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114 The Physics TeacherVol. 48, February 2010 DOI: 10.1119/1.3293660

Learning Nuclear Science with Marbles

Zach Constan, National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI

Nuclei are small: if an atom was the size of a footballfield, the nucleus would be an apple sitting on the50-yd line. At the same time, nuclei are dense: the

Earth, compressed to nuclear density, could fit inside fourSears Towers. The subatomic level is strange and exotic. For

that reason, its not hard to get young minds excited aboutnuclear science. But how does one move beyond analogieslike those above and offer a better understanding of theextraordinary world of the nucleus? This is the challengefaced by the outreach program at Michigan State UniversitysNational Superconducting Cyclotron Laboratory (NSCL), aNational Science Foundation-supported facility specializing

in the creation and study of rare isotopes. It was necessaryto devise a model of the nucleus that students could inter-act with and even use to approximate the nuclear reactionsthat create exotic nuclei. The solution was to use magneticmarbles.

The marble nucleus

The atom is composed of an electron cloud surround-ing a nucleus at its center. The nucleus contains two kinds ofnucleons: positively charged protons and uncharged neutrons(Fig. 1). The marble model of the nucleus is therefore quite

simple, using two colors of magnetic marbles to represent the

two types of nucleons. In the example here (Fig. 2), yellow andgreen marbles represent protons and neutrons, respectively.The magnetic force that pulls them together is standing in forthe strong force1 that actually binds nucleons together into anucleus. The magnets in the marbles arent very strong, so onemust add a spherical neodymium (rare-earth) magnet at thecenter to hold the nucleons together. The point must be madethat this magnet does not represent a particle, nor is it an ac-

curate representation of the strong force.With these three components, one can build a number ofdifferent nuclei. The maximum atomic mass (total numberof protons and neutrons) of the model will depend on thenumber of marbles you attach to your neodymium magnet. A

magnet of the same size as the marbles (~5/8 in or 1.6 cm) canfit 12 nucleons in a shell around it. A 1-in magnet can fit 20nucleons on the first layer, but is significantly more expensive.More can be added beyond the first layer, but they are lesstightly boundthe weaker binding of exterior marbles can beused as an instructional tool, however.

Demonstrations with the marble nucleusIt should be stressed to the students that a marble nucleus isonly a model and not intended to accurately represent the cor-rect scale or shape of an actual nucleus. Protons and neutronsare commonly represented by spheres, but in fact a marble isnot an accurate representation of a nucleon magnified a mil-lion billion times.

The marble nucleus model has many advantages in help-ing students learn nuclear science through hands-on activi-ties. It appeals to the kinesthetic learner, stimulating mindsdifferently than descriptions or visual representations of the

nucleus. The marbles and magnets are fairly inexpensive and

widely available. A particular benefit of this model is that itcan be built/changed simply and quickly. The magnetic bondsbetween parts are easily broken and re-formed, allowing stu-dents to modify a nucleus as often as necessary. This flexibilityallows for the demonstration of many different concepts innuclear science with marble nuclei. Several such demonstra-tions are presented below.

Organization and classification

The periodic table is an important toolused to organize and classify known ele-ments. Each element is distinguished by

its atomic number, or simply the numberof protons in its nucleus. It is a simplematter to show the meaning of atomicnumber by altering the number of pro-tons on a marble nucleus. This reveals

that widely disparate elements are createdby small changes in the nucleus.

The above exercise can lead studentsto question the significance of neutrons inthe nucleus. Varying the number of neu-trons on ones marble nucleus will producemany varieties of the same element. This

N

P

N

NNP

PNP

Be9

Fig. 1. Beryllium-9: an illustration. Fig. 2. A marble model of the nucleus.

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The Physics TeacherVol. 48, February2010 115

generates discussion of isotopes and guides the class to see the

need for a Chart of the Nuclides (Fig. 3)a graph that plotsthe number of protons versus neutrons in the nucleus, layingout every (known) isotope of every element. Students can bechallenged to identify a marble nucleus isotope or construct achosen isotope with their marbles.

Radioactive decay

A cursory study of the Chart of the Nuclides reveals thatvery few isotopes are stable. The unstable ones decay aftersome time, releasing particles/energy to approach a morestable configuration. This process is readily approximated

with a marble nucleus.

Beta decays (Fig. 4) are the most common form of radioac-tive decay among unstable isotopes and can be achieved by in-troducing two new marbles: blue to represent an electron andpink to represent a positron. To reproduce the beta-minusdecay that is common among neutron-heavy isotopes, stu-dents can imagine that one of the green neutrons transformsinto a yellow proton and a blue electron. After replacing onegreen marble with a yellow and a blue, the student pulls theelectron away to simulate the beta-minus particle radiat-ing from the nucleus. This process also releases energy in theform of an anti-neutrino, which is not represented by a marblehere but should be noted nonetheless. A beta-plus decay,

where a proton transforms into a green neutron and a pinkpositron, follows a similar pattern.

In the realm of very heavy nuclei, alpha decay (the releaseof a helium nucleus) is more prevalent. It is simple to repro-duce by pulling two green and two yellow marbles from the

nucleus. Fission also occurs in this class of isotopes. By grasp-ing a marble nucleus with both hands and pulling it apart,one can readily see how two new fission products would beformed by this process. Nuclei that are very proton-rich candecay by emitting one or more protons, which is easily repro-duced with the marble nuclei.2

The ability to simulate radioactivity also means that marble

nuclei can be used to replicate decay chains. For example, stu-

dents could build a carbon-9 marble nucleus and find on thechart that it will undergo beta-plus decay. After simulating thatdecay, their resulting nucleus is a boron-9, a proton emitter.Removing one yellow marble gives a beryllium-8, which willundergo alpha decay. This decay chain leaves students withtwo helium nuclei, a free proton, a positron, and a neutrino.They may notice how those components could add up to be acarbon-9 nucleus.

A class of students, each with their own marble nucleus, canwork together to demonstrate half-life. After they all build be-ryllium-10 nuclei (unstable beta-minus emitters), the teacher

announces the passage of 1.6 million years, which happens to

be beryllium-10s half-life. One half of the class will put theirnuclei through beta-minus decay, resulting in stable boron-10nuclei, while the other half does not. After another 1.6 millionyears, half of those who still have Be-10s would have decayed,and so on. Thus, the teacher can show that even a relativelylong-lived isotope will become very rare on a 4-billion-year-old planet such as Earth.

Nuclear structure

While the number of protons and neutrons in the nucleusinfluences such things as elemental properties and stabil-ity, their relative locations in the nucleus are also important.

Marble nuclei can be used to explore ways nucleons maybe organized within a single nucleus. One can imagine andconstruct many shapes other than a simple sphere, and it isknown that nuclei can take on forms similar to those of afootball, pancake, or pear.1

Students can also experiment with different arrangementsof nucleons. While protons and neutrons have similar mass,their charge difference gives significance to their distributionthroughout the nucleus. For instance, a nucleus with an outershell composed entirely of neutrons approximates in someways matter that only contains neutrons, such as a neutronstar.

O

15.9994

N

14.0067

O 13

8.9ms

O 14

70.5s

O 15

122ms

O 16

99.758%

O 17

0.038%

O 18

0.204%

O 19

26.8s

O 20

13.5s

C

12.011

N 12

11.0ms

N 13

9.97m

N 1499.63%

N 150.37%

N 167.10s

N 174.17s

N 180.63s

N 190.42s

C 9127ms

C 1019.3s

C 1120.3m

C 1298.89%

C 131.11%

C 14 C 152.45s

C 160.75s

B10.81

Be9.01218

B 8770ms

B 1020%

B 1180%

B 1220.4ms

B 1317.3ms

B 1416ms

Be 753.28d

Be 8~1E-16s

alpha

B 9~8E-19s

proton

Be 9100%

Be 101.6E6y

Be 1113.8s

Be 12

Li6.941

He4.00260

H1.0079

Li 67.5%

Li 792.5%

Li 8844ms

Li 9177ms

He 30.0001% 99.9999%

~11.4ms

99.985%

He 4 He 6805ms

He 8122ms

H 1 H 20.015%

H 312.33y

n 110.4m

1

2

3

4

5

6

7

8

1 20

3 4 5 6

7 8

9 10

11 12 13 14 15 16

Neutrons (Isotopes)

Protons(Elements)

P

N

Li11

Stable

Beta-minus decay

Beta-plus decay

8.6ms

Be 144.6ms

B 1510ms

B 175.1ms

C 1892ms5730y

C 190.05s

N 200.13s

N 210.08s

N 2228ms

N 2314ms

O 213.4s

O 222.2s

O 230.08s

O 2465ms

C 200.01s

C 229ms

B 193.3ms

C 170.19s

CHART OF THE NUCLIDES

Fig. 3. A small portion of the Chart of the Nuclides.

P

N NP

N

N P

P N

N

e-P

N NP

N

N P

P N

P

Fig. 4. A beta-minus decay changes the nucle-

us from one isotope to another.

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116 The Physics TeacherVol. 48, February2010

1) Scattering: for low-energy/low-mass beams making glanc-ing collisions, the beam nucleus may bounce off, changingdirection but causing no damage to either nucleus.

2) Fusion: for head-on collisions at low energy, the two nucleimay combine.

3) Fragmentation: at high beam energies, one or both nucleilose nucleons, resulting in new isotopes that may be veryrare. Multiple fragmentation events will show that the cre-ated isotopes can take many forms, with some statisticallymore likely than others.

The models can behave in several ways that closely resem-ble an actual fragmentation process: the cleaving of nucleonsas the beam nucleus passes the target is accurate, as are theloose nucleons that fall near the fragment, which could comefrom the collision or a cooling period when the excited

beam nucleus lowers its energy by releasing a few protons/neutrons.4 However, some nonphysical results are also pos-sible and should be noted as such, for example, the formationof a very strangely shaped (chain-like) target or beam nucleus,or the creation of unbound isotopes that are too proton- orneutron-rich to exist.

Nuclear reactionsNuclei undergo many different reactions when colliding withother nuclei and particles, depending on the nuclei involvedand the energy (speed) with which they interact. Marblenuclei can serve as a visual aid for these events.

The nuclear fusion reactions occurring in our Sun andother stars can also be modeled using marble nuclei. The p-pchain, involving hydrogen/helium fusion, is readily repro-duced with the marbles. The triple-alpha reaction3 (Fig. 5),two nearly simultaneous reactions creating Be-8 and thenC-12, can be recreated by dropping a neodymium magnet into

the midst of three helium marble nuclei (Fig. 6). Again, the

neodymium magnet does not represent any particle or force,but simply allows the three marble nuclei to fuse togetherquickly and (almost) simultaneously. The triple-alpha reactionmay be responsible for the generation of stellar carbon and,through the recycling of material after a stars death, the pos-sibility of carbon-based life forms on planets such as Earth.

Fragmentation, the collision of two nuclei that results inone or both losing some nucleons, is probably the most excit-ing demonstration using marble nuclei. Fragmentation is usedat accelerator facilities like NSCL to generate rare, unstableisotopes. A fragmentation box (Fig. 7) was constructed toapproximate the way our laboratory produces neutron- or

proton-rich isotopes in flight for research purposes.The acrylic display box contains a target marble nucleus

magnetically suspended from a screw. A fast beam nucleus isaccelerated down a polyvinyl chloride (PVC) pipe and entersthe box [Fig. 8(a)], smashing into the target and sending mar-

bles flying [Fig. 8(b)]. The collision involves many variables:the size/mass of beam or target nucleus, the energy of theincoming beam (by altering the height of the PVC pipe), andthe impact parameter of the collision (whether it is a glancingblow or a head-on crash). Given differences in these values,there are three possible results for a collision:

N

PP

N

NN P

N

P

PN

NP

PN

N

P

PN

N

PPN

P

Fig. 5. The triple-alpha fusion reaction that creates carbon in

a star.

Fig. 6. Three helium marble nuclei ready to fuse (by add-

ing one magnet) into carbon-12.

Fig. 7. The fragmentation box. Fast beam nuclei come

down the PVC pipe at left and crash into the suspended

target nucleus.

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The Physics TeacherVol. 48, February2010 117

Acknowlegments

Many thanks to Lindsay Hebeler, Katie McAlpine, HendrikSchatz, and Remco Zegers. This outreach program issupported by NSCL and the Joint Institute for NuclearAstrophysics (JINA), an NSF Physics Frontier Center.

References1. The ABCs of nuclear science, Phys. Teach. 40, 190 (March2002); http://www.lbl.gov/abc.

2. http://en.wikipedia.org/wiki/Radioactive_decay lists manytypes of decay beyond alpha, beta, and gamma, and provides

more background.

3. D. A. Ostlie and B. W. Carroll, An Introduction to Modern Stel-lar Astrophysics (Addison-Wesley, San Francisco, 2007).

4. http://www.nscl.msu.edu/science/nuclearscience describes

how the fragmentation process leads to an excited (hot) nucleusfrom which particles can evaporate.

Zach Constan, Outreach Coordinator at National Superconducting

Cyclotron Laboratory, welcomes your comments or further ideas on using

the marble nuclei or other programs on www.nscl.msu.edu/outreach at

constan@nscl.msu.edu.

Summary

To help teachers include nuclear science in their class-room, a lesson plan for grades 7-12 is available at http://www.jinaweb.org/outreach/marble. The exercises in this lesson canbe teacher-led or self-guided, and incorporate most of theabove activities/demonstrations. Several classes have partici-

pated in this lesson during their visits to NSCL, often as anintroduction to our research before taking a tour. They were

visibly engaged by their hands-on time with the marble nuclei,and their comments show that it is an effective and enjoyableway to learn about the questions of nuclear science. It has alsobeen used to teach the basics to science teachers and studentsin Physics of Atomic Nuclei, NSCLs summer nuclear scienceprogram, preparing them for lectures on nuclear research.

Using the models in the ways listed above (and the lessonplan built around them) can ground students in the meaningof several nuclear science concepts. The marbles help bridge

the gap between the human-scale world and the impossibly

small and abstract domain of the nucleus. Amazing factsabout the nucleus may get peoples attention, but students arebrought much closer to the world of nuclear science by put-ting it in their hands.

Fig. 8. Two marble nuclei, fast beam and target, (a) before and (b) during fragmentation.

a) b)

Early Muslim Leaders in

Scientific Thought

Yet it was our Muslim forefathers who first held up the torch of rationality, tolerance, and

the advancement of knowledge throughout the dark ages of medieval Europe. Centuries

before the European scholars Bacon, Descartes, and Galileo considered the scientific

method, the great thinker Ibn Al-Haytham (10th century) laid down the rules of the

empirical approach, describing how the scientific method should operate through obser-

vation, measurement, experiment, and conclusion, the purpose being to search for truth,

not support of opinions. Likewise, Ibn Al-Nafis (13th century) stressed the importance of

accepting contrarian views, subject to the test of evidence and rational analysis.1

1. Ismail Serageldin, Science 321, 745 (8 Aug. 2008). Dr. Serageldin is the Director of the Library

of Alexandria, Alexandria, Egypt.

etcetera... EditorAlbert A. BartlettDepartment of PhysicsUniversity of Colorado

Boulder, CO 80309-0390

e

tcetera...