A. A. Careno, Ja Cornegie-Mellon University Pittsburgh, - Pennsylvania 15213 and T. T. Sugihara Texas ABM Lnversity College Station, Texos 77843
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Nuclear Concepts as Part of the Undergraduate Chemistry Curriculum
The Westheimer committee, which in 1964-1965 surveyed the structure and quality of basic chemical research, found i t more meaningful to divide the field of chemistry into the categories Synthesis, Structure and Physical Properties, Chemical Dynamics, Chemistry of Condensed States, Theoretical Chemistry, and Nuclear Chemistry instead of using the traditional division into inorganic, organic, analytical, and physical chemistry (I). The study of the nucleus by chemists was properly considered by the committee to be a major subdivision in chemical research. I n the same vein, the ideas of nuclear science should he included in any soundly based chemistry curriculum. If chemistry is "the science dealing with materials, their properties, and the transformations they undergo" (I), the nucleus must also be studied. The remarks made by the distinguished theoretical physicist John Wheeler on the occasion of the centenary of the birth of Marie Curie, are particularly relevant in this context (2). Tracing the development of chemistry in this period, he states that during her life
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.chemistry became physics-snd much of the physic8 of suhstance became transformed into a new and broader chemistry. What difference in principle was there after 811 between the bonding of atoms in a molecule and the binding of atoms in a solid? What distinction between the pairing of electrons in a superconductor snd the pairing of electrons in a giant dye molecule? What sets off the photoelectric energy of an electron in a metal from the valence energy of an atomic electron? All of these effects and much besides reduced to the dynamics of fast moving electrons and slow moving nuclei-and to nothing more. If, nevertheless, much of chemistry looked complex, how could it he otherwise when the bindina at stake were the very small residuals of the much larger energies.
Professor Wheeler continues If during the life of Marie Sklodowska Curie chemistry learned from physical law to master the machinery of molecules and metals, today chemistry has added the nucleus to its domain of Presented at the Symposium on the Place of Nuclear Science Concepts in the Chemistry Curriculum at the 156th National Meeting of the American Chemical Society, Atlantic City, New Jersey, September 8-13, 1968. Supported in pert by the U. S. Atomic Energy Commission under Contract AT(30-1)2897 at Carnegie-Mellon University and Contract AT(4&1)3786 at Texas A&M University. Many of the topics praented here arose as suggestions s t the "Conference on Introducing the Concepts of Nuclear Science into the Undergraduate Chemistry Courses," sponsored by the S u b committee on Radiochemistry of the Committee on Nuclear Science, Division of Physical Sciences, National Academy of Sciences, National Research Council and the Advisory Council on College Chemistry, held in Washington D.C., November 13,14, 1967. In particular, the authors wish to acknowledge sssistance from Professors G. R. Choppin, H. M. Clark, C. D. Coryell, L. A. Haskins, J. M. Miller, F. S. Rowland, R. W. Ramette, D. E. Troutner, R. L. Wolfgang, and L. Yaffe and Drs. G. Friedlander, J. R. Grover, and E. S. Pierce.
interest. Call it nuclear chemistry or nuclear physics as one will, it is remarkably similar to molecular chemistry and atomic ~hvsicsin its historv and wav of thounht. In both eases the really rnp~dadvnnrr in u n d r r t a n d i n ~o ~ d yheg1111wiTh the identifiwrion of rhe d y n n m i r entity-the elertruu i u 1887, the missing I I I I C ~ P I > Ii L n 3933. _ \ p p t o ~ ~ m aorhib te and qunutum numhrrs we have for nucleons in the nucleus as for electrons in the molecule. The analysis of the regularities from nucleus to nucleu, like the analysis of the regularities from molecule to molecule, often provides s better answer and deeper understanding than any sttempt at a. calculation from first principles. We speak with admiration when we speak of nuclear chemistry.
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The Freshman Chemistry Curriculum I t is proposed that there are distinct advantages to a freshman curriculum which introduces nuclear concepts simultaneously with the discussion of analogous atomic and molecular concepts. Not trivial to this argument is the interest demonstrated yearly by freshman students in the usual lectures on nuclear chemistry near the end of the course. However, other pedagogical arguments can be made for the proposal. 'While still covering the "traditional" physico-chemical topics such as stoichiometry, the mole, gas laws and kinetic theory, solutions, redox, etc., many courses now include considerable emphasis on the quantum nature of matter. I n a freshman course which addresses itself to the development of the quantum nature of matter, the proper framework is present to demonstrate the universality of the quantum concept: molecules, atoms, electrons, and nuclei are quantized. The same fundamental laws of quantum mechanics apply to the nucleus as to other parts of atoms and molecules. The nucleus also provides an excellent way of developing the concept of periodicity; it frequently provides a useful tool to reveal some of the intricacies of molecular structure (e.g., Mossbauer effect). When the nucleus itself is unstable, it pmvides a powerful means of obtaining information concerning synthesis, reaction mechanisms, reaction kinetics, etc. The use of hot atoms as a tool for understanding molecular reactions as well as the discussion of elementary molecular beam experiments (3) provide a means of presenting freshmen with the latest "state of the art" even though recognizing that this must be on a cursory level. Some of the particular topics1 for which nuclear phenomena may be related, or presented as the foundation germane to the development of conventional concepts are as follows. Moss-Energy Conservation The development of the molecular equation to illustrate the conservation of the number of moles of each Volume 47, Number 8, August 1970 / 569
reacting element could be extended to illustrate the conservation of neutrons and protons, hence nucleons. From the conservation of protons, the conservation of the number of electrons naturally follows which helps to indicate general charge conservation. The mass-energy relationship is well known by most freshmen. An approximate application of E = mc2 for a simple molecular reaction such as HZ O2 HzOand compared with a nuclear reaction such as 'H n + 2H will serve to illustrate the relative magnitudes of the energy terms in both cases, the nature of the molecular force as compared to the nuclear, and the origin of the molecular term: heats of reaction. The principle of the minimization of energy as a ''d nvmg ' ' force" can be illustrated for various nuclear reactions. For example, a fusion reaction such as 'H 'H zH e+ u a t sufficiently high temperatures, and the fission of uranium, are spontaneous exoergic (exothermic) reactions which lead to a minimization of energy. This can be generalized most readily by consideration of the plot of binding energy per nucleon versus number of nucleons. In order to develop such a plot the student must be acquainted with the term binding energy. At this point it can be applied not only to nuclei, but also to electrons in atoms and molecules. It can also be pointed out that an objective of the chemist is to try to develop analogous binding-energy curves for various molecular systems. For example, one "learns" chemistry when one compares the AH for the gaseous dissociation of the halogen molecules into atoms. A plot of AHD~..versus halogen atomic number provides similar information to binding energy plots for nuclides. Certain phenomena are more thoroughly understood or proven in the realm of the molecular system, others in the realm of the nuclear, and appropriate examples should be chosen whenever possible. For example, nuclear reactions taking place in the sun and other stars excite interest in freshmen. Further, they offer an example of the use of entropy and free energy to estimate solar temperatures and probable reactions. Freshmen a t Carnegie-Mellon University are generally intrigued in seeing that the application of simple thermodynamics to the reaction 'He -t 4 'H yields an equilibrium temperature of about 10'0 OK. The role of the minimization of energy in nuclear and molecular reactions leads naturally to the importance of the randomization (entropy) in molecular systems. A fairly easy approach to this phenomenon is the illustration of randomness versus composition for the HrHD-DZsystem.
Uncertainty Principle, Pauli Principle, etc.) which r e quire the quantal point of view. With this background, one can develop the variation of quantal levels according to the nature of the interaction potential. If presented with proper analogies, the freshman student would be able to understand that a given level sequence is a consequence of the assumed interaction potential. He will also be able to appreciate that the atomic level scheme, presented in textbooks, may be the theoretical scheme and hence differs from reality because the actual potential is more complicated or at least different from that which was employed. The presentation of the nuclear level scheme enables the student to obtain some understanding of nuclear spin, and later, nuclear spin-electron spin interactions. The excited states of nuclei can be understood in terms of nucleon configuration, and deexcitation processes (r-ray deexcitation) can be seen as an extension of the electromagnetic spectrum to higher energies. A comparison of atomic and nuclear structure should include the arrangement (composition) of stable nuclides. Thus, the array of stable and unstable nuclides on a plot of proton number Z (i.e., the atomic number) versus neutron number N is particularly instructive. On such a plot the meaning of the locus of stability in terms of binding energy, based on liquid-drop considerations (volume, surface, and coulombic energies) becomes readily understandable. With reference to such a plot, exoergic (spontaneous) processes such as fission and fusion can be illustrated in terms of the increase in binding energy. At this point the direct comparison to the molecular system can be made for a number of simple systems, such as the increase in binding energy (negative enthalpy) resulting from the formation of NaCl from its elements. In consideration of nuclear phenomena, plots of Z versus N and binding energy per nucleon versus number of nucleons can be used to illustrate the natural abundances of the stable elements, the large number of tin (Z = 50) isotopes, etc. In addition, for nuclides off the stability valley, the concept of beta and alpha decay should be discussed. It is certainly not too much to present the freshman with the logic behind the concept of the neutrino in b e t d e c a y processes. This is an ideal example of the conservation of energy, linear momentum, and angular momentum. Finally, the concept of nucleon spin, besides providing the necessary connection with nmr studies, provides an explanation for nuclear magnetic moments, and, on the atomic or molecular scale, an easily comprehensible picture of ortho and para hydrogen.
Comparison o f Atomic and Nuclear Structure
Kinetics
The discussion of atomic and molecular structure can be interwoven with a discussion of the nucleus. The development of nuclear structure together with atomic structure is natural. The differences of the building blocks, electrons for atoms and molecules versus nucleons for nuclei, would have to be described. Because of these differences,the different level schemes could be discussed and justified. In such a discussion it would be instructive to present side-by-side diagrams of atomic and nuclear levels. The discussion at this point should include the various facts (discontinuity of energy, spin, conservation of angnlar momentum,
It is well known that one of the best examples of a firsborder decay is nuclear disintegration. With easily obtainable equipment the lecturer can perform a simple decay experiment in a lecture room for four or five hundred students (4). The concept of the steady state is also easier to understand and can also be readily verified experimentally. The activation energy necessary for reaction can be discussed in terms of the coulomb barrier, tunneling, neutron-to-proton ratios, etc., and the analogy with molecular reaction activation barriers explained. The mechanism for low-energy nuclear reactions is
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certainly a matter of interest to chemists. A discussion of the probability of amalgamation of the incident particle with the target nucleus (compound-nucleus formation cross section) is analogous to the probability (rate) of formation of the activated complex in molecular reactions. The probability of decay is then considered for both cases as a competition among the various energetically feasible possibilities. The distinction should be made at this point that the molecular kineticist generally measures average quantities (rate constants) based on a Boltzmann distribution of aenterof-mass velocities for the reacting molecules, while the nuclear kineticist measures the average probability for each collision event at a fixed center-of-mass velocity (hence a cross section). Thus, the necessity to study atomic and molecular beam experiments can be mentioned as a means of obtaining the detailed kinds of information for molecular reactions, now only available for the nuolear reaction. The obvious use of radioactive nuclides as tracers to aid in the elucidation of various reaction mechanisms; etc., has been mentioned many times. Such discussions, however, should include mention of exchange mechanisms, isotope effects, and other effects based on mass diierences. The variation in decay rates for certain electron-capture processes or internal-conversion processes with changes in electron density near the nucleus should be pointed out. The relationship between equilibrium constants and free energies, enthalpies and entropies is normally an important consideration in the freshman course. The discussion of tracers, as an important tool for the elucidation of reaction mechanisms, can also be used to provide further insight into the role of entropy in equilibrium expressions. Molecular reactions of the type H2 DP = 2HD, which has ab.eqnilibriurn constant value of K = 4 can be compared to reactions of the typeHCOOH DCOOD = HCOOD DCOOH which has an equilibrium constant of K = 1. For both of these reactions the enthdpy, AH = 0 and thus the diierence in K is due to differences in entropy. EXamples of this type provide a clear insight as to why processes which lead to an increase in randomness, hence entropy, are spontaneous. The subject of elemental synthesis is always of interest to freshmen. A brief description of the origin and distribution of the elements and isotopes provides a relevant method of discussing much descriptive chemistry regarding why certain elements are found together, the competition of iron for oxygen, etc. The synthesis of new elements should also be discussed. Most freshmen would be fascinated to hear about attempts to find new elements in underground atomic explosions and the irradiation of uranium with up to 12 moles/cma of neutrons. The need to search for processes by which one can cause the uranium nucleus to capture a large number of neutrons (up to seventeen has been achieved) is illustrative of several relevant phenomena. For example, the variation in the binding energy as each successive neutron is added must be considered, as well as the conditions favoring fission and alpha decay, and the general aspects of structure and stability. The properties anticipated for these new elements can be related to atomic strncture. The probability of having multiple capture by a single target nucleus is certainly
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an interesting problem of kinetics. Considerable descriptive and nuclear chemistry, particularly of the rare earths and actinides, can be brought in a t this point. The Advanced Undergraduate Chemistry Curriculum and Nuclear Chemistry
Since advanced undergraduate courses of the same title tend to vary widely in content from institution to institution, the discussion which follows will be developed along the lines of specific topics rather than in terms of courses. The topics discussed are frequently a part of courses in physical chemistry, inorganic chemistry, or instrumental analysis. Some of these topics should also be presented in the freshman course as has been discussed above. Such topics are mentioned here but no further comments are made unless a rather different approach is involved. The pedagogical reasons for introducing nuclear concepts can be divided into three general classes, each of which will be discussed briefly. I n Table 1 are listed some phenomena which are quite generally discussed in chemistry courses and which are concerned with a nuclear property or may be in part a nuclear process. In such discussions adequate treatment of the phenomenon must surely require consideration of the nuclear property or process. For example, a description of the interaction of a nuclear magnetic moment with an external magnetic field in the phenomenon called nuclear magnetic resonance is hardly comprehensible unless the student knows some of the properties of nuclei. If he thinks of the nucleus only as a massive point charge, nmr indeed appears to be mysterious. Similarly in discussions of nuclear quadrupole coupling or the Mossbauer effect, nuclear characteristics cannot be treated as merely incidental to the study of extranuclear phenomena. Other examples of class I are concerned with radioactivity. Interestingly enough, the applications of radioactive species to studies in chemistry, whether in activation analysis or in the use of tracers generally, are commonly a part of chemistry curricula. The nuclear chemist would comment at this point that while radioactivity is an interesting and useful property of nuclei, other characteristics of nuclei-their synthesis, structure, and physical properties, nuclear dynamics, nuclear condensed states, and nuclear theory, if we paraphrase the terminology of the Westheimer report-are equally interesting. We see no reason to Table 1.
Commonly Discussed Phenomena Which Involve Nuclear Processes or Nuclear Properties
Isotopy, maaa spectrometry, atomic weights Activation analvaia Interaction of nuclear moments with external field*: nuclear magnetic reaooanoe, nuolear quadrupole coupling M0asbauer effect 1aotopic tracers
Toble 2.
Principles Well Demonstrated by ~ x o m ~ l e s from Nuclear World
Barrier penetration: alpha decay, spontaneous fiaaian Squ(1r~-wellpotential: deuteron Mass-energy equivalanos: nuclidic masasa Hydrogen-like atom: poaitronium, muonium Firstorder rate law: radioactive decay Poisson statistics: radioactive decay
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restrict discussion of nuclei in chemistry curricula to radioactive ones. A second category (see Table 2) consists of topics in which a nuclear example might be the most interesting or most illuminating way of getting an idea across. Here personal tastes of the lecturer are involved, and any list proposed is likely to be illustrative only. A universally nsed example to demonstrate barrier penetration is alpha decay. Spontaneous fission might also be used. I n elementary quantum mechanics, potential-well problems are frequently solved to show the student how the solution to the Schrodinger equation changes as the form of the potential changes. The square well is characterized by having only a finite number of bound states. The deuteron, whioh has no hound excited states, might well be used as an example to illustrate the squarewell exercise. There are a number of other such examples: nuclide masses clearly reveal mass-energy equivalence. For some purposes (e.g., demonstrating the effect of reduced mass) positronium or muonium may well be examples as informative as the hydrogen atom in solving the Schrodinger equation for a Coulomb potential. The wave character of particles is illustrated by neutrons as well as electrons. Radioactive decay is commonly used to demonstrate the firsborder rate law in kinetics and the decay of a collection of unstable nuclei is d e scribed by Poisson statistics. These are all commonplace examples; there are many others whioh fit this category of nuclear examples which can clarify topics found in any chemistry curriculum. Table 3. Principles or Phenomena Which Could b e Illustrated by Nuclear as well a s Atomic or Molecular Examples -
Rsaotion kinetics: a n l o. w between molecular reactions and nualear . reactions Vibrating rotor: nuolesr excited states Harmonic oaoillator potential: nuclear shell model Spin-orbit coupling: nuo1eons i n nuclei Behavior of liqmda: liquid-dm0 model of nuclei Syntheaia of oom~ounds: svnthesia of nuclei Svmmetric too: soheroidallv deformed nuolei
The last category (Table 3) to be discussed may involve more controversy than the first two. The basic notion is the following: too often chemistry students get the idea that the principles, theories, laws, etc. which they are learning apply only to electrons or perhaps to atoms and molecules. I n many textbooks one can find statements such as "the Pauli Exclusion Principle declares that no two electrons can exist in the same quantum state" (6). One might conclude that the Pauli principle is concerned only with electrons. The ideas we teach are rather more general than the students are led to believe, whether inadvertently or not. A list of topics in this category can be made very long. Only a few will be discussed here. Molecular-beam and chemical-accelerator experiments are increasingly popular among physical chemists because of the great variety of fundamental information which those experiments are newly revealing about intermolecular potentials. Part of the collection of papers (5) presented at a recent conference on molecular dynamics, sponsored by the Advisory Council on College Chemistry, is devoted to this new approach to molecular kinetics and how such ideas should be 572
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fitted into the chemistry curriculum. This subject is raised here because the general character of the beam experiments as well as the formalism nsed to analyze the results are very similar to the corresponding aspects of nuclear reactions which have been known for many years. The similarity between molecular dynamics and nuclear dynamics should be emphasized. Nuclear excited states bear a marked similarity to excited states of molecules. The excited states of some nuclei can very well be ascribed to collective motion of the nucleus and characterized as a vibration or a r o t a
e ' 0' 0 ' . _ - - -- LEVELS I N A SPHEWAL NUCLEUS
K=O LEVELS I N A DEFORMED NUCLEUS
Idealized representotion (6) of collective energy levels for nuclei in which u both the n..t.~n number number are wen. he tot01 ~ momentum I and parity ore indicated for each level. In a rpheriml nucleus the level sporilig is that of a harmonic oscillator; in a deformed nucleus the level spacing is that of a prolate symmetric top. The quontvm number K, which corresponds to the pro[ection of I on the symmetry axis, is zero for the ground-state "rotation01 bond" and row or fwo for rotational bmnds built on higher lying vibrational leveis. The dotted lines indicate the relationship b e w e e n levels in spherical ond deformed nuclei.
tion or a coupled mixture. In the figure an idealized example is shown (6) of low-lying excited states of a nucleus with even numbers of protons and neutrons. In a spherical nucleus the level spacing is that of a quadrupole harmonic oscillator. For symmetry reasons only certain spins and parities are allowed. In a spheroidally deformed nucleus, the energies of the levels can be interpreted in terms of the eigenvalues of a synmetric'top (7), which is characterized by a quantum number K in addition to the total angular momentum qnantumbumber I. The example shows sets of rotational states based on higher lying "vibratioual" states, one of K = 0 and one of K = 2. Sheline (6) has explored the analogy between molecular and collective nuclear states at some length. The pedagogic point here is that in discussing the place of harmonic oscillators, rotors, and symmetric tops in chemistry, one should use nuclear examples i~well as the more familiar molecular ones. A modified harmonic oscillator potential is used also to develop "intrinsic" nuclear excited states, that is, the excitation of single nucleons in a nucleus as contrasted to collective behavior, in generating the nuclear shell model. This subject is discussed in another paper in this symposium (8). These are then the reasons for introducing nuclear
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concepts in undergraduate chemistry courses: (1) the phenomenon is a t least in part attributable to nuclear properties; (2) a nuclear example may be a particularly apt one; and (3) the principles of chemistry may embrace nuclei. Integration Problems
If we adopt the premise that these notions have merit, we are faced by several problems. Chemists who are not nuclear chemists already know of many non-nuclear examples to illustrate the concepts they teach. Why venture into an area in which they do not feel technically competent? It is the responsibility of nuclear chemists to cite appropriate examples, convince their colleagues of the pedagogic value of nuclear examples, and cooperate with authors in revising the next generation of textbooks to include such examples. Eventually all chemists should have a working knowledge of the rudiments of nuclear chemistry in the same sense that physical chemists and organic chemists now understand each other's fields; then the feeling of unfamiliarity will disappear. A different argument against the point of view espoused here is that already too much information exists to be covered in undergraduate courses. If the scope is to be broadened to include the nucleus as well as biochemical genetics and marine geochemistry, onesemester courses may turn out to last a year. While there may be no answer satisfactory to us all, each of us who teaches has faced this problem before and has solved it in his own way. A particularly compelling answer is that a united presentation of the concepts of physical science in undergraduate courses saves time.
Apparently different phenomena-nuclear and moleculaf-can often be shown to be only different manifestations of the same unifying principle. A modest coverage of nuclear topics in chemistry courses, simply because it makes pedagogic sense to do so, is the substance of this proposal. The details of phenomenology and theory pertaining to nuclear structure and nuclear dynamics and the many applications of nuclear properties and processes to answer non-nuclear questions should be left to specialized courses. This is common practice; quantum mechanics, for example, is currently taught in several courses a t varying levels of sophistication before finally appearing in a specialized course called quantum mechanics. Just as 35 years ago when a plea was made for including quantum mechanics in chemistry courses (9),so the nuclear chemists now urge the chemistry community to adopt the nucleus as one of its own. Literature Cited (1) "Chemistry: Opportunities and Needs." National Academy of Sdenoes, NationaiReaearoh Council Publication 1292, Printing and Publishin. Office. Nationel Aoademv of Sciences. Washington. D.C. ~0418.1965. (2) WHEELER, JORN A,. Scisnoe, IM), 1197 (19681. (3) HAMMOND. G ~ o n o 8.. s AND GRAY.HARRYB.. J. CXEW.EDDO..45. 354 (1968); W o ~ ~ a ~ x R ol c.n ~ n o .J. C x r ; ~ .Eouc.. 45, 359 (1968): OREENE,E. F.. AND KUPPEBIIAN, A,, J. CHEW.EDDC.,45,361 (1968). (4) HEBBBB, R. H.. J. CRBM.EDuC.(this SUB). (5) Moons, W A L T ~ BJ.. "Physioal Chemistry" (3rd Ed.). PrenticeHall. Ine.. Englewood Cliffa, New Jersw, 1962 p. 501. (6) SAELIND, R. K., Re.. Mod. PAW., 32. l(1960). (7) DAVIS,JEFF C.. JB., "Advanoed Physical Chemistry," T h e Ronald Preas Company. Nev York. 1965, pp. 313-22. (8) Gonoos. G. E., A N D Conrem. C. D., Paper 50. Division oi Nuclear Chemistry and Teohnolopy. 156th Meeting of the American Chemical Soeimty, Atlantic City, New Jersey, September 8-13, 1968. (9) Symposium on Moderni~ingthe Course in General Chemistry, conducted by t h e Division of Chemical Eduoation. Wth Meeting of the American Chemioal Society. Cleveland. Ohio, September 12. 1934; see papers of D n s ~ n r *Snub, ~, J. CHBI.EDITC., 12,217, 214,326,381, 436, 485, 529, 581 (1935): 13, 32. 84, 132, 179, 287. 333,385 (1936).
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