Nuclei are small: if an atom was the size of a football field, the nucleus would be an apple sitting on the 50-yd line. At the same time, nuclei are dense: the Earth, compressed to nuclear density, could fit inside four Sears Towers. The subatomic level is strange and exotic. For that reason, it's not hard to get young minds excited about nuclear science. But how does one move beyond analogies like those above and offer a better understanding of the extraordinary world of the nucleus? This is the challenge faced by the outreach program at Michigan State University's National Superconducting Cyclotron Laboratory (NSCL), a National Science Foundation-supported facility specializing in the creation and study of rare isotopes. It was necessary to devise a model of the nucleus that students could interact with and even use to approximate the nuclear reactions that create exotic nuclei. The solution was to use magnetic marbles.
The atom is composed of an electron cloud surrounding a nucleus at its center. The nucleus contains two kinds of nucleons: 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 and green marbles represent protons and neutrons, respectively. The magnetic force that pulls them together is standing in for the strong force1 that actually binds nucleons together into a nucleus. The magnets in the marbles aren't very strong, so one must add a spherical neodymium (rare-earth) magnet at the center to hold the nucleons together. The point must be made that this magnet does not represent a particle, nor is it an accurate representation of the strong force.
Figure 1. 
Figure 2. With these three components, one can build a number of different nuclei. The maximum atomic mass (total number of protons and neutrons) of the model will depend on the number of marbles you attach to your neodymium magnet. A magnet of the same size as the marbles (~5/8 in or 1.6 cm) can fit 12 nucleons in a shell around it. A 1-in magnet can fit 20 nucleons on the first layer, but is significantly more expensive. More can be added beyond the first layer, but they are less tightly bound—the weaker binding of exterior marbles can be used as an instructional tool, however.
It should be stressed to the students that a marble nucleus is only a model and not intended to accurately represent the correct scale or shape of an actual nucleus. Protons and neutrons are commonly represented by spheres, but in fact a marble is not an accurate representation of a nucleon magnified a million billion times.
The marble nucleus model has many advantages in helping students learn nuclear science through hands-on activities. It appeals to the kinesthetic learner, stimulating minds differently 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 it can be built/changed simply and quickly. The magnetic bonds between parts are easily broken and re-formed, allowing students to modify a nucleus as often as necessary. This flexibility allows for the demonstration of many different concepts in nuclear science with marble nuclei. Several such demonstrations are presented below.
• Organization and classification The periodic table is an important tool used to organize and classify known elements. Each element is distinguished by its atomic number, or simply the number of protons in its nucleus. It is a simple matter to show the meaning of atomic number by altering the number of protons on a marble nucleus. This reveals that widely disparate elements are created by small changes in the nucleus.
The above exercise can lead students to question the significance of neutrons in the nucleus. Varying the number of neutrons on one's marble nucleus will produce many varieties of the same element. This generates discussion of isotopes and guides the class to see the need for a Chart of the Nuclides (Fig. 3)—a graph that plots the number of protons versus neutrons in the nucleus, laying out every (known) isotope of every element. Students can be challenged to identify a marble nucleus' isotope or construct a chosen isotope with their marbles.
• Radioactive decay A cursory study of the Chart of the Nuclides reveals that very few isotopes are stable. The unstable ones decay after some time, releasing particles/energy to approach a more stable configuration. This process is readily approximated with a marble nucleus.
Beta decays (Fig. 4) are the most common form of radioactive decay among unstable isotopes and can be achieved by introducing two new marbles: blue to represent an electron and pink to represent a positron. To reproduce the “beta-minus” decay that is common among neutron-heavy isotopes, students can imagine that one of the green neutrons transforms into a yellow proton and a blue electron. After replacing one green marble with a yellow and a blue, the student pulls the “electron” away to simulate the beta-minus particle radiating from the nucleus. This process also releases energy in the form of an anti-neutrino, which is not represented by a marble here but should be noted nonetheless. A beta-plus decay, where a proton transforms into a green neutron and a pink positron, follows a similar pattern.
In the realm of very heavy nuclei, alpha decay (the release of a helium nucleus) is more prevalent. It is simple to reproduce by pulling two green and two yellow marbles from the nucleus. Fission also occurs in this class of isotopes. By grasping a marble nucleus with both hands and pulling it apart, one can readily see how two new fission products would be formed by this process. Nuclei that are very proton-rich can decay by emitting one or more protons, which is easily reproduced with the marble nuclei.2
The ability to simulate radioactivity also means that marble nuclei can be used to replicate decay chains. For example, students could build a carbon-9 marble nucleus and find on the chart that it will undergo beta-plus decay. After simulating that decay, their resulting nucleus is a boron-9, a proton emitter. Removing one yellow marble gives a beryllium-8, which will undergo alpha decay. This decay chain leaves students with two helium nuclei, a free proton, a positron, and a neutrino. They may notice how those components could “add up” to be a carbon-9 nucleus.
A class of students, each with their own marble nucleus, can work together to demonstrate half-life. After they all build beryllium-10 nuclei (unstable beta-minus emitters), the teacher announces the passage of 1.6 million years, which happens to be beryllium-10's half-life. One half of the class will put their nuclei through beta-minus decay, resulting in stable boron-10 nuclei, while the other half does not. After another 1.6 million years, half of those who still have Be-10s would have decayed, and so on. Thus, the teacher can show that even a relatively long-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 nucleus influences such things as elemental properties and stability, their relative locations in the nucleus are also important. Marble nuclei can be used to explore ways nucleons may be organized within a single nucleus. One can imagine and construct many shapes other than a simple sphere, and it is known that nuclei can take on forms similar to those of a football, pancake, or pear.1
Students can also experiment with different arrangements of nucleons. While protons and neutrons have similar mass, their charge difference gives significance to their distribution throughout the nucleus. For instance, a nucleus with an outer “shell” composed entirely of neutrons approximates in some ways matter that only contains neutrons, such as a neutron star.
• Nuclear reactions Nuclei undergo many different reactions when colliding with other nuclei and particles, depending on the nuclei involved and the energy (speed) with which they interact. Marble nuclei can serve as a visual aid for these events.
The nuclear fusion reactions occurring in our Sun and other stars can also be modeled using marble nuclei. The p-p chain, involving hydrogen/helium fusion, is readily reproduced with the marbles. The “triple-alpha” reaction3 (Fig. 5), two nearly simultaneous reactions creating Be-8 and then C-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 together quickly and (almost) simultaneously. The triple-alpha reaction maybe responsible for the generation of stellar carbon and, through the recycling of material after a star's death, the possibility of carbon-based life forms on planets such as Earth.
Fragmentation, the collision of two nuclei that results in one or both losing some nucleons, is probably the most exciting demonstration using marble nuclei. Fragmentation is used at accelerator facilities like NSCL to generate rare, unstable isotopes. A “fragmentation box” (Fig. 7) was constructed to approximate the way our laboratory produces neutron- or proton-rich isotopes in flight for research purposes.
Figure 3. 
Figure 4. 
Figure 5. 
Figure 6. 
Figure 7. The acrylic display box contains a target marble nucleus magnetically suspended from a screw. A “fast beam” nucleus is accelerated down a polyvinyl chloride (PVC) pipe and enters the box [Fig. 8(a)], smashing into the target and sending marbles flying [Fig. 8(b)]. The collision involves many variables: the size/mass of beam or target nucleus, the energy of the incoming beam (by altering the height of the PVC pipe), and the impact parameter of the collision (whether it is a glancing blow or a head-on crash). Given differences in these values, there are three possible results for a collision:
1) Scattering: for low-energy/low-mass beams making glancing collisions, the beam nucleus may bounce off, changing direction but causing no damage to either nucleus.
2) Fusion: for head-on collisions at low energy, the two nuclei may combine.
3) Fragmentation: at high beam energies, one or both nuclei lose nucleons, resulting in new isotopes that may be very rare. Multiple fragmentation events will show that the created isotopes can take many forms, with some statistically more likely than others.
Figure 8a. 
Figure 8b. The models can behave in several ways that closely resemble an actual fragmentation process: the cleaving of nucleons as the beam nucleus passes the target is accurate, as are the loose nucleons that fall near the fragment, which could come from 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 possible and should be noted as such, for example, the formation of a very strangely shaped (chain-like) target or beam nucleus, or the creation of unbound isotopes that are too proton- or neutron-rich to exist.
To help teachers include nuclear science in their classroom, a lesson plan for grades 7–12 is available at http://www.jinaweb.org/outreach/marble. The exercises in this lesson can be teacher-led or self-guided, and incorporate most of the above activities/demonstrations. Several classes have participated in this lesson during their visits to NSCL, often as an introduction 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 enjoyable way to learn about the questions of nuclear science. It has also been used to teach the basics to science teachers and students in Physics of Atomic Nuclei, NSCL's summer nuclear science program, preparing them for lectures on nuclear research.
Using the models in the ways listed above (and the lesson plan built around them) can ground students in the meaning of 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 facts about the nucleus may get people's attention, but students are brought much closer to the world of nuclear science by putting it in their hands.
Many thanks to Lindsay Hebeler, Katie McAlpine, Hendrik Schatz, and Remco Zegers. This outreach program is supported by NSCL and the Joint Institute for Nuclear Astrophysics (JINA), an NSF Physics Frontier Center.
References
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.
Full figure (31 kB)Fig. 1. Beryllium-9: an illustration. First citation in article
Full figure (31 kB)Fig. 2. A marble model of the nucleus. First citation in article
Full figure (129 kB)Fig. 3. A small portion of the Chart of the Nuclides. First citation in article
Full figure (46 kB)Fig. 4. A beta-minus decay changes the nucleus from one isotope to another. First citation in article
Full figure (54 kB)Fig. 5. The “triple-alpha” fusion reaction that creates carbon in a star. First citation in article
Full figure (28 kB)Fig. 6. Three helium marble nuclei ready to fuse (by adding one magnet) into carbon-12. First citation in article
Full figure (29 kB)Fig. 7. The “fragmentation box.” Fast beam nuclei come down the PVC pipe at left and crash into the suspended target nucleus. First citation in article
Full figure (34 kB)Fig. 8a. Two marble nuclei, “fast beam” and “target,” (a) before fragmentation. First citation in article
Full figure (32 kB)Fig. 8b. Two marble nuclei, “fast beam” and “target,” (b) during fragmentation. First citation in article