes et ah, 1989 Montoya et ah, 1991 Pennock et ah, 1988 Wada, 1980 Wada and Hattori, 1978), and zooplankton excretion (Checkley and Miller, 1989).

PodosekF. A. and Cassen P. (1994) Theoretical, observational, and isotopic estimates of the lifetime of the solar nebula. Meteoritics 29, 6-25. 

More direct measurements of methane oxidation rates, particularly in wetlands and ocean waters, are needed. The use of stable isotope estimates of methane oxidation, which give an indication of total oxidation, should continue, but direct rate measurements using both " C-CH4 and H-CH4 should be a priority. Pulse-labeling experiments conducted through a growing season are needed to resolve the effect of plant phenology on methane emission. The methane oxidation threshold suggested by a number of open ocean rate measurements should be studied in open ocean samples from areas near and well removed from shelf vent sources. 

Phinney D (1972) Ar, Kr, and Xe in terrestrial materials. Earth Planet Sci Lett 16 413-420 Phinney D, Tennyson J, Frick U (1978) Xenon in CO2 well gas revisited. J Geophys Res 83 2313-2319 Podosek FA, CassenP (1994) Theoretical, observational, and isotopic estimates of the lifetime of the solar nebula. Meteoritics 29 6-25... 

Krypton clathrates have been prepared with hydroquinone and phenol. 85Kr has found recent application in chemical analysis. By imbedding the isotope in various solids, kryptonates are formed. The activity of these kryptonates is sensitive to chemical reactions at the surface. Estimates of the concentration of reactants are therefore made possible. Krypton is used in certain photographic flash lamps for high-speed photography. Uses thus far have been limited because of its high cost. Krypton gas presently costs about 30/1. 

Twenty isotopes are known. Radon-22, from radium, has a half-life of 3.823 days and is an alpha emitter Radon-220, emanating naturally from thorium and called thoron, has a half-life of 55.6 s and is also an alpha emitter. Radon-219 emanates from actinium and is called actinon. It has a half-life of 3.96 s and is also an alpha emitter. It is estimated that every square mile of soil to a depth of 6 inches contains about 1 g of radium, which releases radon in tiny amounts into the atmosphere. Radon is present in some spring waters, such as those at Hot Springs, Arkansas. 

The uses of nuclear fuels to generate electrical power, to make isotopes for peaceful purposes, and to make explosives are well known. The estimated world-wide capacity of the 429 nuclear power reactors in operation in January 1990 amounted to about 311,000 megawatts. 

A more detailed study of the nitration of quinolinium (l) in 80-05 % sulphuric acid at 25 °C, using isotopic dilution analysis, has shown that 3-) 5-) 6-, 7- and 8-nitroquinoline are formed (table 10.3). Combining these results with the kinetic ones, and assuming that no 2- and 4-nitration occurs, gives the partial rate factors listed in table 10.4. Isoquinolinium is 14 times more reactive than quinolinium. The strong deactivation of the 3-position is in accord with an estimated partial rate factor of io for hydrogen isotope exchange at the 3-position in the pyridinium ion. It has been estimated that the reactivity of this ion is at least 10 less than that of the quinolinium ion. Based on this estimate, the partial rate factor for 3-nitration of the pyridinium ion would be less than 5 x io . 

Predict the products formed when each of the following isotopically substituted denvatives of chlorobenzene is treated with sodium amide in liquid ammonia Estimate as quantitatively as possible the composition of the product mixture The astensk ( ) in part (a) designates C and D in part (b) is... 

A further important use of El mass spectrometry lies in measuring isotope ratios, which can be used in estimating the ages of artifacts, rocks, or fossils. Electron ionization affects the isotopes of any one element equally, so that the true isotope ratio is not distorted by the ionization step. Further information on isotopes can be found in Chapter 46. 

Figure 7.9 shows a schematic representation of this effect, in which the ratio of the two isotopes changes with time. To obtain an accurate estimate of the ratio of ion abundances, it is better if the relative ion yields decrease linearly (Figure 7.9) which can be achieved by adjusting the filament temperature continuously to obtain the desired linear response. An almost constant response for the isotope ratio can be obtained by slow evaporation of the sample, viz., by keeping the filament temperature as low as is consistent with sufficient sensitivity of detection (Figure 7.9). 

Schematic illustrations of the effect of temperature and surface density (time) on the ratio of two isotopes, (a) shows that, generally, there is a fractionation of the two isotopes as time and temperature change the ratio of the two isotopes changes throughout the experiment and makes difficult an assessment of their precise ratio in the original sample, (b) illustrates the effect of gradually changing the temperature of the filament to keep the ratio of ion yields linear, which simplifies the task of estimating the ratio in the original sample. The best method is one in which the rate of evaporation is low enough that the ratio of the isotopes is virtually constant this ratio then relates exactly to the ratio in the original sample.

This accurate measurement of the ratio of abundances of isotopes is used for geological dating, estimation of the ages of antiquities, testing athletes for the use of banned steroids, examining fine details of chemical reaction pathways, and so on. These uses are discussed in this book under various headings concerned with isotope ratio mass spectrometry (see Chapters 7, 14, 15, 16, 17, 47, and 48). 

In a similar vein, mean seawater temperatures can be estimated from the ratio of 0 to 0 in limestone. The latter rock is composed of calcium carbonate, laid down from shells of countless small sea creatures as they die and fall to the bottom of the ocean. The ratio of the oxygen isotopes locked up as carbon dioxide varies with the temperature of sea water. Any organisms building shells will fix the ratio in the calcium carbonate of their shells. As the limestone deposits form, the layers represent a chronological description of the mean sea temperature. To assess mean sea temperatures from thousands or millions of years ago, it is necessary only to measure accurately the ratio and use a precalibrated graph that relates temperatures to isotope ratios in sea water. 

The small differences in physical properties of substances containing elements with isotopes are manifested through mea.surement of isotope ratios. When water evaporates, the vapor is richer in its lighter isotopes ( Hj O) than the heavier one ( Hj O). Such differences in vapor pressures vary with temperature and have been used, for example, to estimate sea temperatures of 10,000 years ago (see Chapter 47). 

Although isotope-dilution analysis can be very accurate, a number of precautions need to be taken. Some of these are obvious ones that any analytical procedure demands. For example, analyte preparation for both spiked and unspiked sample must be as nearly identical as possible the spike also must be intimately mixed with the sample before analysis so there is no differential effect on the subsequent isotope ration measurements. The last requirement sometimes requires special chemical treatment to ensure that the spike element and the sample element are in the same chemical state before analysis. However, once procedures have been set in place, the highly sensitive isotope-dilution analysis gives excellent precision and accuracy for the estimation of several elements at the same time or just one element. 

Plutonium (Pu) is an artificial element of atomic number 94 that has its main radioactive isotopes at 2 °Pu and Pu. The major sources of this element arise from the manufacture and detonation of nuclear weapons and from nuclear reactors. The fallout from detonations and discharges of nuclear waste are the major sources of plutonium contamination of the environment, where it is trapped in soils and plant or animal life. Since the contamination levels are generally very low, a sensitive technique is needed to estimate its concentration. However, not only the total amount can be estimated. Measurement of the isotope ratio provides information about its likely... 

The growth rate for tracers labeled with short-Hved isotopes such as P and was about 10—15% per year from 1990 through 1994. This trend reflects the increased use of these radiochemicals for research in molecular biology and genetics I-labeled tracers have also exhibited similar growth rates in this period. On the other hand, the market for C- and H-labeled chemicals essentiaHy leveled off The overaH growth rate for aH tracer chemicals was estimated at 5%/yr for 1990—1994. 

Rhenium, atomic wt 186.2, occurs in nature as two nucHdes Re [14391-28-7] mass 184.9530, in 37.500% abundance and Re [14391-29-8], mass 186.9560, in 62.500% abundance. The latter isotope is radioactive, emitting very low energy radiation and having a half-life estimated at 4.3 ( 0.5) X 10 ° yr. The radioactive decay of this isotope has been used to date accurately the time of Earth s formation. 

Comparison of the measured isotope distributions with simulation data is carried out within the framework of the models corresponding to various developments, accompanied accident of 1986. Estimations of characteristics of physical influence (temperature, etc.) to which ChAPS s concrete stmcture have been undergone are discussed. 

Due to the relative uniformity of ion formation by the RF spark (although its timing is erratic), the most widely used method of quantitation in SSMS is to assume equal sensitivity for all elements and to compare the signal for an individual element with that of the total number of ions recorded on the beam monitor. By empirically calibratii the number of ions necessary to produce a certain blackness on the plate detector, one can estimate the concentration. The signal detected must be corrected for isotopic abundance and the known mass response of the ion-sensitive plate. By this procedure to accuracies within a factor of 3 of the true value can be obtained without standards. 

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