What Is the Number of Neutrons in Carbon

Surface and Ground Water, Weathering, and Soils

C. Kendall , D.H. Doctor , in Treatise on Geochemistry, 2003

5.11.1.2.1. Basic principles

Isotopes are atoms of the same element that have different numbers of neutrons but the same number of protons and electrons. The difference in the number of neutrons between the various isotopes of an element means that the various isotopes have different masses. The superscript number to the left of the element abbreviation indicates the number of protons plus neutrons in the isotope. For example, among the hydrogen isotopes, deuterium (denoted as ²H or D) has one neutron and one proton. This is approximately twice the mass of protium (¹H), whereas tritium (³H) has approximately three times the mass of protium.

The stable isotopes have nuclei that do not decay to other isotopes on geologic timescales, but may themselves be produced by the decay of radioactive isotopes. Radioactive (unstable) isotopes have nuclei that spontaneously decay over time to form other isotopes. For example, ¹⁴C, a radioisotope of carbon, is produced in the atmosphere by the interaction of cosmic-ray neutrons with stable ¹⁴N. With a half-life of ∼5,730 yr, ¹⁴C decays back to ¹⁴N by emission of a beta particle. The stable ¹⁴N produced by radioactive decay is called "radiogenic" nitrogen. This chapter focuses on stable, nonradiogenic isotopes. For a more thorough discussion of the fundamentals of isotope geochemistry, see Clark and Fritz (1997) and Kendall and McDonnell (1998).

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Analytical Geochemistry/Inorganic INSTR. Analysis

A. Stracke , ... B.C. Reynolds , in Treatise on Geochemistry (Second Edition), 2014

15.4.2.2 'Double Spiking' for IC Measurements

For IC measurements by mass spectrometry, the addition of two spike isotopes and analyses of four or more isotopes of an element can help distinguish the isotope fractionation that occurs before the equilibration of the spike-sample mixture from any isotope fractionation that occurs afterward. This so-called double-spike technique is used to separate natural isotope fractionations from those induced by chemical processing and analytical measurements. Alternatively, the addition of two spike isotopes may enable mass fractionation corrections to be made for elements that do not have enough stable nonradiogenic isotopes available for internal normalization, such as Pb ( Compston and Oversby, 1969; Galer, 1999). Owing to the increasing impact of natural stable isotope fractionation on earth and planetary science research that has been sparked by analytical advances in mass spectrometry, there has been renewed interest in applying this well-established method. Double-spike techniques are particularly useful for correcting for instrumental mass fractionation and for quantifying natural stable isotope variations for elements ranging from Ca to U (e.g., DePaolo, 2004; Stirling et al., 2007).

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Surface And Groundwater, Weathering and Soils

C. Kendall , ... M.B. Young , in Treatise on Geochemistry (Second Edition), 2014

7.9.1.2.1 Basic principles

Isotopes are atoms of the same element that have different numbers of neutrons but the same number of protons and electrons. The difference in the number of neutrons between the various isotopes of an element means that the various isotopes have different masses. The superscript number to the left of the element abbreviation indicates the number of protons plus neutrons in the isotope. For example, among the hydrogen isotopes, deuterium (denoted as ²H or D) has one neutron and one proton. This is approximately twice the mass of protium (¹H), whereas tritium (³H) has approximately three times the mass of protium.

The stable isotopes have nuclei that do not decay to other isotopes on geologic time scales but may themselves be produced by the decay of radioactive isotopes. Radioactive (unstable) isotopes have nuclei that spontaneously decay over time to form other isotopes. For example, ¹⁴C, a radioisotope of carbon, is produced in the atmosphere by the interaction of cosmic-ray neutrons with stable ¹⁴N. With a half-life of about 5730 years, ¹⁴C decays back to ¹⁴N by emission of a beta particle. The stable ¹⁴N produced by radioactive decay is called 'radiogenic' nitrogen. This chapter not only focuses on stable, nonradiogenic, isotopes of several elements (hydrogen, oxygen, carbon, nitrogen, and sulfur) but also includes brief discussion of radioisotopes of these elements (³H, ¹⁴C, ³⁵S) that are important hydrological tracers. For a more thorough discussion of the fundamentals of isotope geochemistry, see chapters in Clark and Fritz (1997) and the Kendall and Caldwell (1998) chapter in Kendall and McDonnell (1998).

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Nuclear Waste

Paul K. Andersen , ... Majid Ghassemi , in Encyclopedia of Energy, 2004

3.9 Plutonium

Isotopes of plutonium (Pu, atomic number 94) are generated by neutron capture in uranium-238 or thorium-232. Plutonium-239 (half-life 24,110 years) is of greatest concern because it is fissionable. Other important isotopes are plutonium-238 (half-life 87.7 years), plutonium-240 (half-life 6564 years), plutonium-241 (half-life 13 years), and plutonium-242 (half-life 3.76×10 ⁵ years). All of these isotopes have very high radiotoxicity.

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Analytical Geochemistry/Inorganic INSTR. Analysis

J.W. Olesik , in Treatise on Geochemistry (Second Edition), 2014

15.17.11.4.3 Internal standardization using a pair of isotopes of another element

Isotopes of an element other than the analyte element can be added to the sample for mass bias correction. Tl isotopes have been used for Pb mass bias correction, Tl for Hg, Zn for Cu, Cu for Zn, Zr for Mo, Ru for Mo, Zr for Sr, and Zr for Rb. In order to correct for element-dependent mass bias, the signals for the added isotopes can be calibrated against a certified reference material. In this approach, the concentrations of the analyte element and added element in the sample must be carefully matched to those in the standard.

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Geochemistry of Estuaries and Coasts

M.F. Fitzsimons , ... G.E. Millward , in Treatise on Estuarine and Coastal Science, 2011

4.04.4.6 The Use of Isotopes as Tracers of SPM-Associated Trace Metals

Isotopes have been used as tracers of SPM-associated trace metals, and to identify the export of these metals from estuarine environments ( Bergquist and Boyle, 2006; Ingri et al., 2006; de Jong et al., 2007; Escoube et al., 2009). For example, Fe isotopes have been employed to identify the two major suspended fractions of colloidal Fe in river water: the oxyhydroxide phase, which shows positive δ⁵⁶Fe values, and the fulvic fraction, which has a more negative signal (Ingri et al., 2006). River water–seawater mixing experiments by Bergquist and Boyle (2006) have shown that aggregated Fe was enriched in heavy isotopes. Therefore, the aggregation and sedimentation of the oxyhydroxide fraction during estuarine mixing should remove heavy isotopes from surface SPM, resulting in a more negative signal in the suspended phase (Breitbarth et al., 2010). A recent study examined the process of potential fractionation of Fe-isotopes during estuarine mixing and flocculation and found that it produced minimal Fe-isotope fractionation suggesting that the δ⁵⁶Fe of the dissolved Fe pools preserved during estuarine mixing (Escoube et al., 2009). Cycling of Fe in coastal areas appears to result in the export of a negative Fe isotope signal from benthic sources and slightly positive δ⁵⁶Fe values from rivers in the truly dissolved fraction. Thus, Fe-isotopes can provide valuable tracers to distinguish the various Fe-sources in coastal oceans (Escoube et al., 2009). A similar result was found for δ⁶⁵Cu, where the isotopically heavy dissolved phase of all the rivers originates in an isotopic partitioning of the weathered pool of δ⁶⁵Cu between a light fraction, adsorbed to particulates, and a heavy, dissolved fraction dominated by δ⁶⁵Cu bound to strong organic complexes (Vance et al., 2008). Recent advances suggest that Fe and Cu isotope measurements have the potential to provide important, new information on trace metal cycling and transport from coastal areas to the open ocean and their potential impact in marine ecosystems.

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Carbon Isotope Stratigraphy

Darren R. Gröcke , in Stratigraphy & Timescales, 2020

1.2 Definition of isotope stratigraphy

Isotope stratigraphy can be broadly defined as the variation of a stable isotope signature preserved in the sedimentary record through a period of time. It is a sub-discipline of chemostratigraphy that looks at the chemical signature of sediments through time; most chemostratigraphic studies, however, use stratigraphic changes in trace element and rare earth element abundances to define and correlate sedimentary packages (e.g., Hines et al., 2019; LaGrange et al., 2020; Mackey and Stewart, 2019). With respect to the definition of isotope stratigraphy, time can be defined as anything greater than seasonal, and therefore include research in many other disciplines, such as limnology, glaciology, archeology and pedology. Isotope stratigraphy also relies on similar principles in Darwin's theory of evolution. That is, in order for isotope stratigraphy to work and be informative about the history of biogeochemical cycles, it must rely on the fact that the stable isotope ratio (δX, where X is any isotope system of interest, e.g., ¹³C or ¹⁵N or ³⁴S) will evolve/change through time, and those changes are dictated by climate/environmental changes in that global cycle.

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Physical Properties of Water

K.M. Stewart , in Encyclopedia of Inland Waters, 2009

Isotopes

An isotope is one of two or more forms of the same chemical element. Different isotopes of an element have the same number of protons in the nucleus, giving them the same atomic number, but a different number of neutrons giving each elemental isotope a different atomic weight. Isotopes of the same element have different physical properties (melting points, boiling points) and the nuclei of some isotopes are unstable and radioactive. For water (H ₂O), the elements hydrogen (atomic number 1) and oxygen (atomic number 16) each have three isotopes: ¹H, ²H, and ³H for hydrogen; ¹⁶O, ¹⁷O, and ¹⁸O for oxygen. In nature, the ¹H and ¹⁶O (usually just given as O) isotopes are by far the most common. In water, the water molecule may be given as ¹H₂O or hydrogen oxide, ²H₂O or deuterium oxide, and ³H₂O or tritium oxide, the radioactive one. Both of the latter two are sometimes called heavy water because of their increased mass. However, the phrase 'heavy water' gained notoriety primarily because of the association of ²H₂O or deuterium oxide, also called the deuterated form of water, in the development of nuclear weapons. Many elements have isotopes, but the isotopes of hydrogen and oxygen are of particular interest because fractionation occurs in vapor–liquid–solid phase changes. Heavier molecular 'species' tend to be enriched in the condensation phase and lighter molecular 'species' in the vapor phase. Some isotopes can be used to great advantage as tracers in understanding water movements and exchanges within atmospheric, oceanic, lake, stream, and ground water systems.

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Volume 5

Yan Hu , Fang-Zhen Teng , in Encyclopedia of Geology (Second Edition), 2021

Mass-Independent Isotope Fractionation

Isotope fractionation in most terrestrial and extraterrestrial samples is mass-dependent, i.e., the magnitude of fractionation among three or more isotopes directly depends on their mass differences. For example, mass difference between ¹⁷O and ¹⁶O is about half of that between ¹⁸O and ¹⁶O, hence the fractionation between ¹⁷O and ¹⁶O is about half of that of ¹⁸O and ¹⁶O. However, studies of extraterrestrial materials by Clayton et al. (1973) revealed the first mass-independent fractionation of O isotopes, originally interpreted as a result of nucleosynthetic effect and later explained by the involvement of photochemical reactions (Dauphas and Schauble, 2016). Subsequent studies also observed large mass-independent fractionation of S isotopes in geological record (Farquhar and Wing, 2003), which was also produced primarily by photochemical reactions.

Many non-traditional stable isotopes have high atomic numbers with more than two stable isotopes, which allows studies of mass-independent fractionation. Mercury isotopes display the most significant mass-independent isotope fractionation among both odd and even isotopes, reflecting magnetic isotope effects and nuclear volume effects during photochemical reactions (Blum et al., 2014). Non-traditional stable isotopes of many other heavy elements (e.g., Cr, Ni, Mo, Ba, Nd) also display mass-independent fractionation in meteorites. These isotopic anomalies mainly result from nucleosynthetic effects during formation of the Solar System (Dauphas and Schauble, 2016); chapters dedicated to nucleosynthesis (Yokoyama and Tsujimoto) and nucleosynthetic heterogeneities in meteorites (Steele) can be found in this Encyclopedia.

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Volume 5

Jennifer C. Stern , Scott T. Wieman , in Encyclopedia of Geology (Second Edition), 2021

Equilibrium and Kinetic Isotope Fractionation

Isotope fractionations are usually discussed in terms of whether they are equilibrium or kinetic processes. These two designations cover most fractionations, with kinetic fractionation referring to a broad range of non-equilibrium processes such as evaporation and diffusion. Equilibrium isotope fractionation occurs primarily due to differences in vibrational frequencies of isotopologues, and as such is a function of temperature. The consequence of this is that heavier isotopes form stronger bonds than light isotopes, and at equilibrium, the heavier isotope will partition into the phase with the stronger bond ( White, 2015). Isotope fractionation is large at Earth's surface temperatures and decreases with increasing temperature until α approaches 1 at igneous temperatures. This temperature dependence forms the basis for stable isotope geothermometry and paleothermometry. Equilibrium fractionation factors can be predicted by quantum statistical mechanics (Chacko et al., 2001), although most fractionation factors in stable isotope geochemistry have also been determined experimentally.

Kinetic isotope fractionation is caused by uni-directional reactions such as distillation, evaporation, diffusion, crystallization, and redox reactions. In these reactions, lighter isotopes, because they form weaker bonds that are more readily broken, react faster than heavier isotopes. Biological reactions in particular can exhibit large kinetic fractionation effects and these large fractionations can be used as tracers of biological activity and specific metabolic processes.

Fractionations are also dependent on whether the system is open, and product is removed or cannot back-react, or closed, and products may back-react. Rayleigh fractionation or distillation describes open system equilibrium fractionation and kinetic fractionation by uni-directional reactions with a finite source of reactant, which is functionally analogous to open system equilibrium reactions where products are removed and not allowed to back react . Rayleigh fractionation can be expressed as the equation:

(6) $\mathbf{R}\mathbf{=}{\mathbf{R}}_{\mathbf{0}}\cdot {\mathit{f}}^{\left(\mathbf{\alpha }-\mathbf{1}\right)}$

where R, the isotopic composition of a phase is a function of the initial isotope ratio R₀, the fraction of material f remaining in the reservoir, and the fractionation factor α. Fig. 1 shows Rayleigh fractionation of water during evaporation, a kinetic process that can be described by the Rayleigh equation. As water with R₀  =   0‰ evaporates (curve A), the residual water becomes heavier due to the removal of the light isotope, following Eq. 6. The δ¹⁸O of instantaneous vapor (curve B) is 10‰ lighter than the residual water, but also becomes heavier as the reaction progresses. The accumulated vapor (curve C) does not exceed the fractionation dictated by the equilibrium fractionation factor between water and water vapor at a given temperature. Closed system equilibrium fractionation is demonstrated by lines D and E.

Fig. 1. In an open system described by Rayleigh fractionation, water vapor is removed as it evaporates. As liquid water A with δ¹⁸O   =   0 evaporates, the δ¹⁸O of instantaneous water vapor B is 10‰ lighter than water. As the reaction progresses, the remaining liquid water reservoir A becomes increasingly depleted in ¹⁸O, as does the forming vapor B. If the reaction goes to completion, and no liquid water remains, accumulated vapor C has the same δ¹⁸O as the starting liquid. Dotted lines D and E describe a two phase, closed system. A, B, and C also describe closed system kinetic isotope fractionation (in which there is a finite source of reactant), where A is the reactant, B is the instantaneous product, and C is the accumulated product.

Redrawn from Gat JR and Gonfiantini R (1981) Stable Isotope Hydrology. Deuterium and Oxygen-18 in the Water Cycle. In: Gat JR and Gonfiantini R (eds.), International Atomic Energy Agency: Vienna as published in International Atomic Energy Agency, Stable Isotope Hydrology, Technical Reports Series No. 210, Vienna: IAEA.

Most isotope fractionation is mass dependent. When there are more than two stable isotopes of an element, such as oxygen or sulfur, isotope fractionations between different pairs of isotope ratios (e.g., ¹⁶O/¹⁷O and ¹⁶O/¹⁸O) can be predicted based on the relative mass difference between the isotopes and are therefore called mass dependent isotope fractionations. When fractionation significantly deviates from this relationship, it is called mass independent fractionation (MIF). For example, the mass dependent fractionation between the three isotopes of oxygen can be predicted by the relationship δ¹⁷O   ≈   0.5 δ¹⁸O, reflecting the relative mass differences between ¹⁶O, ¹⁷O, and ¹⁸O. The line with slope ≈   0.5 produced by plotting δ¹⁷O vs. δ¹⁸O is referred to as the terrestrial fractionation line. When this slope departs significantly from the prediction, fractionation is caused by something other than, or addition to, mass difference. MIF is reported using Δ or cap delta, which represents the difference between the expected mass-dependent fractionation and the actual fractionation measured.

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What Is the Number of Neutrons in Carbon

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