Mass of isotope

STRATEGY The total mass of isotope in a sample is proportional to the number of nuclei of that isotope that the sample contains therefore, the time dependence of the mass follows the radioactive decay law, Eq. 3. We let m denote the total mass of the radioactive isotope at time t and m0 its initial mass. 

Mass spectrometers can measure the masses of isotopes and molecules with high accuracy. Scientists use this capability to solve a variety of problems. Mass spectrometers are essential instruments in labora-tories that study topics as varied as drug identification and climatic change. 

Element Atomic Isotope Atomic mass of isotope % abundance... 

First tabulate the isotopes symbols, the mass of isotope and its associated packing fraction. 

Isotope Symbol Mass of Isotope (u) Packing Fraction... 

The last step in Urey s derivation is the application of the Redlich-Teller product rule (e.g., Angus et al. 1936 Wilson et al. 1955), which relates the vibrational frequencies, moments of inertia, and molecular masses of isotopically substituted molecules. For CIO,... 

The masses of isotopes can be measured with accuracies better than parts per billion (ppb), e.g., m40Ar = 39.9623831235 0.000000005 u. Unfortunately, determinations of abundance ratios are less accurate, causing errors of several parts per million (ppm) in relative atomic mass. The real limiting factor, however, comes from the variation of isotopic abundances from natural samples, e.g., in case of lead which is the final product of radioactive decay of uranium, the atomic weight varies by 500 ppm depending on the Pb/U ratios in the lead ore. [8]... 

This fundamental equation explains that the velocity of heavier ions (iq of ions with mass m,) is lower than of lighter ions (v2 of ions with mass m2, with m, > m2). Equation (10) is used directly in time resolved measurements, for example in time-of-flight mass spectrometers (ToF-MS). The charged ions of the extracted and accelerated ion beam are separated by their mass-to-charge ratio, m/z, in the mass analyzer. Mass-separated ion beams are subsequently recorded by an ion detection system either as a function of time or simultaneously. Mass spectrometers are utilized for the determination of absolute masses of isotopes, atomic weights, relative abundance of isotopes and for quite different applications in survey, trace, ultratrace and surface analysis as discussed in Chapters 8 and 9. 

Furthermore, isotope analysis is relevant for determining the atomic weight (Ar(E)) of elements. The Ar(E) is the average of all masses of all naturally occurring stable isotopes (taking into account the abundances of isotopes) of a chemical element (see Appendix I10). By consideration of the masses of isotopes (/ ,) and the known relative abundances of all stable isotopes (Xi) with i = 1 to n of a selected chemical element, the average atomic weight (Ar(E)) of this element can be calculated ... 

The use of the isotope effect to study rate-determining steps in a sequence of chemical reactions represents an additional advantage of radiotracer methodology. The term isotope effect (to be discussed more fully later) refers to the influence on a reaction rate of the difference in the masses of isotopes. This effect may create significant problems in the use of radioisotopes as tracers but can, nevertheless, be used to advantage in a limited number of cases in order to understand the kinetics of certain chemical reactions. 

The table below lists some common spectral interferences that are encountered in inductively coupled plasma mass spectrometry (ICP-MS), as well as the resolution that is necessary to analyze them.1 The resolution is presented as a dimensionless ratio. As an example, the relative molecular mass (RMM) of the polyatomic ion 15N160+would be 15.000108 + 15.994915 = 30.995023. This would interfere with 31P at a mass of 30.973762. The required resolution would be RMM/8RMM, or 30.973762/0.021261 = 1457. One should bear in mind that as resolution increases, the sensitivity decreases with subsequent effects on the price of the instrument. Note that small differences exist in the published exact masses of isotopes, but for the calculation of the required resolution, these differences are trivial. Moreover, recent instrumentation has provided rapid, high-resolution mass spectra with an uncertainty of less than 0.01%. 

Average atomic mass Average of atomic masses of isotopes by their fractional abundance. 

There the intensity ratios between ion clusters were taken from experimental measurement of low resolution MS [89], but intensity ratios within each isotope cluster was calculated as the sum of binary distributions of the natural abundance of each isotope involved. High resolution m/z values of major peaks (for HRMS) were calculated as sums of exact masses of isotopes. This simulation method (ISOCLUST) developed by the present author (J. Paasivirta) is operable with a desk computer. Low resolution electron impact MS is suitable for TCBT determinations, especially by selected ion monitoring (SIM). In this mode, focusing to four ions, m/z 213.0,283.0,285.0, and 320.0, which are not interfered with by PCBs is recommended. In a TCBT study, quantitative results were based on their sum intensity for better signal to noise ratio [91]. 

Isotope/element Natural abundance (%) Half-life (yr) Energy per atom (X10 J) Heat production per unit mass of isotope/element (Wkg-i)... 

The mass spectrometer is used to measure masses of isotopes as well as isotopic abundances, that is, the relative amounts of the isotopes. Helium occurs in nature almost exclusively as He. Its atomic mass can be determined in an experiment such as that illustrated in Figure 5-8. 

Experimentally, we observe that the masses of atoms other than H are always less than the sum of the masses of their constituent particles. We now know why this mass deficiency occurs. We also know that the mass deficiency is in the nucleus of the atom and has nothing to do with the electrons however, because tables of masses of isotopes include the electrons, we shall also include them. 

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