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Origin of the Elements. Isotopes and Atomic Weights

Origin of the Elements. Isotopes and Atomic Weights

1 2 H He

3 4 5 6 7 8 9 10 Li Be B C N O F Ne

11 12 13 14 15 16 17 18 Na Mg Al Si PSCl Ar

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Rb Sr YZrNb Mo Tc Ru Rh Pd Ag Cd ln Sn Sb Te IXe

55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

87 88 89 104 105 106 107 108 109 110 111 112 Fr Ra Ac Rf Db Sg Bh Hs Mt Uun Uuu Uub

58 59 60 61 62 63 64 65 66 67 68 69 70 71 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

90 91 92 93 94 95 96 97 98 99 100 101 102 103 Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 1 Origin of the Elements. and Atomic Weights

1.1 Introduction what is a currently acceptable theory which interprets the known facts. The tentative nature of This book presents a unified treatment of the our knowledge is perhaps nowhere more evident chemistry of the elements. At present 112 ele- than in the first few sections of this chapter ments are known, though not all occur in nature: dealing with the origin of the chemical elements of the 92 elements from to all and their present isotopic composition. This is not except and are found on surprising, for it is only in the last few decades earth and technetium has been detected in some that progress in this enormous enterprise has been stars. To these elements a further 20 have been made possible by discoveries in , added by artificial nuclear syntheses in the labo- astrophysics, relativity and quantum theory. ratory. Why are there only 90 elements in nature? Why do they have their observed abundances and why do their individual isotopes occur with the 1.2 Origin of the Universe particular relative abundances observed? Indeed, At present, the most widely accepted theory we must also ask to what extent these isotopic for the origin and evolution of the universe to abundances commonly vary in nature, thus caus- its present form is the “hot ”..1/ It ing variability in atomic weights and possibly is supposed that all the matter in the universe jeopardizing the classical means of determining chemical composition and structure by chemical 1 J. SILK, The Big Bang: The Creation and Evolution analysis. of the Universe, 2nd edn., W. H. Freeman, New York, Theories abound, and it is important at all 1989, 485 pp. J. D. BARROW and J. SILK, The Left Hand times to distinguish carefully between what has of Creation: The Origin and Evolution of the Expanding Universe, Heinemann, London, 1984, 256 pp. E. W. KOLB been experimentally established, what is a useful andM.S.TURNER, The Early Universe, Addison-Wesley, model for suggesting further experiments, and Redwood City, CA, 1990, 547 pp.

1 2 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 was once contained in a primeval nucleus of of radiation would have immediately decomposed immense density (¾1096 gcm3) and temperature them back to and . Subsequently, (¾1032 K) which, for some reason, exploded the continuing expansion of the universe was and distributed radiation and matter uniformly such that the particle density was too low throughout space. As the universe expanded for these strong (but short-range) interactions it cooled; this allowed the four main types to occur. Thus, within the time slot of about of force to become progressively differentiated, eight minutes, it has been calculated that about and permitted the formation of various types one-quarter of the mass of the universe was of particle to occur. Nothing scientific can be converted to nuclei and about three- said about the conditions obtaining at times quarters remained as hydrogen. Simultaneously, 5 1/2 3 shorter than the Planck time, tP [.Gh/c / D a minute 10 % was converted to deuterons and 1.33 ð 1043 s] at which moment the forces of about 106% to nuclei. These remarkable gravity and electromagnetism, and the weak and predictions of the big bang cosmological theory strong nuclear forces were all undifferentiated are borne out by experimental observations. and equally powerful. At 1043 s after the big Wherever one looks in the universe the oldest bang (T D 1031 K) gravity separated as a distinct stars in our own galaxy, or the “more recent” stars force, and at 1035 s(1028 K) the strong nuclear in remote galaxies the universal abundance of force separated from the still combined electro- helium is about 25%. Even more remarkably, weak force. These are, of course, inconceivably the expected concentration of has been short times and unimaginably high temperatures: detected in interstellar clouds. Yet, as we shall for example, it takes as long as 1024 sfor shortly see, stars can only destroy deuterium a photon (travelling at the speed of light) to as soon as it is formed; they cannot create traverse a distance equal to the diameter of an any appreciable equilibrium concentration of . When a time interval of 1010 s deuterium nuclei because of the high temperature had elapsed from the big bang the temperature of the stellar environment. The sole source of is calculated to have fallen to 1015 K and this deuterium in the universe seems to be the big enabled the electromagnetic and weak nuclear bang. At present no other cosmological theory forces to separate. By 6 ð 106 s .1.4 ð 1012 K/ can explain this observed ratio of H:He:D. protons and neutrons had been formed from Two other features of the universe find quarks, and this was followed by stabilization ready interpretation in terms of the big bang of electrons. One after the big bang, theory. First, as observed originally by E. Hubble after a of extensive particle antiparticle in 1929, the light received on earth from annihilation to form electromagnetic photons, distant galaxies is shifted increasingly towards the universe was populated by particles which the red end of the spectrum as the distance sound familiar to chemists protons, neutrons of the source increases. This implies that and electrons. the universe is continually expanding and, on Shortly thereafter, the strong nuclear force certain assumptions, extrapolation backwards ensured that large numbers of protons and in time indicates that the big bang occurred neutrons rapidly combined to form deuterium some 15 billion years ago. Estimates from nuclei (p C n), then helium (2p C 2n). The several other independent lines of evidence process of element building had begun. During give reassuringly similar values for the age of this small niche of cosmic history, from about the universe. Secondly, the theory convincingly 10 500 s after the big bang, the entire universe explains (indeed predicted) the existence of is thought to have behaved as a colossal an all-pervading isotropic cosmic black-body homogeneous fusion reactor converting hydrogen radiation. This radiation (which corresponds to a into helium. Previously no helium nuclei could temperature of 2.735 š 0.06 K according to the exist the temperature was so high that the sea most recent measurements) was discovered in §1.3 Abundances of the elements in the universe 3

1965 by A. A. Penzias and R. W. Wilson.2/ and (i) Abundances decrease approximately is seen as the dying remnants of the big bang. No exponentially with increase in atomic other comological theory yet proposed is able to mass number A until A ¾ 100 (i.e. Z ¾ interpret all these diverse observations. 42); thereafter the decrease is more grad- ual and is sometimes masked by local fluctuations. 1.3 Abundances of the (ii) There is a pronounced peak between Z D 23 28 including V, Cr, Mn, Fe, Co and Elements in the Universe Ni, and rising to a maximum at Fe which is ¾103 more abundant than expected Information on the abundances of at least some from the general trend. of the elements in the sun, stars, gaseous (iii) Deuterium (D), Li, Be and B are rare nebulae and the interstellar regions has been compared with the neighbouring H, He, obtained from detailed spectroscopic analysis C and N. using various regions of the electromagnetic (iv) Among the lighter nuclei (up to Sc, Z D spectrum. This data can be supplemented by 21), those having an number direct analysis of samples from the earth, from A divisible by 4 are more abundant than meteorites, and increasingly from comets, the their neighbours, e.g. 16O, 20Ne, 24Mg, moon, and the surfaces of other planets and 28Si, 32S, 36Ar and 40Ca (rule of G. Oddo, satellites in the solar system. The results indicate 1914). extensive differentiation in the solar system and (v) with A even are more abundant in some stars, but the overall picture is one of than those with A odd. (This is seen in astonishing uniformity of composition. Hydrogen Fig. 1.1 as an upward displacement of is by far the most abundant element in the the curve for Z even, the exception at universe, accounting for some 88.6% of all being due to the non-existence atoms (or nuclei). Helium is about eightfold 8 9 of 4Be, the 4Be being the stable less abundant (11.3%), but these two elements species.) together account for over 99.9% of the atoms and nearly 99% of the mass of the universe. Two further features become apparent when Clearly nucleosynthesis of the heavier elements abundances are plotted against A rather than Z: from hydrogen and helium has not yet proceeded (vi) Atoms of heavy elements tend to be neu- very far. tron rich; heavy -rich are Various estimates of the universal abundances rare. of the elements have been made and, although (vii) Double-peaked abundance maxima occur these sometimes differ in detail for particular ele- at A D 80, 90; A D 130, 138; and A D ments, they rarely do so by more than a factor 196, 208 (see Fig. 1.5 on p. 11). of 3 (100.5) on a scale that spans more than 12 orders of magnitude. Representative values are It is also necessary to explain the existence of plotted in Fig. 1.1, which shows a number of naturally occurring radioactive elements whose features that must be explained by any satisfac- half-lives (or those of their precursors) are sub- tory theory of the origin of the elements. For stantially less than the presumed age of the uni- example: verse. As a result of extensive studies over the past 2 R. W. WILSON, The cosmic microwave background four decades it is now possible to give a detailed radiation, pp. 113 33 in Les Prix Nobel 1978, Almqvist & and convincing explanation of the experimental Wiksell International, Stockholm 1979. A. A. PENZIAS,The origin of the elements, pp. 93 106 in Les Prix Nobel 1978 abundance data summarized above. The histori- (also in Science 105, 549 54 (1979)). cal sequence of events which led to our present 4 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 atoms 6 U Th (Ra) Bi (Rn) (At) (Fr) (Ac) (Pa) Pb (Po) Hg Tl Au Pt Ir Re Os W Ta Hf 46 (1973), with some updating.) Lu Yb Tm Er , 121 Ho Dy 15 Tb Gd Eu Sm Nd (Pm) Pr Ce La Ba Cs Xe Space Sci. Rev. I . Abundances are expressed as numbers of atoms per 10 Z Te Z Sb Sn Cd In Pd Ag Ru Rh Mo (Tc) Atomic number, Nb Zr Y Sr Kr Rb Se Br Ge As Zn Ga Ni Cu Fe Mn Co V Cr Ti Sc Ca Ar K S Cl Si P Al Mg Na Ne F O B B N 10 11 C Be Li Li 6 He 7 Cosmic abundances of the elements as a function of atomic number of Si and are plotted on a logarithmic scale. (From A. G. W. Cameron, D H 0 102030405060708090

9 8 7 6 5 4 3 2 1 0 1 2 3

11 10 − − −

10 N log Figure 1.1 §1.4 Stellar evolution and the spectral classes of stars 5 understanding is briefly summarized in the Panel. hydrogen and helium. For a star the size As the genesis of the elements is closely linked and mean density of the sun (mass D 1.991 ð 30 with theories of stellar evolution, a short descrip- 10 kg D 1Mþ) this might take ¾20 y. This tion of the various types of star is given in the gravitational contraction releases heat energy, next section and this is then followed by a fuller some of which is lost by radiation; however, the discussion of the various processes by which the continued contraction results in a steady rise in chemical elements are synthesized. temperature until at ¾107 K the core can sustain nuclear reactions. These reactions release enough additional energy to compensate for radiational 1.4 Stellar Evolution and the losses and a temporary equilibrium or steady state Spectral Classes of Stars(3,4) is established. When ¾10% of the hydrogen in the core has been consumed gravitational contraction again In broad outline stars are thought to evolve by the ¾ ð 8 following sequence of events. First, there is self- occurs until at a temperature of 2 10 K gravitational accretion from the cooled primordial helium burning (fusion) can occur. This is followed by a similar depletion, contraction and temperature rise until nuclear reactions involving 3 I. S. SHKLOVSKII, Stars: Their Birth, Life and Death (trans- lated by R. B. Rodman), W. H. Freeman, San Francisco, 1978, 442 pp. M. HARWIT, Astrophysical Concepts (2nd edn) L. A. MARSCHALL, The Supernova Story, Plenum Press, New Springer Verlag, New York, 1988, 626 pp. York, 1989, 276 pp. P. MURDIN, End in Fire: The Supernova 4 D. H. CLARK and F.R.STEPHENSON, The Historical in the Large Magellanic Cloud, Cambridge University Press, Supernovae, Pergamon Press, Oxford, 1977, 233 pp. 1990, 253 pp.

Genesis of the Elements Historical Landmarks

1890s First systematic studies on the terrestrial abundances of the elements F. W. Clarke; H. S. Washington and others 1905 Special relativity theory: E D mc2 A. Einstein 1911 Nuclear model of the E. Rutherford 1913 First observation of isotopes in a stable element (Ne) J. J. Thompson 14 17 1919 First artificial transmutation of an element 7 N.˛,p/ 8 O E. Rutherford 1925 8 First abundance data on stars (spectroscopy) Cecilia H. Payne; H. N. Russell 1929 First proposal of stellar nucleosynthesis by proton fusion to helium R. D’E. Atkinson and and heavier nuclides F. G. Houtermans 1937 The “missing element” Z D 43 (technetium) synthesized by C. Perrier and E. G. Segre´ 99 99 42Mo(d,n)43Tc 1938 Catalytic CNO process independently proposed to assist nuclear syn- H. A. Bethe; C. F. von Weizsacker¨ thesis in stars 1938 Uranium fission discovered experimentally O. Hahn and F. Strassmann 239 1940 First transuranium element 93 Np synthesized E. M. McMillan and P. Abelson 1947 The last “missing element” Z D 61 (Pm) discovered among uranium J. A. Marinsky, L. E. Glendenin fission products and C. D. Coryell 1948 Hot big-bang theory of expanding universe includes an (incorrect) R. A. Alpher, H. A. Bethe and theory of nucleogenesis G. Gamow 1952 4 Helium burning as additional process for nucleogenesis E. E. Salpeter; F. Hoyle 1954 Slow absorption added to stellar reactions A. G. W. Cameron 1955 7 Comprehensive theory of stellar synthesis of all elements in observed E. M. Burbidge, G. R. Burbidge, cosmic abundances W. A. Fowler and F. Hoyle 1965 2.7 K radiation detected A. P. Penzias and R. W. Wilson 6 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 still heavier nuclei (Z D 8 22) can occur at chemical composition of stars the identity of ¾109 K. The time scale of these processes the elements present and their relative concentra- depends sensitively on the mass of the star, tions. In addition, the “red shift” or Doppler effect 12 taking perhaps 10 yforastarofmass0.2Mþ, can be used to gauge the relative motions of the 1010 y for a star of 1 solar mass, 107 yfor stars and their distance from the earth. More sub- 4 mass 10 Mþ, and only 8 ð 10 y for a star tly, the surface temperature of stars can be deter- of 50 Mþ; i.e. the more massive the star, the mined from the spectral characteristics of their more rapidly it consumes its nuclear fuel. Further “blackbody” radiation, the higher the temperature catastrophic changes may then occur which result the shorter the wavelength of maximum emission. in much of the stellar material being ejected into Thus cooler stars appear red, and successively space, where it becomes incorporated together hotter stars appear progressively yellow, white, with further hydrogen and helium in the next and blue. Differences in colour are also associ- generation of stars. It should be noted, however, ated with differences in chemical composition as that, as is at the maximum of the nuclear indicated in Table 1.1. binding energy curve, only those elements up to If the spectral classes (or temperatures) of stars iron (Z D 26) can be produced by exothermic are plotted against their absolute magnitudes (or processes of the type just considered, which occur luminosities) the resulting diagram shows several automatically if the temperature rises sufficiently. preferred regions into which most of the stars fall. Beyond iron, an input of energy is required to Such diagrams were first made, independently, promote further element building. by E. Hertzsprung and H. N. Russell about 1913 The evidence on which this theory of stellar and are now called HR diagrams (Fig. 1.2). More evolution is based comes not only from known than 90% of all stars fall on a broad band called nuclear reactions and the relativistic equivalence the main sequence, which covers the full range of mass and energy, but also from the spectro- of spectral classes and magnitudes from the large, scopic analysis of the light reaching us from the hot, massive O stars at the top to the small, dense, stars. This to the spectral classification of reddish M stars at the bottom. However, it should stars, which is the cornerstone of modern exper- be emphasized that the terms “large” and “small” imental astrophysics. The spectroscopic analysis are purely relative since all stars within the main of starlight reveals much information about the sequence are classified as dwarfs.

Table 1.1 Spectral classes of stars Class.a/ Colour Surface (T/K) Spectral characterization Examples OBlue >25 000 Lines of ionized He and other 10 Lacertae elements; H lines weak B Blue-white 11 000 25 000 H and He prominent Rigel, Spica A White 7500 11 000 H lines very strong Sirius, Vega F Yellow-white 6000 7000 H weaker; lines of ionized Canopus, metals becoming prominent Procyon G Yellow 5000 6000 Lines of ionized and neutral Sun, Capella metals prominent (especially Ca) K Orange 3500 5000 Lines of neutral metals and Arcturus, band spectra of simple rad- Aldebaran icals (e.g. CN, OH, CH) M Red 2000 3500 Band spectra of many simple Betelgeuse, compounds prominent (e.g. TiO) Antares

.a/Further division of each class into 10 subclasses is possible, e.g. ... F8,F9,G0,G1,G2,... The sun is G2 with a surface temperature of 5780 K. This curious alphabetical sequence of classes arose historically and can perhaps best be remembered by the mnemonic “Oh Be A Fine Girl (Guy), Kiss Me”. §1.4 Stellar evolution and the spectral classes of stars 7

Figure 1.2 The Hertzsprung-Russell diagram for stars with known luminosities and spectra.

The next most numerous of stars lie above and to the right of the main sequence and are called red giants. For example, Capella and the sun are both G-type stars yet Capella is 100 times more luminous than the sun; since they both have the same temperature it is concluded that Capella must have a radiating surface 100 times larger than the sun and thus has about 10 times its radius. Lying above the red giants are the super- giants such as Antares (Fig. 1.3), which has a surface temperature only half that of the sun but is 10 000 times more luminous: it is concluded that its radius is 100 times that of the sun. By contrast, the lower left-hand corner of the HR diagram is populated with relatively hot stars of low luminosity which implies that they are very small. These are the white dwarfs such as Sirius B Figure 1.3 The comparison of various stars on the which is only about the size of the earth though HR diagram. The number in parentheses indicates the approximate diameter of the its mass is that of the sun: the implied density star (sun D 1.0). 8 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 of ¾5 ð 104 gcm3 indicates the extraordinarily main sequence stars. If the initial mass is compact nature of these bodies. greater than about 3.5 solar masses, current It is now possible to connect this description theories suggest that gravitational collapse may of stellar types with the discussion of the thermo- be so catastrophic that the system implodes nuclear processes and the synthesis of the ele- beyond nuclear densities to become a black ments to be given in the next section. When a hole. For main sequence stars in the mass range protostar begins to form by gravitational con- 1.4 3.5 Mþ, implosion probably halts at nuclear traction from interstellar hydrogen and helium, densities to give a rapidly rotating neutron its temperature rises until the temperature in its star (density ¾1014 gcm3) which may be core can sustain proton burning (p. 9). A star of observable as a pulsar emitting electromagnetic approximately the mass of the sun joins the main radiation over a wide range of frequencies in sequence at this point and spends perhaps 90% pulses at intervals of a fraction of a second. of its life there, losing little mass but generating During this process of star implosion the sudden colossal amounts of energy. Subsequent exhaus- arrest of the collapsing core at nuclear densities tion of the hydrogen in the core (but not in the yields an enormous temperature (¾1012 K) and outer layers of the star) leads to further contrac- tion to form a helium-burning core which forces high pressure which produces an outward-moving much of the remaining hydrogen into a vast ten- shock wave. This strikes the star’s outer envelope uous outer envelope the star has become a red with resulting rapid compression, a dramatic rise giant since its enormous radiating surface area in temperature, the onset of many new nuclear can no longer be maintained at such a high tem- reactions, and explosive ejection of a significant perature as previously despite the higher core fraction of the star’s mass. The overall result is temperature. Typical red giants have surface tem- a supernova up to 108 times as bright as the peratures in the range 3500 5500 K; their lumi- original star. At this point a single supernova nosities are about 102 104 times that of the sun is comparable in brightness to the whole of and diameters about 10 100 times that of the sun. the rest of the galaxy in which it is formed, burning (p. 10) can follow in older red after which the brightness decays exponentially, giants followed by the ˛-process (p. 11) during often with a half-life of about two months. its final demise to white dwarf status. Supernovae, novae, and unstable variables from Many stars are in fact partners in a binary sys- dying red giants are thus all candidates for the tem of two stars revolving around each other. If, synthesis of heavier elements and their ejection as frequently occurs, the two stars have different into interstellar regions for subsequent processing masses, the more massive one will evolve faster in later generations of condensing main sequence and reach the white-dwarf stage before its part- stars such as the sun. It should be stressed, ner. Then, as the second star expands to become however, that these various theories of the origin a red giant its extended atmosphere encompasses of the chemical elements are all very recent and the neighbouring white dwarf and induces insta- the detailed processes are by no means all fully bilities which result in an outburst of energy and transfer of matter to the more massive partner. understood. Since this is at present a very active During this process the luminosity of the white area of research, some of the conclusions given dwarf increases perhaps ten-thousandfold and the in this chapter are correspondingly tentative, and event is witnessed as a nova (since the preced- will undoubtedly be modified and refined in ing binary was previously invisible to the naked the light of future experimental and theoretical eye). studies. With this caveat we now turn to a more As we shall see in the description of the detailed description of the individual nuclear e-process and the -process (p. 12), even more processes thought to be involved in the synthesis spectacular instabilities can develop in larger of the elements. §1.5.1 Hydrogen burning 9 1.5 Synthesis of the Table 1.2 Thermonuclear consumption of protons Elements(5 9) Reaction Energy Reaction evolved, Q time.a/

1 1 2 C 10 The following types of nuclear reactions have H C H ! H C e C ve 1.44 MeV 1.4 ð 10 y been proposed to account for the various types 2H C 1H ! 3He C 5.49 MeV 0.6 s of stars and the observed abundances of the ele- 3He C 3He ! 4He C 21H 12.86 MeV 106 y ments: .a/The reaction time quoted is the time required for half the constituents involved to undergo reaction this is sensi- (i) Exothermic processes in stellar interiors: tively dependent on both temperature and density; the figures these include (successively) hydrogen given are appropriate for the centre of the sun, i.e. 1.3 ð 7 3 burning, helium burning, carbon burning, 10 K and 200 g cm . 1 MeV per atom Á 96.485 ð 106 kJ mol1. the ˛-process, and the equilibrium or e-process. (ii) processes: these include Making allowance for the energy carried away the s-process (slow neutron capture) and by the 2 neutrinos (2 ð 0.25 MeV) this leaves the r-process (rapid neutron capture). a total of 26.22 MeV for radiation, i.e. 4.20 pJ (iii) Miscellaneous processes: these include peratomofheliumor2.53 ð 109 kJ mol1. This the p-process (proton capture) and spal- vast release of energy arises mainly from the lation within the stars, and the x-process difference between the rest mass of the helium- which involves spallation (p. 14) by 4 nucleus and the 4 protons from which it was galactic cosmic rays in interstellar regions. formed (0.028 atomic mass units). There are several other peripheral reactions between the protons, deuterons and 3He nuclei, but these 1.5.1 Hydrogen burning need not detain us. It should be noted, however, that only 0.7% of the mass is lost during When the temperature of a contracting mass of this transformation, so that the star remains hydrogen and helium atoms reaches about 107 K, approximately constant in mass. For example, a sequence of thermonuclear reactions is possi- in the sun during each second, some 600 ð 106 ble of which the most important are as shown in ð 9 Table 1.2. tonnes (600 10 kg) of hydrogen are processed into 595.5 ð 106 tonnes of helium, the remaining The overall reaction thus converts 4 protons 6 into 1 helium nucleus plus 2 and 2 neu- 4.5 ð 10 tonnes of matter being transformed into trinos: energy. This energy is released deep in the sun’s interior as high-energy -rays which interact with 1 4 C 4 H ! He C 2e C 2ve; Q D 26.72 MeV stellar material and are gradually transformed into photons with longer wavelengths; these work 6 5 D. N. SCHRAMM and R. WAGONER, Element production in their way to the surface taking perhaps 10 yto the early universe, A. Rev. Nucl. Sci. 27,37 74 (1977). emerge. 6 E. M. BURBIDGE, G.R.BURBIDGE,W.A.FOWLER and In fact, the sun is not a first-generation F. HOYLE, Synthesis of the elements in stars, Rev. Mod. Phys. 29, 547 650 (1957). This is the definitive review on which main-sequence star since spectroscopic evidence all later work has been based. shows the presence of many heavier elements 7 L. H. ALLER, The Abundance of the Elements, Inter- thought to be formed in other types of stars and science, New York, 1961, 283 pp. 7a L. H. AHRENS (ed.), Origin and Distribution of the subsequently distributed throughout the galaxy Elements, Pergamon Press, Oxford, 1979, 920 pp. for eventual accretion into later generations of 8 R. J. TAYLOR, The Origin of Chemical Elements, Wyke- main-sequence stars. In the presence of heavier ham Publications, London, 1972, 169 pp. elements, particularly carbon and , a 9 W. A. FOWLER, The quest for the origin of the elements (Nobel Lecture), Angew. Chem. Int. Edn. Engl. 23, 645 71 catalytic sequence of nuclear reactions aids (1984). the fusion of protons to helium (H. A. Bethe 10 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 can occur. The hydrogen forms a vast tenuous 4He 1H 2 12C 1 envelope around this core with the result that the 6 104y ~ 106y star evolves rapidly from the main sequence to 1H become a red giant (p. 7). It is salutory to note 1 4.97 1.94 γ MeV MeV that hydrogen burning in main-sequence stars has 15N 13N 7 7 so far contributed an amount of helium to the

+ universe which is only about 20% of that which e was formed in the few minutes directly following 3 min2.76 2.22 15 min the big bang (p. 2). MeV MeV + e 1.5.2 Helium burning and carbon 15O 13C 8 6 7.29 7.55 burning γ MeV MeV 1 H 2.108y 2.105y 1 The main nuclear reactions occurring in helium 14N burning are: 7 1H γ 1 4He C 4He )* 8Be Figure 1.4 Catalytic C N O cycle for conversion and 1 4 of Hto He. The times quoted are the 8 4 12 Ł 12 calculated half-lives for the individual Be C He )* C ! C C steps at 1.5 ð 107 K. The nucleus 8Be is unstable to ˛-particle 16 emission (t1/2 ¾ 2 ð 10 s) being 0.094 MeV and C. F. von Weizsacker,¨ 1938) (Fig. 1.4). The less stable than its constituent helium nuclei; overall reaction is precisely as before with the under the conditions obtaining in the core of evolution of 26.72 MeV, but the 2 neutrinos now a red giant the calculated equilibrium ratio carry away 0.7 and 1.0 MeV respectively, leaving of 8Be to 4He is ¾109. Though small, 25.0 MeV (4.01 pJ) per cycle for radiation. The this enables the otherwise improbable 3-body coulombic energy barriers in the C N Ocycle collision to occur. It is noteworthy that, from are some 6 7 times greater than for the direct consideration of stellar nucleogenesis, F. Hoyle proton proton reaction and hence the catalytic predicted in 1954 that the nucleus of 12C would cycle does not predominate until about 1.6 ð have a radioactive excited state 12CŁ 7.70 MeV 107 K. In the sun, for example, it is estimated above its ground state, some three years before that about 10% of the energy comes from this this activity was observed experimentally at process and most of the rest comes from the 7.653 MeV. Experiments also indicate that the straightforward proton proton reaction. energy difference Q.12CŁ 34He/ is 0.373 MeV, When approximately 10% of the hydrogen thus leading to the overall reaction energy in a main-sequence star like the sun has been consumed in making helium, the outward thermal 34He ! 12C C ; Q D 7.281 MeV pressure of radiation is insufficient to counteract the gravitational attraction and a further stage Further helium-burning reactions can now follow of contraction ensues. During this process the during which even heavier nuclei are synthesized: helium concentrates in a dense central core ( ¾ 105 gcm3) and the temperature rises to perhaps 12C C 4He ! 16O C ; Q D 7.148 MeV 2 ð 108 K. This is sufficient to overcome the 16O C 4He ! 20Ne C ; Q D 4.75 MeV coulombic potential energy barriers surrounding the helium nuclei, and helium burning (fusion) 20Ne C 4He ! 24Mg C ; Q D 9.31 MeV §1.5.3 The a-process 11 These reactions result in the exhaustion of helium Some of the released ˛-particles can also scour previously produced in the hydrogen-burning out 12Ctogivemore16Oandthe24Mg formed process and an inner core of carbon, can react further by 24Mg.˛, /28Si. Likewise and develops which eventually undergoes for 32S, 36Ar and 40Ca. It is this process that gravitational contraction and heating as before. is considered to be responsible for building up At a temperature of ¾5 ð 108 K carbon burning the decreasing proportion of these so-called ˛- becomes possible in addition to other processes particle nuclei (Figs. 1.1 and 1.5). The relevant which must be considered. Thus, ageing red giant numerical data (including for comparison those stars are now thought to be capable of generating for 20Ne which is produced in helium and carbon a carbon-rich core at densities of burning) are as follows: the order of 104 gcm3. Typical initial reactions would be: (20Ne) 24Mg 28Si 32S 36Ar 40Ca 44Ca 48Ti Q˛/MeV (9.31) 10.00 6.94 6.66 7.04 5.28 9.40 9.32 12 12 24 Relative C C C ! Mg C ; Q D 13.85 MeV abundance (as obser- 12C C 12C ! 23Na C 1H; Q D 2.23 MeV ved) (8.4) 0.78 1.00 0.39 0.14 0.052 0.0011 0.0019 12C C 12C ! 20Ne C 4He; Q D 4.62 MeV The time scale of such reactions is calculated H to be ¾105 yat6ð 108 Kand¾1yat8.5 ð Big bang and H burning 108 K. It will be noticed that hydrogen and 10 He ) helium nuclei are regenerated in these processes 6 and numerous subsequent reactions become 10

= 8 He-burning possible, generating numerous nuclides in this D mass range. 6 Iron group H-burning α e 1.5.3 The a-process 4 The evolution of a star after it leaves the red-giant s N = 50 phase depends to some extent on its mass. If it 2 r s is not more than about 1.4 Mþ it may contract N = 82 r s N = 126 appreciably again and then enter an oscillatory 0 Li-Be-B r s phase of its life before becoming a white dwarf r-decay Logarithm of relative abundance (Si (p. 7). When core contraction following helium p s-cycle and carbon depletion raises the temperature −2 above ¾109 Kthe -rays in the stellar assembly become sufficiently energetic to promote the 20 16 50 100 150 200 (endothermic) reaction Ne. ,˛/ O. The ˛- Atomic weight particle released can penetrate the coulomb barrier of other neon nuclei to form 24Mg in a Figure 1.5 Schematic representation of the main fea- strongly exothermic reaction: tures of the curve of cosmic abundances shown in Fig. 1.1, labelled according 20Ne C ! 16O C 4He; to the various stellar reactions consid- Q D4.75 MeV ered to be responsible for the synthesis 20 4 24 of the elements. (After E. M. Burbidge Ne C He ! Mg C ; et al..6/.) Q DC9.31 MeV 20 16 24 i.e. 2 Ne ! O C Mg C ; In a sense the ˛-process resembles helium Q DC4.56 MeV burning but is distinguished from it by the quite 12 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 different source of the ˛-particles consumed. The time in the main sequence. Helium reactions straightforward ˛-process stops at 40Ca since begin in their interiors long before the hydrogen 44TiŁ is unstable to electron-capture decay. Hence is exhausted, and in the middle part of their (and including atomic numbers Z as subscripts life they may expand only slightly. Eventually for clarity): they become unstable and explode violently, emitting enormous amounts of material into 40 4 44 Ł 20Ca C 2He ! 22Ti C interstellar space. Such explosions are seen on earth as supernovae, perhaps 10 000 times 44TiŁ C e ! 44ScŁ C v ; 22 21 C more luminous than ordinary novae. In the t1/2 ¾ 49 y (or minutes) preceding this catastrophic 44 Ł 44 C outburst, at temperatures above ¾3 ð 109 K, 21Sc ! 20Ca C ˇ C vC; t 3.93 h many types of nuclear reactions can occur in 1/2 great profusion, e.g. ( ,˛), ( ,p), ( ,n), (˛,n), 44 4 48 Then 20Ca C 2He ! 22Ti C (p, ), (n, ), (p,n), etc. (Fig. 1.6). This enables numerous interconversions to occur with the The total time spent by a star in this ˛-phase may rapid establishment of a statistical equilibrium 2 4 be ¾10 10 y (Fig. 1.6). between the various nuclei and the free protons and neutrons. This is believed to explain the cosmic abundances of elements from 22Ti to 56 Explosion 29Cu. Specifically, since Fe is at the peak of r-process 26 1010 Seconds p-process the nuclear binding-energy curve, this element Time scale Years e-process Thousand of years is considerably more abundant than those further 109 removed from the most stable state. α 7 -process T/K 10 years 108 108 years s-process 1010 years He-burning 1.5.5 The s- and r-processes (slow Core contraction Cooling and rapid neutron absorption) 107 H-burning Slow neutron capture with emission of -rays

109 106 103 0 is thought to be responsible for synthesizing Time (years) most of the isotopes in the mass range A D 63 209 and also the majority of non-˛-process Figure 1.6 The time-scales of the various processes nuclei in the range A D 23 46. These processes of element synthesis in stars. The curve probably occur in pulsating red giants over a gives the central temperature as a func- time span of ¾107 y, and production loops for tion of time for a star of about one solar mass. The curve is schematic..6/ individual isotopes are typically in the range 102 105 y. Several stellar neutron sources have been proposed, but the most likely candidates are 1.5.4 The e-process (equilibrium the exothermic reactions 13C(˛,n)16O (2.20 MeV) process) and 21Ne(˛,n)24Mg (2.58 MeV). In both cases the target nuclei (A D 4n C 1) would be produced by More massive stars in the upper part of the main- a(p, ) reaction on the more stable 4n nucleus sequence diagram (i.e. stars with masses in the followed by emission. range 1.4 3.5 Mþ) have a somewhat different Because of the long time scale involved in history to that considered in the preceding the s-process, unstable nuclides formed by (n, ) sections. We have seen (p. 6) that such stars reactions have time to decay subsequently by ˇ consume their hydrogen much more rapidly decay (electron emission). The crucial factor in than do smaller stars and hence spend less determining the relative abundance of elements §1.5.7 The x-process 13 formed by this process is thus the neutron capture understood on the basis of secular equilibria cross-section of the precursor nuclide. In this way with radioactive precursors, and their relative the process provides an ingenious explanation of concentrations are determined by the various the local peaks in abundance that occur near A D half-lives of the isotopes in the radioactive 90, 138 and 208, since these occur near unusu- series which produce them. The problem then ally stable nuclei (neutron “magic numbers” 50, devolves on explaining the cosmic presence 82 and 126) which have very low capture cross- of and uranium, the longest lived 232 10 sections (Fig. 1.5). Their concentration therefore of whose isotopes are Th (t1/21.4 ð 10 y), 238 9 235 8 builds up by resisting further reaction. In this U .t1/24.5 ð 10 y) and U .t1/27.0 ð 10 y). way the relatively high abundances of specific The half-life of thorium is commensurate with 89 90 138 140 10 isotopes such as 39Yand40Zr, 56Ba and 58Ce, the age of the universe (¾1.5 ð 10 y) and so 208 209 causes no difficulty. If all the present terrestrial 82Pb and 83Bi can be understood. In contrast to the more leisured processes uranium was produced by an r-process in a single 9 considered in preceding paragraphs, conditions supernova event then this occurred 6.6 ð 10 y can arise (e.g. at ¾109 K in supernovae ago (p. 1257). If, as seems more probable, many outbursts) where many neutrons are rapidly added supernovae contributed to this process, then such successively to a nucleus before subsequent ˇ- events, distributed uniformly in time, must have 10 decay becomes possible. The time scale for the started ¾10 y ago. In either case the uranium r-process is envisaged as ¾0.01 10 s, so that, appears to have been formed long before the 9 for example, some 200 neutrons might be added formation of the solar system .4.6 5.0/ ð 10 y to an iron nucleus in 10 100 s. Only when ago. More recent considerations of the formation 232 235 238 ˇ instability of the excessively neutron-rich and decay of Th, Uand U suggest that 10 product nuclei becomes extreme and the cross- our own galaxy is .1.2 2.0/ ð 10 yold. section for further neutron absorption diminishes near the “magic numbers”, does a cascade of some 8 10 ˇ emissions bring the product back 1.5.6 The p-process (proton capture) into the region of stable isotopes. This gives a Proton capture processes by heavy nuclei have convincing interpretation of the local abundance already been briefly mentioned in several of the peaks near A D 80, 130 and 194, i.e. some preceding sections. The (p, ) reaction can also 8 10 mass units below the nuclides associated be invoked to explain the presence of a number with the s-process maxima (Fig. 1.5). It has of proton-rich isotopes of lower abundance than also been suggested that neutron-rich isotopes those of nearby normal and neutron-rich isotopes of several of the lighter elements might also (Fig. 1.5). Such isotopes would also result from 36 46 be the products of an r-process, e.g. S, Ca, expulsion of a neutron by a -ray, i.e. ( ,n). Such 48 47 49 50 Ca and perhaps Ti, Ti and Ti. These processes may again be associated with super- isotopes, though not as abundant as others of novae activity on a very short time scale. With these elements, nevertheless do exist as stable the exceptions of 113In and 115Sn, all of the 36 species and cannot be so readily synthesized by isotopes thought to be produced in this way have other potential routes. 74 even atomic mass numbers; the lightest is 34Se The problem of the existence of the 196 and the heaviest 80Hg. heavy elements must also be considered. The short half-lives of all and promethium adequately accounts for their 1.5.7 The x-process absence on earth. However, no element with atomic number greater than 83Bi has any stable One of the most obvious features of Figs. 1.1 isotope. Many of these (notably 84Po, 85At, and 1.5 is the very low cosmic abundance of 86Rn, 87Fr, 88Ra, 89Ac and 91Pa) can be the stable , beryllium and 14 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 ..10/ Paradoxically, the problem is not to is called, produces lighter nuclei from heavier explain why these abundances are so low but ones. Conversely, high-speed 4He particles may why these elements exist at all since their occasionally collide with interstellar iron-group isotopes are bypassed by the normal chain elements and other heavy nuclei, thus inducing of thermonuclear reactions described on the spallation and forming Li, Be and B (and possibly preceding pages. Again, deuterium and 3He, even some 2Hand3He), on the one hand, and though part of the hydrogen-burning process, are elements in the range Sc Cr, on the other. As also virtually completely consumed by it, so that we have seen, the lighter transition elements their existence in the universe, even at relatively are also formed in various stellar processes, but low abundances, is very surprising. Moreover, the presence of elements in the mass range even if these various isotopes were produced 6 12 suggest the need for a low-temperature in stars, they would not survive the intense low-density extra-stellar process. In addition to internal heat since their bonding energies imply spallation, interstellar (p,˛) reactions in the wake that deuterium would be destroyed above 0.5 ð of supernova shock waves may contribute to the 106 K, Li above 2 ð 106 K, Be above 3.5 ð 106 synthesis of boron isotopes: and B above 5 ð 106. Deuterium and 3He are ˇC absent from the spectra of almost all stars and are 13C.p,˛/10Band14N.p,˛/11C ! 11B. now generally thought to have been formed by nucleosynthesis during the last few seconds of the A further intriguing possibility has recently original big bang; their main agent of destruction been mooted..11/ If the universe were not is stellar processing. completely isotropic and uniform in density It now seems likely that the 5 stable during the first few minutes after the big bang, isotopes 6Li, 7Li, 9Be, 10Band11B are then the high-density regions would have a formed predominantly by spallation reactions greater concentration of protons than expected (i.e. fragmentation) effected by galactic cosmic- and the low-density regions would have more ray bombardment (the x-process). Cosmic rays neutrons; this is because the diffusion of protons consist of a wide variety of atomic particles from high to low density regions would be moving through the galaxy at relativistic inhibited by the presence of oppositely charged velocities. Nuclei ranging from hydrogen to electrons whereas the electrically neutral neutrons uranium have been detected in cosmic rays can diffuse more readily. In the neutron-abundant though 1Hand4He are by far the most lower-density regions certain neutron-rich species abundant components [1H: 500; 4He: 40; all can then be synthesized. For example, in the particles with atomic numbers from 3 to 9: 5; homogeneous big bang, most of the 7Li formed all particles with Z ½ 10: ¾1]. However, there is rapidly destroyed by proton bombardment is a striking deviation from stellar abundances (7Li C p ! 24He) but in a neutron-rich region since Li, Be and B are vastly over abundant as the radioactive isotope 8LiŁ can be formed: are Sc, Ti, V and Cr (immediately preceding 7 8 Ł 4 the abundance peak near iron). The simplest Li C n ! Li .t1/2 0.84 s ! ˇ C 2 He/ interpretation of these facts is that the (heavier) 8 Ł particles comprising cosmic rays, travelling If, before it decays, Li is struck by a preva- 4 11 8 Ł as they do great distances in the galaxy, lent He nucleus then B can be formed ( Li C 4 11 occasionally collide with atoms of the interstellar He ! B C n) and this will survive longer than 11 4 gas (predominantly 1Hand4He) and thereby in a proton-rich environment ( B C p ! 3 He). fragment. This fragmentation, or spallation as it Other neutron-rich species could also be synthe- sized and survive in greater numbers than would

10 H. REEVES, Origin of the light elements, A. Rev. Astron. Astrophys. 12, 437 69 (1974). 11 K. CROSSWELL, New Scientist, 9 Nov. 1991, 42 8. §1.6 Atomic weights 15 be possible with higher concentrations of pro- elements are not necessarily always “constants tons, e.g.: of nature”, and variations are to be expected, particularly among the lighter elements, which 7Li C 3H ! 9Be C n can have appreciable effects on physicochemical 9Be C 3H ! 11B C n measurements and quantitative analysis. The relative abundances of the various isotopes of the light elements Li, Be and B therefore depend (12) to some extent on which detailed model of the big 1.6 Atomic Weights bang is adopted, and experimentally determined abundances may in time permit conclusions to The concept of “atomic weight” or “mean relative be drawn as to the relative importance of these atomic mass” is fundamental to the development processes as compared to x-process spallation of chemistry. originally supposed that reactions. all atoms of a given element had the same In overall summary, using a variety of nuclear unalterable weight but, after the discovery of syntheses it is now possible to account for the isotopes earlier this century, this property was presence of the 270 known stable isotopes of the transferred to them. Today the possibility of 209 elements up to 83Bi and to understand, at least variable isotopic composition of an element in broad outline, their relative concentrations (whether natural or artificially induced) precludes in the universe. The tremendous number of the possibility of defining the atomic weight of hypothetically possible internuclear conversions most elements, and the tendency nowadays is and reactions makes detailed computation to define an atomic weight of an element as extremely difficult. Energy changes are readily “the ratio of the average mass per atom of an calculated from the known relative atomic masses element to one-twelfth of the mass of an atom of of the various nuclides, but the cross-sections 12C”. It is important to stress that atomic weights (probabilities) of many of the reactions are (mean relative atomic masses) of the elements unknown and this prevents precise calculation of are dimensionless numbers (ratios) and therefore reaction rates and equilibrium concentrations in have no units. the extreme conditions occurring even in stable Because of their central importance in stars. Conditions and reactions occurring during chemistry, atomic weights have been continually supernova outbursts are even more difficult refined and improved since the first tabulations by to define precisely. However, it is clear that Dalton (1803 5). By 1808 Dalton had included substantial progress has been made in the last few 20 elements in his list and these results were decades in interpreting the bewildering variety of substantially extended and improved by Berzelius isotopic abundances which comprise the elements during the following decades. An illustration used by chemists. The approximate constancy of the dramatic and continuing improvement in of the isotopic composition of the individual accuracy and precision during the past 100 y is elements is a fortunate result of the quasi-steady- given in Table 1.3. In 1874 no atomic weight state conditions obtaining in the universe during was quoted to better than one part in 200, the time required to form the solar system. but by 1903 33 elements had values quoted It is tempting to speculate whether chemistry to one part in 103 and 2 of these ( and could ever have emerged as a quantitative science if the elements had had widely varying 12 N. N. GREENWOOD, Atomic weights, Ch. 8 in Part I, isotopic composition, since gravimetric analysis Vol. 1, Section C, of Kolthoff and Elving’s Treatise on would then have been impossible and the great Analytical Chemistry, pp. 453 78, Interscience, New York, developments of the nineteenth century could 1978. This gives a fuller account of the history and techniques of atomic weight determinations and their significance, and hardly have occurred. Equally, it should no longer incorporates a full bibliographical list of Reports on Atomic cause surprise that the atomic weights of the Weights. 16 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 ) were quoted to 1 in 104. Today the all other elements were based entirely on mass- majority of values are known to 1 in 104 and spectrometric data. 26 elements have an accuracy exceeding 1 in Accurate atomic weight values do not 106. This improvement was first due to improved automatically follow from precise measurements chemical methods, particularly between 1900 and of relative atomic masses, however, since the 1935 when increasing use of fused silica ware relative abundance of the various isotopes must and electric furnaces reduced the possibility of also be determined. That this can be a limiting contamination. More recently the use of mass factor is readily seen from Table 1.3: the value for spectrometry has effected a further improvement (which has only 1 stable naturally in precision. Mass spectrometric data were first occurring isotope) has two more significant used in a confirmatory role in the 1935 table of figures than the value for the neighbouring atomic weights, and by 1938 mass spectrometric element which has 4 such isotopes. In values were preferred to chemical determinations the twelve years since the first edition of this for hydrogen and and to gas-density book was published the atomic weight values of values for helium. In 1959 the atomic weight no fewer than 55 elements have been improved, values of over 50 elements were still based on sometimes spectacularly, e.g. Ni from 58.69(1) to classical chemical methods, but by 1973 this 58.6934(2). number had dwindled to 9 (Ti, Ge, Se, Mo, Sn, Sb, Te, Hg and Tl) or to 10 if the coulometric 1.6.1 Uncertainty in atomic weights determination for Zn is counted as chemical. The values for a further 8 elements were based Numerical values for the atomic weights of the on a judicious blend of chemical and mass- elements are now reviewed every 2 y by the spectrometric data, but the values quoted for Commission on Atomic Weights and Isotopic

Table 1.3 Evolution of atomic weight values for selected elements.a/; (the dates selected were chosen for the reasons given below) Element 1873 5 1903 1925 1959 1961 1997 H 1 1.008 1.008 1.0080 1.007 97 1.007 94(7) gmr C 12 12.00 12.000 12.011 15 12.011 15 12.0107(8) g r O 16 16.00 16.000 16 15.9994 15.9994(3) g r P 31 31.0 31.027 30.975 30.9738 30.973 761(2) Ti 50 48.1 48.1 47.90 47.90 47.867(1) Zn 65 65.4 65.38 65.38 65.37 65.39(2) Se 79 79.2 79.2 78.96 78.96 78.96(3) Ag 108 107.93 107.880 107.880 107.870 107.8682(2) g I 127 126.85 126.932 126.91 126.9044 126.90447(3) Ce 92 140.0 140.25 140.13 140.12 140.116(1) g Pr 140.5 140.92 140.92 140.907 140.907 65(2) Re 188.7.b/ 186.22 186.22 186.207(1) Hg 200 200.0 200.61 200.61 200.59 200.59(2)

.a/The annotations g, m and r appended to some values in the final column have the same meanings as those in the definitive table (facing inside front cover). The numbers in parentheses are the uncertainties in the last digit of the quoted value. .b/The value for was first listed in 1929. Note on dates: 1874 Foundation of the American Chemical Society (64 elements listed). 1903 First international table of atomic weights (78 elements listed). 1925 Major review of table (83 elements listed). 1959 Last table to be based on oxygen D 16 (83 elements listed). 1961 Complete reassessment of data and revision to 12C D 12 (83 elements). 1997 Latest available IUPAC values (84 C 28 elements listed). §1.6.1 Uncertainty in atomic weights 17 Abundances of IUPAC (the International Union and U) and carbon also approaches this category of Pure and Applied Chemistry). Their most (13C 1.11% abundant). recent recommendations.13/ are tabulated on the Known variations in the isotopic composition inside front fly sheet. From this it is clear that of normal terrestrial material prevent a more there is still a wide variation in the reliability accurate atomic weight being given for 13 of the data. The most accurately quoted value is elements and these carry the footnote r in the that for fluorine which is known to better than Table of Atomic Weights. For each of these 1 part in 38 million; the least accurate is for elements(H,He,Li,B,C,N,O,Si,S,Ar,Cu, boron (1 part in 1500, i.e. 7 parts in 104). Apart Sr and Pb) the accuracy attainable in an atomic from boron all values are reliable to better than weight determination on a given sample is greater 5partsin104 and the majority are reliable to than that implied by the recommended value better than 1 part in 104. For some elements since this must be applicable to any sample and (such as boron) the rather large uncertainty arises so must embrace all known variations in isotopic not because of experimental error, since the use composition from commercial terrestrial sources. of mass-spectrometric measurements has yielded For example, for hydrogen the present attainable results of very high precision, but because the accuracy of calibrated mass-spectrometric atomic natural variation in the relative abundance of weight determinations is about š1 in the sixth the 2 isotopes 10Band11B results in a range significant figure, but the recommended value of values of at least š0.003 about the quoted of 1.007 94(š7) is so given because of the value of 10.811. By contrast, there is no known natural terrestrial variation in the deuterium variation in isotopic abundances for elements content. The most likely value relevant to such as and osmium, but calibrated laboratory chemicals (e.g. H2O) is 1.007 97, mass-spectrometric data are not available, and the but it should be noted that hydrogen gas used existence of 6 and 7 stable isotopes respectively in laboratories is often inadvertently depleted for these elements makes high precision difficult during its preparation by , and for to obtain: they are thus prime candidates for such samples the atomic weight is close to improvement. 1.007 90. By contrast, intentional fractionation Atomic weights are known most accurately for to yield (thousands of tonnes elements which have only 1 stable isotope; the annually) or deuterated chemicals implies an relative atomic mass of this isotope can be deter- atomic weight approaching 2.014, and great mined to at least 1 ppm and there is no possibility care should be taken to avoid contamination of variability in nature. There are 20 such ele- of “normal” samples when working with or ments: Be, F, Na, Al, P, Sc, Mn, Co, As, Y, Nb, disposing of such enriched materials. Rh, I, Cs, Pr, Tb, Ho, Tm, Au and Bi. (Note that Fascinating stories of natural variability could all of these elements except beryllium have odd be told for each of the 13 elements having the atomic numbers why?) footnote r and, indeed, determinations of such Elements with 1 predominant isotope can variations in isotopic composition are now an also, potentially, permit very precise atomic essential tool in unravelling the geochemical weight determinations since variations in isotopic history of various ore bodies. For example, composition or errors in its determination have the atomic weight of obtained from a correspondingly small effect on the mass- virgin Texas sulfur is detectably different spectrometrically determined value of the atomic from that obtained from sulfate ores, and an weight. Nine elements have 1 isotope that is more overall range approaching š0.01 is found for than 99% abundant (H, He, N, O, Ar, V, La, Ta terrestrial samples; this limits the value quoted to 32.066(6) though the accuracy of atomic 13 IUPAC Inorganic Chemistry Division, Atomic Weights of weight determinations on individual samples the Elements 1995, Pure Appl. Chem. 68, 2339 59 (1996). is š0.000 15. Boron is even more adversely 18 Origin of the Elements. Isotopes and Atomic Weights Ch. 1 affected, as previously noted, and the actual varying atomic weight. Whether this variation atomic weight can vary from 10.809 to 10.812 is chemically significant depends on the half- depending on whether the mineral source is life of the transition and the relative abundance Turkey or the USA. of the various isotopes. Similarly, the actual Even more disconcerting are the substantial concentration of stable isotopes of several deviations in atomic weight that can occur elements (e.g. Ar, Ca and Pb) may be influenced in commercially available material because of by association of those elements with radioactive inadvertent or undisclosed changes in isotopic precursors (i.e. 40K, 238U, etc.) which generate composition (footnote m in the Table of Atomic potentially variable amounts of the stable isotopes Weights). This situation at present obtains for concerned. Again, some elements (such as 8 elements (H, Li, B, Ne, Cl, Kr, Xe and U) technetium, promethium and the transuranium and may well also soon affect others (such as elements) are synthesized by nuclear reactions C, N and O). The separated or partially enriched which produce a single isotope of the element. isotopes of Li, B and U are now extensively used The “atomic weight” therefore depends on which in nuclear reactor technology and weaponry, and particular isotope is being synthesized, and the unwanted residues, depleted in the desired the concept of a “normal” atomic weight is isotopes, are sometimes dumped on the market irrelevant. For example, cyclotron production of 97 6 and sold as “normal” material. Thus lithium technetium yields Tc (t1/2 2.6 ð 10 y) with salts may unsuspectingly be purchased which an atomic weight of 96.9064, whereas fission have been severely depleted in 6Li (natural 99 5 product technetium is Tc (t1/2 2.11 ð 10 y), abundance 7.5%), and a major commercial atomic weight 98.9063, and the isotope of longest supplier has marketed lithium containing as little 98 6 half-life is Tc (t1/2 4.2 ð 10 y), atomic weight as 3.75% of this isotope, thereby inducing an 97.9072. atomic weight change of 0.53%. For this reason At least 19 elements not usually considered practically all lithium compounds now obtainable to be radioactive do in fact have naturally in the USA are suspect and quantitative data occurring unstable isotopes. The minute traces obtained on them are potentially unreliable. 3 14 of naturally occurring H(t1/2 12.33 y) and C Again, the practice of “milking” fission-product (t1/2 5730 y) have no influence on the atomic rare gases from reactor fuels and marketing these weights of these elements though, of course, materials, produces samples with anomalous they are of crucial importance in other areas isotopic compositions. The effect, particularly on of study. The radioactivity of 40K(t 1.28 ð physicochemical computations, can be serious 1/2 109 y) influences the atomic weights of its and, whilst not wishing to strike an alarmist daughter elements (by ) note, the possibility of such deviations must and (by ˇ emission) but fortunately continually be borne in mind for elements does not significantly affect the atomic weight carrying the footnote m in the Table of Atomic of itself because of the low absolute Weights. abundance of this particular isotope (0.0117%). The related problem arising from radioactive The half-lives of the radioactive isotopes of the elements is considered in the next section. 16 other “stable” elements are all greater than 1010 y and so normally have little influence 1.6.2 The problem of radioactive on the atomic weight of these elements even 115 14 elements when, as in the case of In (t1/2 4.41 ð 10 y, 187 10 95.7% abundant) and Re (t1/2 4.35 ð 10 y, Elements with radioactive nuclides amongst 62.6% abundant), they are the most abundant their naturally occurring isotopes have a built- isotopes. Note, however, that on a geological time in time variation of the relative concentration scale it has been possible to build up significant of their isotopes and hence a continually concentrations of 187Os in rhenium-containing §1.6.2 The problem of radioactive elements 19 ores (by ˇ decay of 187Re), thereby generating (resulting from the ˇ decay of 87Rb), Ra, Th samples of osmium with an anomalous atomic and U. A spectacular example, which affects weight nearer to 187 than to the published value virtually every element in the central third of the of 190.23(3). was the first element known periodic table, has recently come to light with the to be subject to such isotopic disturbances and, discovery of prehistoric natural nuclear reactors indeed, the discovery and interpretation of the at Oklo in Africa (see p. 1257). Fortunately this significance of isotopes was itself hastened by mine is a source of uranium ore only and so will the reluctant conclusion of T. W. Richards at the not affect commercially available samples of the turn of the century that a group of lead samples other elements involved. of differing geological origins were identical In summary, as a consequence of the factors chemically but differed in atomic weight the possible variation is now known to span almost considered in this and the preceding section, the the complete range from 204 to 208. Such atomic weights of only the 20 mononuclidic ele- elements, for which geological specimens are ments can be regarded as “constants of nature”. known in which the element has an anomalous For all other elements variability in atomic weight isotopic composition, are given the footnote g in is potentially possible and in several instances is the Table of Atomic Weights. In addition to Ar, known to occur to an extent which affects the Ca, Os and Pb just discussed, such variability reliability of quantitative results of even modest affects at least 38 other elements, including Sr precision.

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