Mass (mass spectrometry)

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J. J. Thomson discovered the isotopes of neon using mass spectrometry. Discovery of neon isotopes.JPG
J. J. Thomson discovered the isotopes of neon using mass spectrometry.

The mass recorded by a mass spectrometer can refer to different physical quantities depending on the characteristics of the instrument and the manner in which the mass spectrum is displayed.

Contents

Units

The dalton (symbol: Da) is the standard unit that is used for indicating mass on an atomic or molecular scale (atomic mass). [1] The unified atomic mass unit (symbol: u) is equivalent to the dalton. One dalton is approximately the mass of one a single proton or neutron. [2] The unified atomic mass unit has a value of 1.660538921(73)×10−27  kg . [3] The amu without the "unified" prefix is an obsolete unit based on oxygen, which was replaced in 1961.

Molecular mass

Theoretical isotope distribution for the molecular ion of caffeine Caffeine mass.gif
Theoretical isotope distribution for the molecular ion of caffeine

The molecular mass (abbreviated Mr) of a substance, formerly also called molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u (equal to 1/12 the mass of one atom of 12C). Due to this relativity, the molecular mass of a substance is commonly referred to as the relative molecular mass, and abbreviated to Mr.

Average mass

The average mass of a molecule is obtained by summing the average atomic masses of the constituent elements. For example, the average mass of natural water with formula H2O is 1.00794 + 1.00794 + 15.9994 = 18.01528 Da.

Mass number

The mass number, also called the nucleon number, is the number of protons and neutrons in an atomic nucleus. The mass number is unique for each isotope of an element and is written either after the element name or as a superscript to the left of an element's symbol. For example, carbon-12 (12C) has 6 protons and 6 neutrons.

Nominal mass

The nominal mass for an element is the mass number of its most abundant naturally occurring stable isotope, and for an ion or molecule, the nominal mass is the sum of the nominal masses of the constituent atoms. [4] [5] Isotope abundances are tabulated by IUPAC: [6] for example carbon has two stable isotopes 12C at 98.9% natural abundance and 13C at 1.1% natural abundance, thus the nominal mass of carbon is 12. The nominal mass is not always the lowest mass number, for example iron has isotopes 54Fe, 56Fe, 57Fe, and 58Fe with abundances 6%, 92%, 2%, and 0.3%, respectively, and a nominal mass of 56 Da. For a molecule, the nominal mass is obtained by summing the nominal masses of the constituent elements, for example water has two hydrogen atoms with nominal mass 1 Da and one oxygen atom with nominal mass 16 Da, therefore the nominal mass of H2O is 18 Da.

In mass spectrometry, the difference between the nominal mass and the monoisotopic mass is the mass defect. [7] This differs from the definition of mass defect used in physics which is the difference between the mass of a composite particle and the sum of the masses of its constituent parts. [8]

Accurate mass

The accurate mass (more appropriately, the measured accurate mass [9] ) is an experimentally determined mass that allows the elemental composition to be determined. [10] For molecules with mass below 200 Da, 5 ppm accuracy is often sufficient to uniquely determine the elemental composition. [11]

Exact mass

The exact mass of an isotopic species (more appropriately, the calculated exact mass [9] ) is obtained by summing the masses of the individual isotopes of the molecule. For example, the exact mass of water containing two hydrogen-1 (1H) and one oxygen-16 (16O) is 1.0078 + 1.0078 + 15.9949 = 18.0105 Da. The exact mass of heavy water, containing two hydrogen-2 (deuterium or 2H) and one oxygen-16 (16O) is 2.0141 + 2.0141 + 15.9949 = 20.0229 Da.

When an exact mass value is given without specifying an isotopic species, it normally refers to the most abundant isotopic species.

Monoisotopic mass

The monoisotopic mass is the sum of the masses of the atoms in a molecule using the unbound, ground-state, rest mass of the principal (most abundant) isotope for each element. [12] [5] The monoisotopic mass of a molecule or ion is the exact mass obtained using the principal isotopes. Monoisotopic mass is typically expressed in daltons.

For typical organic compounds, where the monoisotopic mass is most commonly used, this also results in the lightest isotope being selected. For some heavier atoms such as iron and argon the principal isotope is not the lightest isotope. The mass spectrum peak corresponding to the monoisotopic mass is often not observed for large molecules, but can be determined from the isotopic distribution. [13]

Most abundant mass

Theoretical isotope distribution for the molecular ion of glucagon (C153H224N42O50S) Glucagon mass.gif
Theoretical isotope distribution for the molecular ion of glucagon (C153H224N42O50S)

This refers to the mass of the molecule with the most highly represented isotope distribution, based on the natural abundance of the isotopes. [14]

Isotopomer and isotopologue

Isotopomers (isotopic isomers) are isomers having the same number of each isotopic atom, but differing in the positions of the isotopic atoms. [15] For example, CH3CHDCH3 and CH3CH2CH2D are a pair of structural isotopomers.

Isotopomers should not be confused with isotopologues, which are chemical species that differ in the isotopic composition of their molecules or ions. For example, three isotopologues of the water molecule with different isotopic composition of hydrogen are: HOH, HOD and DOD, where D stands for deuterium (2H).

Kendrick mass

The Kendrick mass is a mass obtained by multiplying the measured mass by a numeric factor. The Kendrick mass is used to aid in the identification of molecules of similar chemical structure from peaks in mass spectra. [16] [17] The method of stating mass was suggested in 1963 by the chemist Edward Kendrick.

According to the procedure outlined by Kendrick, the mass of CH2 is defined as 14.000 Da, instead of 14.01565 Da. [18] [19]

The Kendrick mass for a family of compounds F is given by [20]

.

For hydrocarbon analysis, F=CH2.

Mass defect (mass spectrometry)

The mass defect used in nuclear physics is different from its use in mass spectrometry. In nuclear physics, the mass defect is the difference in the mass of a composite particle and the sum of the masses of its component parts. In mass spectrometry the mass defect is defined as the difference between the exact mass and the nearest integer mass. [21] [22]

The Kendrick mass defect is the exact Kendrick mass subtracted from the nearest integer Kendrick mass. [23]

Mass defect filtering can be used to selectively detect compounds with a mass spectrometer based on their chemical composition. [7]

Packing fraction (mass spectrometry)

Francis William Aston won the 1922 Nobel Prize in Chemistry for his discovery, by means of his mass spectrograph, of isotopes, in a large number of non-radioactive elements, and for his enunciation of the whole number rule. Francis William Aston.jpg
Francis William Aston won the 1922 Nobel Prize in Chemistry for his discovery, by means of his mass spectrograph, of isotopes, in a large number of non-radioactive elements, and for his enunciation of the whole number rule.

The term packing fraction was defined by Aston as the difference of the measured mass M and the nearest integer mass I (based on the oxygen-16 mass scale) divided by the quantity comprising the mass number multiplied by ten thousand: [26]

.

Aston's early model of nuclear structure (prior to the discovery of the neutron) postulated that the electromagnetic fields of closely packed protons and electrons in the nucleus would interfere and a fraction of the mass would be destroyed. [27] A low packing fraction is indicative of a stable nucleus. [28]

Nitrogen rule

The nitrogen rule states that organic compounds containing exclusively hydrogen, carbon, nitrogen, oxygen, silicon, phosphorus, sulfur, and the halogens either have an odd nominal mass that indicates an odd number of nitrogen atoms are present or an even nominal mass that indicates an even number of nitrogen atoms are present in the molecular ion. [29] [30]

Prout's hypothesis and the whole number rule

The whole number rule states that the masses of the isotopes are integer multiples of the mass of the hydrogen atom. [31] The rule is a modified version of Prout's hypothesis proposed in 1815, to the effect that atomic weights are multiples of the weight of the hydrogen atom. [32]

See also

Related Research Articles

The molecular mass (m) is the mass of a given molecule: it is measured in daltons. Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quantity relative molecular mass, as defined by IUPAC, is the ratio of the mass of a molecule to the unified atomic mass unit and is unitless. The molecular mass and relative molecular mass are distinct from but related to the molar mass. The molar mass is defined as the mass of a given substance divided by the amount of a substance and is expressed in g/mol. The molar mass is usually the more appropriate figure when dealing with macroscopic (weigh-able) quantities of a substance.

The mole (symbol: mol) is the base unit of amount of substance in the International System of Units (SI). It is defined as exactly 6.02214076×1023elementary entities ("particles"), which may be atoms, molecules, ions, or electrons.

The dalton or unified atomic mass unit is a unit of mass widely used in physics and chemistry. It is defined as 1⁄12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. The atomic mass constant, denoted mu is defined identically, giving mu = m(12C)/12 = 1 Da. A unit dalton is also approximately numerically equal to the molar mass of the same expressed in grams per mole. Prior to the 2019 redefinition of the SI base units these were numerically identical by definition and are still treated as such for most purposes.

In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

Ion source Device that creates charged atoms and molecules (ions)

An ion source is a device that creates atomic and molecular ions. Ion sources are used to form ions for mass spectrometers, optical emission spectrometers, particle accelerators, ion implanters and ion engines.

Mass spectrum Tool in chemical analysis

A mass spectrum is an intensity vs. m/z (mass-to-charge ratio) plot representing a chemical analysis. Hence, the mass spectrum of a sample is a pattern representing the distribution of ions by mass (more correctly: mass-to-charge ratio) in a sample. It is a histogram usually acquired using an instrument called a mass spectrometer. Not all mass spectra of a given substance are the same. For example, some mass spectrometers break the analyte molecules into fragments; others observe the intact molecular masses with little fragmentation. A mass spectrum can represent many different types of information based on the type of mass spectrometer and the specific experiment applied; however, all plots of intensity vs. mass-to-charge are referred to as mass spectra. Common fragmentation processes for organic molecules are the McLafferty rearrangement and alpha cleavage. Straight chain alkanes and alkyl groups produce a typical series of peaks: 29 (CH3CH2+), 43 (CH3CH2CH2+), 57 (CH3CH2CH2CH2+), 71 (CH3CH2CH2CH2CH2+) etc.

Isotopic labeling is a technique used to track the passage of an isotope through a reaction, metabolic pathway, or cell. The reactant is 'labeled' by replacing specific atoms by their isotope. The reactant is then allowed to undergo the reaction. The position of the isotopes in the products is measured to determine the sequence the isotopic atom followed in the reaction or the cell's metabolic pathway. The nuclides used in isotopic labeling may be stable nuclides or radionuclides. In the latter case, the labeling is called radiolabeling.

Isotopologues are molecules that differ only in their isotopic composition. They have the same chemical formula and bonding arrangement of atoms, but at least one atom has a different number of neutrons than the parent.

Fast atom bombardment

Fast atom bombardment (FAB) is an ionization technique used in mass spectrometry in which a beam of high energy atoms strikes a surface to create ions. It was developed by Michael Barber at the University of Manchester in 1980. When a beam of high energy ions is used instead of atoms, the method is known as liquid secondary ion mass spectrometry (LSIMS). In FAB and LSIMS, the material to be analyzed is mixed with a non-volatile chemical protection environment, called a matrix, and is bombarded under vacuum with a high energy beam of atoms. The atoms are typically from an inert gas such as argon or xenon. Common matrices include glycerol, thioglycerol, 3-nitrobenzyl alcohol (3-NBA), 18-crown-6 ether, 2-nitrophenyloctyl ether, sulfolane, diethanolamine, and triethanolamine. This technique is similar to secondary ion mass spectrometry and plasma desorption mass spectrometry.

Monoisotopic mass (Mmi) is one of several types of molecular masses used in mass spectrometry. The theoretical monoisotopic mass of a molecule is computed by taking the sum of the accurate masses of the most abundant naturally occurring stable isotope of each atom in the molecule. For small molecules made up of low atomic number elements the monoisotopic mass is observable as an isotopically pure peak in a mass spectrum. This differs from the nominal molecular mass, which is the sum of the mass number of the primary isotope of each atom in the molecule and is an integer. It also is different from the molar mass, which is a type of average mass. For some atoms like carbon, oxygen, hydrogen, nitrogen, and sulfur the Mmi of these elements is exactly the same as the mass of its natural isotope, which is the lightest one. However, this does not hold true for all atoms. Iron's most common isotope has a mass number of 56, while the stable isotopes of iron vary in mass number from 54 to 58. Monoisotopic mass is typically expressed in daltons (Da), also called unified atomic mass units (u).

The nitrogen rule states that organic compounds containing exclusively hydrogen, carbon, nitrogen, oxygen, silicon, phosphorus, sulfur, and the halogens either have (1) an odd nominal mass that indicates an odd number of nitrogen atoms are present or (2) an even nominal mass that indicates an even number of nitrogen atoms in the molecular formula of the molecular ion. The nitrogen rule is not a rule as much as a general principle which may prove useful when attempting to solve organic mass spectrometry structures.

Isotope-ratio mass spectrometry

Isotope-ratio mass spectrometry (IRMS) is a specialization of mass spectrometry, in which mass spectrometric methods are used to measure the relative abundance of isotopes in a given sample.

History of mass spectrometry

The history of mass spectrometry has its roots in physical and chemical studies regarding the nature of matter. The study of gas discharges in the mid 19th century led to the discovery of anode and cathode rays, which turned out to be positive ions and electrons. Improved capabilities in the separation of these positive ions enabled the discovery of stable isotopes of the elements. The first such discovery was with the element neon, which was shown by mass spectrometry to have at least two stable isotopes: 20Ne and 22Ne. Mass spectrometers were used in the Manhattan Project for the separation of isotopes of uranium necessary to create the atomic bomb.

Whole number rule

In chemistry, the whole number rule states that the masses of the isotopes are whole number multiples of the mass of the hydrogen atom. The rule is a modified version of Prout's hypothesis proposed in 1815, to the effect that atomic weights are multiples of the weight of the hydrogen atom. It is also known as the Aston whole number rule after Francis W. Aston who was awarded the Nobel Prize in Chemistry in 1922 "for his discovery, by means of his mass spectrograph, of isotopes, in a large number of non-radioactive elements, and for his enunciation of the whole-number rule."

Mass spectral interpretation

Mass spectral interpretation is the method employed to identify the chemical formula, characteristic fragment patterns and possible fragment ions from the mass spectra. Mass spectra is a plot of relative abundance against mass-to-charge ratio. It is commonly used for the identification of organic compounds from electron ionization mass spectrometry. Organic chemists obtain mass spectra of chemical compounds as part of structure elucidation and the analysis is part of many organic chemistry curricula.

Atomic mass Rest mass of an atom in its ground state

The atomic mass is the mass of an atom. Although the SI unit of mass is the kilogram, atomic mass is often expressed in the non-SI unit atomic mass unit (amu) or unified mass (u) or dalton, where 1 amu or 1 u or 1 Da is defined as 1⁄12 of the mass of a single carbon-12 atom, at rest. The protons and neutrons of the nucleus account for nearly all of the total mass of atoms, with the electrons and nuclear binding energy making minor contributions. Thus, the numeric value of the atomic mass when expressed in daltons has nearly the same value as the mass number. Conversion between mass in kilograms and mass in daltons can be done using the atomic mass constant .

The Kendrick mass is defined by setting the mass of a chosen molecular fragment, typically CH2, to an integer value in amu (atomic mass units). It is different from the IUPAC definition, which is based on setting the mass of 12C isotope to exactly 12 amu. The Kendrick mass is often used to identify homologous compounds differing only by a number of base units in high resolution mass spectra. This definition of mass was first suggested in 1963 by chemist Edward Kendrick, and it has been adopted by scientists working in the area of high-resolution mass spectrometry, environmental analysis, proteomics, petroleomics, metabolomics, polymer analysis, etc.

Petroleomics is the identification of the totality of the constituents of naturally occurring petroleum and crude oil using high resolution mass spectrometry. In addition to mass determination, petroleomic analysis sorts the chemical compounds into heteroatom class, type. The name is a combination of petroleum and -omics.

Nanoscale secondary ion mass spectrometry

NanoSIMS is an analytical instrument manufactured by CAMECA which operates on the principle of secondary ion mass spectrometry. The NanoSIMS is used to acquire nanoscale resolution measurements of the elemental and isotopic composition of a sample. The NanoSIMS is able to create nanoscale maps of elemental or isotopic distribution, parallel acquisition of up to seven masses, isotopic identification, high mass resolution, subparts-per-million sensitivity with spatial resolution down to 50 nm.

Position-specific isotope analysis

Position-specific isotope analysis, also called site-specific isotope analysis, is a branch of isotope analysis aimed at determining the isotopic composition of a particular atom position in a molecule. Isotopes are elemental variants with different numbers of neutrons in their nuclei, thereby having different atomic masses. Isotopes are found in varying natural abundances depending on the element; their abundances in specific compounds can vary from random distributions due to environmental conditions that act on the mass variations differently. These differences in abundances are called "fractionations," which are characterized via stable isotope analysis.

References

  1. ↑ Bureau International des Poids et Mesures (2019): The International System of Units (SI) , 9th edition, English version, page 134. Available at the BIPM website.
  2. ↑ Stryer, Jeremy M. Berg; John L. Tymoczko; Lubert (2007). "2". Biochemistry (3rd print, 6th ed.). New York: Freeman. p. 35. ISBN   978-0-7167-8724-2.
  3. ↑ Fundamental Physical Constants from NIST
  4. ↑ Jürgen H Gross (14 February 2011). Mass Spectrometry: A Textbook. Springer Science & Business Media. pp. 71–. ISBN   978-3-642-10709-2.
  5. 1 2 J. Throck Watson; O. David Sparkman (9 July 2013). Introduction to Mass Spectrometry: Instrumentation, Applications, and Strategies for Data Interpretation. John Wiley & Sons. pp. 385–. ISBN   978-1-118-68158-9.
  6. ↑ Berglund, Michael; Wieser, Michael E. (2011). "Isotopic compositions of the elements 2009 (IUPAC Technical Report)". Pure and Applied Chemistry. 83 (2): 397–410. doi: 10.1351/PAC-REP-10-06-02 . ISSN   1365-3075.
  7. 1 2 Sleno, Lekha (2012). "The use of mass defect in modern mass spectrometry". Journal of Mass Spectrometry. 47 (2): 226–236. Bibcode:2012JMSp...47..226S. doi:10.1002/jms.2953. ISSN   1076-5174. PMID   22359333.
  8. ↑ Imma Ferrer; E. M. Thurman (6 May 2009). Liquid Chromatography Time-of-Flight Mass Spectrometry. John Wiley & Sons. pp. 18–22. ISBN   978-0-470-42995-2.
  9. 1 2 O. David Sparkman (2006). Mass Spec Desk Reference (2nd. ed.). p. 60. ISBN   0-9660813-9-0.
  10. ↑ Grange AH; Winnik W; Ferguson PL; Sovocool GW (2005), "Using a triple-quadrupole mass spectrometer in accurate mass mode and an ion correlation program to identify compounds", Rapid Commun. Mass Spectrom. (Submitted manuscript), 19 (18): 2699–715, Bibcode:2005RCMS...19.2699G, doi:10.1002/rcm.2112, PMID   16124033.
  11. ↑ Gross, M. L. (1994), "Accurate Masses for Structure Confirmation", J. Am. Soc. Mass Spectrom., 5 (2): 57, doi: 10.1016/1044-0305(94)85036-4 , PMID   24222515.
  12. ↑ "Monoisotopic mass spectrum". IUPAC Compendium of Chemical Terminology. 2009. doi:10.1351/goldbook.M04014. ISBN   978-0-9678550-9-7.Missing or empty |title= (help)
  13. ↑ Senko, Michael W.; Beu, Steven C.; McLaffertycor, Fred W. (1995). "Determination of monoisotopic masses and ion populations for large biomolecules from resolved isotopic distributions". Journal of the American Society for Mass Spectrometry. 6 (4): 229–233. doi: 10.1016/1044-0305(95)00017-8 . ISSN   1044-0305. PMID   24214167.
  14. ↑ Goraczko AJ (2005), "Molecular mass and location of the most abundant peak of the molecular ion isotopomeric cluster", Journal of Molecular Modeling, 11 (4–5): 271–7, doi:10.1007/s00894-005-0245-x, PMID   15928922, S2CID   21949927.
  15. ↑ IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) " isotopomer ". doi : 10.1351/goldbook.I03352
  16. ↑ Kendrick, Edward (1963), "A mass scale based on CH2 = 14.0000 for high resolution mass spectrometry of organic compounds", Anal. Chem. , 35 (13): 2146–2154, doi:10.1021/ac60206a048.
  17. ↑ Marshall AG; Rodgers RP (January 2004), "Petroleomics: the next grand challenge for chemical analysis", Acc. Chem. Res. , 37 (1): 53–9, doi:10.1021/ar020177t, PMID   14730994.
  18. ↑ Mopper, Kenneth; Stubbins, Aron; Ritchie, Jason D.; Bialk, Heidi M.; Hatcher, Patrick G. (2007), "Advanced Instrumental Approaches for Characterization of Marine Dissolved Organic Matter: Extraction Techniques, Mass Spectrometry, and Nuclear Magnetic Resonance Spectroscopy", Chemical Reviews, 107 (2): 419–42, doi:10.1021/cr050359b, PMID   17300139
  19. ↑ Meija, Juris (2006), "Mathematical tools in analytical mass spectrometry", Analytical and Bioanalytical Chemistry, 385 (3): 486–99, doi:10.1007/s00216-006-0298-4, PMID   16514517, S2CID   44611533
  20. ↑ Kim, Sunghwan; Kramer, Robert W.; Hatcher, Patrick G. (2003), "Graphical Method for Analysis of Ultrahigh-Resolution Broadband Mass Spectra of Natural Organic Matter, the Van Krevelen Diagram", Analytical Chemistry, 75 (20): 5336–44, doi:10.1021/ac034415p, PMID   14710810
  21. ↑ J. Throck Watson; O. David Sparkman (4 December 2007). Introduction to Mass Spectrometry: Instrumentation, Applications, and Strategies for Data Interpretation. John Wiley & Sons. pp. 274–. ISBN   978-0-470-51634-8.
  22. ↑ Jürgen H Gross (22 June 2017). Mass Spectrometry: A Textbook. Springer. pp. 143–. ISBN   978-3-319-54398-7.
  23. ↑ Hughey, Christine A.; Hendrickson, Christopher L.; Rodgers, Ryan P.; Marshall, Alan G.; Qian, Kuangnan (2001). "Kendrick Mass Defect Spectrum: A Compact Visual Analysis for Ultrahigh-Resolution Broadband Mass Spectra". Analytical Chemistry. 73 (19): 4676–4681. doi:10.1021/ac010560w. ISSN   0003-2700. PMID   11605846.
  24. ↑ "The Nobel Prize in Chemistry 1922". Nobel Foundation. Retrieved 2008-04-14.
  25. ↑ Squires, Gordon (1998). "Francis Aston and the mass spectrograph". Dalton Transactions (23): 3893–3900. doi:10.1039/a804629h.
  26. ↑ Aston, F. W. (1927). "Atoms and their Packing Fractions1". Nature. 120 (3035): 956–959. Bibcode:1927Natur.120..956A. doi:10.1038/120956a0. ISSN   0028-0836. S2CID   22601204.
  27. ↑ Budzikiewicz, Herbert; Grigsby, Ronald D. (2006). "Mass spectrometry and isotopes: A century of research and discussion". Mass Spectrometry Reviews. 25 (1): 146–157. Bibcode:2006MSRv...25..146B. doi:10.1002/mas.20061. ISSN   0277-7037. PMID   16134128.
  28. ↑ Dempster, A. J. (1938). "The Energy Content of the Heavy Nuclei". Physical Review. 53 (11): 869–874. Bibcode:1938PhRv...53..869D. doi:10.1103/PhysRev.53.869. ISSN   0031-899X.
  29. ↑ Tureček, František; McLafferty, Fred W. (1993). Interpretation of mass spectra. Sausalito, Calif: University Science Books. pp. 37–38. ISBN   978-0-935702-25-5.
  30. ↑ David O. Sparkman (2007). Mass Spectrometry Desk Reference. Pittsburgh: Global View Pub. p. 64. ISBN   978-0-9660813-9-8.
  31. ↑ Budzikiewicz H; Grigsby RD (2006). "Mass spectrometry and isotopes: a century of research and discussion". Mass Spectrometry Reviews. 25 (1): 146–57. Bibcode:2006MSRv...25..146B. doi:10.1002/mas.20061. PMID   16134128.
  32. ↑ Prout, William (1815). "On the relation between the specific gravities of bodies in their gaseous state and the weights of their atoms". Annals of Philosophy . 6: 321–330. Retrieved 2007-09-08.
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