Isotope approximate ratios

Element Isotopes Approximate ratio Exact ratio... 

Approximate ratios of isotope abundance ratios are important in identifying elements. For example, the naturally occurring Cl, Cl isotopes exist in an abundance ratio of about 3 1, and C, exist in a ratio of about 99 1. 

Routine mass spectrometry can be used to identify many elements from their approximate ratios of isotope abundances. For example, mercury-containing compounds give ions having the seven isotopes in an approximate ratio of 0.2 10.1 17.0 23.1 13.2 29.7 6.8. 

Figure 5A shows experimentally derived profiles of pH vs rate for reactions in H2O and D2O [30, 50, 71]. The magnitude of the apparent isotope effect (ratio of rate constants in H2O and D2O) is 4.4 and the profiles appear to support the possibility that a proton is transferred from (Mg -bound) water molecules. However, careful analysis led us to conclude that a metal ion binds directly to the 5 -oxygen. Since the concentration of the deproto-nated 2 -oxygen in H2O should be higher than that in D2O at a fixed pH, we must take into account this difference in pKa, namely ApKa (=pKa °-pKa ), when we analyze the solvent isotope effect of D2O [30, 50, 68, 71]. We can estimate the pKa in D2O from the pKa in H2O using the linear relationship shown in Fig. 5B [30, 68, 73-75]. If the pKa for a Mg -bound water molecule in H2O is 11.4, the ApKa is calculated to be 0.65 (solid line in Fig. 5B). Then, the pKa in D2O should be 12.0. Demonstrating the absence of an intrinsic isotope effect (kH2o/kD20=l)> the resultant theoretical curves closely fit the experimental data, with an approximate 4-fold difference in...

In an experiment two of the sample vessels contain the two different Isotopic solutions. The pressure difference between them is monitored to approximately. 03% or 11).001 mm, whichever Is larger. The other two vessels contain a solution of the normal Isomer being compared against a standard solution, pure solvent, or vacuum. One run over the temperature range therefore furnishes us with a set of data on the total pressure and the Isotopic pressure ratio as a function of temperature. 

In order to reduce systematic errors, such as ion counting errors due to detector dead time, it is better to fix the isotope amount ratio as close to unity as possible. In order to do this it is necessary to know the approximate concentration of the analyte in the sample prior to spiking. An exact 1 1 isotope amount ratio can be achieved by using an iterative matching... 

Very often, one assumes that the vibrational frequencies in the reacting molecule are identical with those in the activated complex with the exception of the vibrational frequency corresponding to the rupture of the bond (vn-). In this approximation, and at low temperatures or high vibrational frequency for the bond of interest, the logarithm of the isotopic rate ratio k /k is given by... 

Geologists have used U-238 to determine the approximate geological history of the Earth. Uranium-238 decays to the stable lead-206 isotope. The ratio of lead to uranium can then be used to estimate the age of a rock. Thus, on Earth all rocks that contain uranium also contain lead. 

Disregarding the tunnel effects (see Sect. 1.5) and staying within the approximation rigid rotator-harmonic oscillator, one may, for the biomolecular reaction A -h B), calculate the kinetic isotopic effect (ratio between the reaction rate constant of the compound with the light isotope and the rate constant K2 of the compound containing the heavy isotope) from the Bigeleisen equation ... 

Isotopes of an element are formed by the protons in its nucleus combining with various numbers of neutrons. Most natural isotopes are not radioactive, and the approximate pattern of peaks they give in a mass spectrum can be used to identify the presence of many elements. The ratio of abundances of isotopes for any one element, when measured accurately, can be used for a variety of analytical purposes, such as dating geological samples or gaining insights into chemical reaction mechanisms. 

Other important areas of mass spectrometric investigation of isotope ratios need accurate, not approximate values. For example, for some investigations in archaeology, pharmaceuticals, and chemistry, very accurate precise ratios of isotope abundances are needed. 

For marble provenance studies, the most successful technique seems to be the measurement, through mass spectrometry, of the abundance ratios of the stable isotopes of carbon and oxygen (116). However, no single technique appears to provide unequivocal results, especially in cases such as the different Mediterranean sources, and a combination is often necessary to arrive at an approximate place of origin (117). 

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. 

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