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392 Journal of Chemical Education

_Vol. 87 No. 4 April 2010

_pubs.acs.org/jchemeduc

_r2010 American Chemical Society and Division of Chemical Education, Inc.

10.1021/ed800120d Published on Web 03/09/2010

In the Classroom

Nuclear Stability and Nucleon-NucleonInteractions in Introductory and General Chemistry

TextbooksAnthony Millevolte

Department of Chemistry, University of Wisconsin Colleges-Barron County,Rice Lake, Wisconsin [email protected]

Most general and introductory chemistry textbooks fail toaddress a fundamental structural feature of atoms larger thanhydrogen: the stability of the nucleus. Although authors arequick to invoke electrostatic forces in accounting for theattraction of electrons to the nucleus, few authors explainwhy the protons in a densely packed nucleus remain in close

contact with each other. This omission creates a substantialopportunity for student misunderstanding. If electrostaticforces are used to account for the structure of matter, thenan explanation for why protons can be so tightly clusteredtogether in the nucleus is needed. Indeed, Ernest Rutherfordand other scientists took up this challenge shortly afterdiscovering the nucleus with its tremendous charge density;they postulated the existence of nuclear electrons that actedto hold the positively charged bodies in the nucleus toge-ther (1). This widely held nuclear electron hypothesis waseventually discarded following Chadwick's discovery of theneutron (2).1

Introductory and general chemistry students deserve atleast a brief account for the stability of the nucleus, lest they

conclude that electrostatic interactions are somehow intermit-tent or that chemists have a poor grasp of physics. A minimalisttextbook or classroom introduction to atomic structure shouldat least acknowledge that repulsive electrostatic forces existbetween the protons in a nucleus and that a different and muchstronger force of attraction exists between nucleons in thenucleus. In a preliminary introduction to the structure ofmatter, there is no need to provide a more elaborate explanationthan this. However, in later discussions of nuclear transforma-tions and nuclide stability, it may be worthwhile to offer a morethorough description of nuclear structure and intranuclearforces (3, 4).

For example, as part of my classroom introduction tonuclear science in second-semester general chemistry, I provide

my students with a brief description of the strong attractiveforce to help account for the stability of some nuclei and forthe instability of others. I also divulge to the students informa-tion known to physicists for more than 40 years: that unlike theelectron, the proton and neutron are notfundamental particlesof matter but are composite structures, each made up of threequarks. Whereas it is my intent to limit both of these digres-sions to a fewminutes, quiteoften interested students challengeme with questions that go considerably beyond the simplifiedmodels I introduce to them. The balance of this article iswritten for two purposes: (i) to help authors address theomissions and misconceptions found in existing textbooks

and (ii) to prepare chemistry instructors for the range ofquestions they invite from their students when they choose tobroach these subjects in class.

The Nuclear Strong Force

For reasons that will become apparent, the term strongforce is somewhat problematic. For the purpose of this article, Iwill use the term nuclear strong force to describe the strongattractive force that exists between nucleons. This nuclearstrong force is independent of charge and exists betweenprotons and protons, between protons and neutrons, andbetween neutrons and neutrons. The magnitude of the nuclearstrong force between adjacent nucleons is approximately 100times stronger than the corresponding electrostatic force.However, the nuclear strong force is not a fundamental forcebut is a secondary interaction that arises between the constitu-ent quarks in adjacent nucleons.

Nucleon Structure

The quark model for nucleons is useful for explaining theorigin of the nuclear strong force, for explaining the similaritiesand differences between the proton and the neutron, and forexposing STEM2 students to a scale of matter below that of thenucleons. Moreover, it is quite accessible to introductory stu-dents.

A nucleon is composed of three quarks that are tightlybound together by a force far stronger than the nuclear strongforce. The proton is composed of two up quarks, u, and onedown quark, d. The neutron is composed of one up quark andtwo down quarks:

An up quark has a charge of2/3 and a down quark acharge of-1/3; the quark compositions thus accounting for thetotal charge on the proton and the neutron. The fundamentalforce of nature that binds quarks together within a nucleon hasbeen known alternatively as the strong force, the stronginteraction, the chromodynamic force, or the color force.For the purpose of this article, I will refer to this primaryinterquark force as the color force to clearly distinguish it from
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394 Journal of Chemical Education



_r2010 American Chemical Society and Division of Chemical Education, Inc.

In the Classroom

principle (similar to electrons, neutrons and protons are alsoFermions with spins of 1/2). To make matters more compli-cated still, the magnitude of the nuclear strong force between twoadjacent nucleons is highly dependent on the nucleons' relativespins. This great spin dependence on the nuclear strong forceaccounts for why the deuterium nucleus is stable (its proton andneutron exist in separate orbitals and can adopt parallel spins,

thus maximizing the nuclear strong force interaction) and whydiprotons (2He) are not stable (because, both protons wouldneed to adopt antiparallelspins to populate the same orbital).The great dependence of the nuclear strong force on the relativespin of nucleons is also a central feature of the continuingcontroversy over the existence of free neutron clusters (nucleiwith no protons!) (11).

Conclusion

Even though a deeper understanding of nuclear structureoffers no additional insight into the chemical behavior of atoms,it is still important that introductory students are aware of theexistence of the nuclear strong force; if for no other reason, so

they can be confident that the existence of the nucleus iscompatible with their understanding of electrostatic forces.Furthermore, insight into the nuclear properties of atomscan be gained by adopting a relatively simple description ofnucleon-nucleon interactions. General chemistry students,many of whom are also students of physics, need not suffer fromthe omissions and outright errors that exist in introductory andgeneral chemistry textbooks today.8. Surely, if there is textbookspace and classroom time to present idealized accounts of J. J.Thompson's discovery of the electron, Rutherford's discovery ofthe nucleus, or Millikan's experiment determining the charge onthe electron, then there ought to be room for a few sentences onwhy nuclei can exist.

Acknowledgment

The author thanks Jack M. Mochel, Department of Physics,University of Illinois at Urbana-Champaign, Kim Kostka,Department of Chemistry, University of Wisconsin Colleges,and the anonymous reviewers for helpful comments and sugges-tions.

Notes1. Nuclear scientists had several other reasons to postulate the

existence ofinner atom or nuclear electrons: (a)-rays werethen known to be high-speed electrons emitted from thenucleus and (b) the nuclear electron model could explain thediscrepancy between the charge on a nucleus and its mass. For

example, Rutherford pictured the helium nucleus as fourprotons and two inner atom electrons tightly bound to twoof the protons, which accounted for the mass and charge of thehelium nucleus. Rutherford suggested that that these inneratom electrons were subject to novel forces (1). The nuclearelectron hypothesis was challenged first on quantum mecha-nicalgrounds inthe late 1920sandthengraduallyfellout offavorfollowing Chadwick's discovery of the neutron in 1932 (2).

2. STEM stands for science, technology, engineering, and mathe-matics. Seethe STEM Educational CoalitionWeb site formoreinformation, http://www.stemedcoalition.org/ (accessed Jan2010).

3. The collection of evidence that first inspired scientists topropose the existence of quarks was a growingzoo of short-lived particles that physicists were discovering in the 1950s.These strongly interacting particles, now calledhadrons, werefirst detected in cosmic rays but were then also generated in theincreasingly powerful particle accelerators that were beingbuilt.Early on, these particles numbered in the dozens, but by the

1960s there were over 200 different hadrons known. In 1961,Gell-Mann and Neeman independently classified these parti-cles into groups, mostly octets, that were based on the relation-ships between theparticlesand their properties (similar to whatMendeleev had done with the elements). Gaps in the classifica-tion scheme led to the successful prediction of previouslyunknown hadrons, many of which were discovered shortlyafterward. As confidence in the scheme increased, its patternsuggested to many that the hadrons possess substructure and

were made up of more fundamental particles. Gell-Mann andZweig independently proposed the existence of three types ofquarks (Zweigcalled hisaces) toaccount for all ofthehadronsthat were known at the time. Today, the quark model presumesthe existence of six different quarks: up, down, strange, charm,

top, and bottom (and their antiquarks) (3, 4). Quarks accountfor the spin, charge, spectra, and decay pathways of more than200 known hadrons, including the proton and neutron. Inaddition to the explanatory power of the quarks in makingsense of the particle zoo of hadrons, physicists have moredirect evidence for quarks: high-energy particle-scattering ex-

periments on protons. These experiments consistently showthat theoverwhelming volumeof the protonis empty space andthat the incident particles are scattered off of extremely smallconstituents within the proton. These small constituents werefound to possess a very high charge density and a spin of 1/2,evidence that is fully consistent with the quark model.

4. The four fundamental forces of nature are, in order of increas-ing strength: gravity, weak (the very short-range force that

mediates -decay), electromagnetic, and strong (color) forces.Physicists do notunderstand the ultimate originof these forces,though some theoretical physicists hope to develop atheory ofeverything, that would uncover the common origin of theforces (at this point, only the weak force and electromagneticforces have been unified). Because the relative strength of theseforces depends greatly on contexts in which they act, they canonly be roughly compared in strength:the nuclear strongforceis100 times stronger than the electromagnetic force; the electro-magnetic force 1011 times stronger than theweak force;and thefeeble force of gravity 1037 times weaker than the electromag-netic force. Although the color force is much stronger than thesecondary nuclear strongforcethat arisesfrom it,no onehas yetbeen able to successfully model a force law to describe it.

5. Baryons, those hadrons that include the nucleons and theheavier particles that decay into nucleons, are all composed ofthree-quark combinations with a zero color charge (similarly,antiparticles like the antiproton and antineutron are combina-tions of three antiquarks with a total color charge of zero).However, the mesons, which have a mass less than that of thenucleons butgreater than that of an electron, are composed of aquark-antiquark pair (the presence of a quark and an anti-quark of the same color also results in a zero color charge).

6. A more thorough discussion of the relationship between thenuclear strong force and the color force is beyond the scope ofthis article. The quark model for the nucleon presented here is


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In the Classroom

necessarily a simplified one and doesnot include the mechanismfor how the color force is mediated between quarks through theexchange of virtual particles called gluons. I refer the reader torefs 3 and 4for descriptions of this interaction. These quark-gluon dynamics are not yet well-understood, and there has not

yet been a force law developed to describe the color force in thesame waythat theotherfundamental forceshave been described

(though it is understood that thecolor force,similar to theweakforce, has a finite range, unlike gravity and electromagneticforces that extend into space with a decreasing magnitude but

without bound). Sophisticated quark models and quantummechanical calculations are required in efforts to better modelthe magnitude of the spin and mass of nucleons (12).

7. The stability associated with magic numbers can be identifiedby the large numbers of stable isotopes that exist for nuclei thatcontain a magic number of protons and by the large number ofstable isotones (nuclei having the same number of neutronsbut a different number of protons) that exist for those nucleihaving magic numbers of neutrons. Additionally, nuclei con-taining magic numbers of protons or neutrons are also char-acterized by their high binding energies and high nuclear

excitation energies andnuclei with a magic number of neutronshave a much lower neutron absorption cross section.

8. After examining the recent versions of 15 popular introductoryand general chemistry textbooks, I found only three texts thatdescribe a strong attractive nuclear force as part of theirintroduction to atomic structure. Approximately half of thetexts did not address the nuclear strong force in later chapterson nuclear physics, even though the chapters includedsections on nuclear stability! Of the texts that didattempt toaddress intranuclear forces in chapters on nuclear physics, twohad admirably clear, succinct, and correct descriptions ofnucleon-nucleon interactions. The other textbooks had moreor less incorrect statements in their descriptions. For example,an error in onetext describesthat ...neutrons function as a kind

of nuclear `glue' that holds nuclei together by overcomingproton-proton repulsions. The more protons there are in thenucleus, the more glue is needed. Another stated that The

weak force is 100 times weaker than the strong force (whereasthe weak force is 1013 times weaker than the nuclear strongforce). An apparently commonerror was found in another text:...[the strong force] can act only over a very short distance;

about the diameter of a nucleus.

This is a significant error,because the range of the strong force is much smaller than atypical nuclear diameter, a feature that can be used to explainthe upper limit for the size of nuclei.

Literature Cited

1. Rutherford, E. Proc. R. Soc. London A1920, 97, 374400.2. Stuewer, R. H. The Nuclear Electron Hypothesis. In Otto Hahn

and the Rise of Nuclear Physics; Shea, W. R., Ed.; Reidel:Boston,1983; pp 19-67.

3. Han, M. Y. Quarks and Gluons;A Century of Particle Charges;World Scientific Publishing Co.: Singapore, 1999.

4. Neeman, Y.; Kirsh, Y. The Particle Hunters, 2nd ed.; Cambridge

University Press: Cambridge, 1996.5. Han, M. Y. Quarks and Gluons;A Century of Particle Charges;

World Scientific Publishing Co.: Singapore, 1999; p 110.

6. Neeman, Y.; Kirsh, Y. The Particle Hunters, 2nd ed.; CambridgeUniversity Press: Cambridge, 1996; pp 214.

7. Han, M. Y. Quarks and Gluons;A Century of Particle Charges;World Scientific Publishing Co.: Singapore, 1999; p 65.

8. Mayer, M. G. Phys. Rev. 1948, 74, 235239.9. Johnson, K. E. Phys. Today 1986, 39(9), 4449.

10. Dean, D. J. Phys. Today 2007, 60(11), 4853.11. Fora short description of thecontroversyover thepossibleexistence

of a tetraneutron, see: Samuel, E.New Sci. 2002, 176(Oct 26), 3033.

12. Jaffe, R. L. Phys. Today 1995, 48(9), 2430.

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