1. Joint Institute for Nuclear Astrophysics
Marble Nuclei: a Guided Tour
For use with “Learning Nuclear Science With Marbles” version 4.2
JINA is supported by the National Science Foundation through the Physics Frontier Center program.

2. JINA-CEE & That Great Nuclear Science Laboratory in the Sky
THEORY
EXPERIMENT
OBSERVATION

3. Nuclear astrophysics National
Michigan State University’s
National
Superconducting
Cyclotron
Laboratory
One of the JINA centers; a focal point for nuclear theory and research
Scientists are learning more about the nucleus at laboratories around the world, including the National Superconducting Cyclotron Laboratory at Michigan State University, pictured below. This project will show you what they’re up to as you build models of nuclei using magnetic marbles.

4. Magnet safety
The silvery magnet at the core of your “nucleus” is a rare-earth or neodymium magnet… very strong for its size.
Don’t put that magnet in contact with anything that is magnetically sensitive (credit cards with a magnetic stripe, for instance)!
If you get two of them together, careful they don’t pinch your fingers!
You will likely drop some (or all) of your marbles. If you can’t find them, they are probably attached to a metal table leg or similar.
Check: do you have 6 yellow & 6 green marbles?
Now: PLAY with the nucleus for two minutes (it’s a toy, after all)!

5. Studying the atomic nucleus
The nucleus
Proton
Neutron
Electron
You are made of atoms. Atoms are tiny building blocks of matter that come in many different types (elements) and make up all the objects you know: pencils, cars, the Earth, the Sun. Atoms are constructed of even smaller “particles”: The electrons exist in a “shell” around the central part of the atom: the “nucleus” where you find the protons and neutrons (see the cartoon at the far left). The “shell” typically has as many electrons as there are protons in the nucleus. The number of electrons determines the chemical properties of that atom.
All matter is made of atoms, and the nucleus is the heavy core of the atom
An atom

6. An atomic nucleus is as small compared to you…
The nucleus is SMALL
An atomic nucleus is as small compared to you…
…as you are compared to our ENTIRE solar system
There are 100 million atoms across your fingernail
The nucleus is 10,000 times smaller than the atom itself

7. Magnetic marbles make it possible!
Build a model nucleus
Proton
Neutron
Electron
Positron
Magnet to hold it all together
The marbles you’ll use to build nuclei come in many colors, to represent different particles.
Magnetic marbles make it possible!

8. Magnetic marbles make it possible!
Build a model nucleus
Proton (positive, heavy)
Neutron (neutral, heavy)
Electron (negative, light)
Positron (positive, light)
(ignore)
The marbles you’ll use to build nuclei come in many colors, to represent different particles.
Magnetic marbles make it possible!

9. Periodic Table and Nuclei
The periodic table is arranged according to “atomic number” which indicates the number of protons (and thus electrons) that each element has. For example, the atomic number for Beryllium is 4, and thus…

10. A nucleus by any other name
Worksheet Part 1
… a beryllium atom’s nucleus has 4 protons, and any nucleus with just 4 protons must be the element beryllium. However, nuclei also contain neutrons… they don’t determine the element, but they do have an effect.
Number of protons determines the element
4 protons = Beryllium
Number of neutrons determines the isotope
5 neutrons (+ 4 protons) = Beryllium-9

11. Name that isotope Beryllium-9 Beryllium-8 Beryllium-10
The number of neutrons in any particular element can go farther up or down, making many varieties called isotopes of beryllium. Compare the three isotopes of beryllium here; they are the same element (same number of protons) with the same chemical properties. Like the number of protons determines what element you have, the number of neutrons determines the isotope. Of course, the periodic table doesn’t contain any information about these isotopes, only the element, so the entry for beryllium actually refers to all isotopes of beryllium.

12. Isotopes on a graph
Every element has many possible isotopes, some more than others. You could imagine organizing all these isotopes on a graph, according to the number of neutrons on the horizontal x-axis and the number of protons on the vertical y-axis. Scientists who study the nucleus have already done this: it’s called the “chart of the nuclides”

13. A Periodic Table for Nuclei
All these carbon isotopes are chemically identical, but different numbers of neutrons gives them diverse nuclear properties
Protons (Elements)
Neutrons (Isotopes)

14. Read your Chart of the Nuclides
Build a random nucleus and name it!

15. Isotopes: stable or unstable?
Worksheet Part 2
Notice different colors and patterns in the boxes on the Chart of the Nuclides? White boxes indicate that isotope is stable, a long-lasting (and common) nucleus. Beryllium-9 is a stable isotope.
Boxes with color patterns represent unstable isotopes. That means the nucleus will eventually decay, emitting energy in the form of a particle or radiation, and become a different nucleus. If you look at the Chart, the vast majority of isotopes are unstable and thus radioactive. Radioactive nuclei are simply the isotopes that release some part of themselves after a time…the part that is released is the radiation. Each color indicates a different kind of radiation coming from that isotope, so you can tell how an isotope will decay by knowing what the colors mean!
Stable nuclei are permanent and common. 100% of beryllium found in nature will be this isotope.
NSCL studies very unstable isotopes

16. What makes an isotope unstable?
(lowest-energy nuclei)
Valley of Stability
Objects in our universe tend to move to the lowest possible energy state

17. Why do unstable isotopes decay?
To get to a lower energy, of course!
The amount of energy in a nucleus is lower when it has:
About equal numbers of protons and neutrons
He-4, Li-6, B-10…
Or slightly fewer protons than neutrons (protons repel)
Li-7, Be-9, B-11, C-13, N-15…
Even numbers of neutrons and/or protons (pairs)
He-4, He-6, He-8! But NOT He-5, He-7.
Build a carbon-12. According to the rules above, should it be low-energy (stable)?
Note: these are general rules from the nuclei we’ve measured, and sometimes these rules can be broken!

18. Beta-minus decays Valley of Stability
Too many neutrons, or not enough protons
Valley of Stability

19. Beta-plus decays Valley of Stability
Not enough neutrons, or too many protons
Valley of Stability

20. How do decays lower energy?
Worksheet Part 2
Notice different colors and patterns in the boxes on the Chart of the Nuclides? White boxes indicate that isotope is stable, a long-lasting (and common) nucleus. Beryllium-9 is a stable isotope.
Boxes with color patterns represent unstable isotopes. That means the nucleus will eventually decay, emitting energy in the form of a particle or radiation, and become a different nucleus. If you look at the Chart, the vast majority of isotopes are unstable and thus radioactive. Radioactive nuclei are simply the isotopes that release some part of themselves after a time…the part that is released is the radiation. Each color indicates a different kind of radiation coming from that isotope, so you can tell how an isotope will decay by knowing what the colors mean!
NSCL studies very unstable isotopes

21. Radioactive decay changes isotopes
Build a carbon-9 nucleus: 6 protons, 3 neutrons. It’s unstable: it has a red diamond box on the chart. It will lose one proton and gain one neutron. What isotope will it become? The newly-formed isotope is also unstable… what will it become (etc.) this is a decay chain!
After a series of decays, carbon-9 becomes helium-4

22. Unstable nuclei have a lifetime
Worksheet Part 3
Be-10 decays to B-10 with a half life of 1.6 million years
(flip something!)
The number under the unstable isotopes indicates their half-life, or the amount of time it takes for half of a sample of that isotope to decay. The shorter the half-life, the faster the isotope disappears. Even beryllium-10, with a very long half-life, will eventually become very rare: every 1.6 million years, half of it has decayed into boron-10. (Have the class build Beryllium-10 nuclei, and all flip coins. Those who get heads decay into Boron-10 (over 1.6 million years). Then repeat with those who still have Boron-10, plotting the number of Boron-10 and Beryllium-10 isotopes over time. Point out that the decays do not happen simultaneously at the 1.6-million-year mark, but gradually distributed over that period!)

23. How new elements and isotopes are made
Nuclear reactions
Worksheet Part 3
How new elements and isotopes are made
Of course, if those unstable isotopes did exist on earth at one time, how were they made in the first place? The answer: nuclear reactions… ways to change a nucleus from one isotope to another. These do occur naturally in stars and sometimes here on earth!
Reactions between tiny nuclei determine such things as:
The lifetime of stars
The elements in the universe
The energy to support life on Earth

24. Decay: unstable nuclei change
You’ve already seen how decay allows the nucleus to release a particle and become something else, so you know that some unstable isotopes can be made when a different one decays. You found that the various isotopes of beryllium actually decay in many different ways!
when a long-lived isotope decays or breaks apart, it could produce some short-lived isotopes that have long ago vanished from the earth. This is one of the few ways that new nuclei are made on our planet. Unstable isotopes have many uses as well, for example:
The decay of carbon-14 lets archaeologists know how long ago mummies lived.
The radiation given off by Americium-241 makes smoke detectors work.
Iodine-131 is used to treat the thyroid for cancers and other conditions

25. Fission: nuclei produce power
The nucleus splits into two smaller ones (fission), releasing three fast neutrons
A neutron strikes a uranium-235 nucleus
Those nuclei undergo fission, and the chain reaction continues
The fast neutrons may run into other nearby nuclei, if there are enough around
Sometimes a nucleus actually breaks apart into two whole nuclei. This splitting is called “fission”, and we use the fission of uranium-235 (92 protons, 143 neutrons) to generate nuclear power.

26. Fusion: sunlight is born
Or what if two or more nuclei ran into each other and stuck, becoming one nucleus? This kind of reaction is called fusion, and it’s the process that produces energy in the sun and other stars! In some stars, the fusion of three helium-4 nuclei forms a carbon-12.
Nuclear reactions are the way stars produce energy and “shine” the light we see. Specifically, light nuclei in the core of a star actually fuse to make a heavier nucleus.
Fusion releases energy because when multiple nuclei combine into something bigger, some of the mass of those protons and neutrons is actually converted into energy. As Einstein pointed out, E=mc2, so a small amount of mass can become a large amount of energy!
To demonstrate this, simulate fusion again like you did above by arranging three helium-4 nuclei and dropping your silver magnet in the center, so all the marbles will “fuse” into a carbon-12 nucleus.
Did energy come out when fusion occurred? It’s not obvious, but it did. Think about what happened when you dropped the silver magnet: did you hear a sound? That was some energy escaping when the marbles combined. Of course, when real nuclei combine, they release light energy.
Make three groups of two yellow and two green marbles (like in the picture at right) and put them close together… these are your helium-4 nuclei. Then drop your silver marble in the middle of them to cause your own fusion reaction and create carbon-12!
During fusion, a tiny amount of mass is converted to energy, and a heavier element is created!
When you “fuse” your marbles, does any energy come out?

27. Fragmentation: when nuclei smash
Another possibility is that two nuclei could hit each other. In that case, the nucleus can “fragment”, breaking into different parts (individual protons, neutrons, and nuclei). The process of fragmentation can create a new nucleus, possibly one that is unstable and very rare!
This is how researchers at NSCL make the rare, unstable isotopes they want to study

28. Nuclear Reactions on Earth
Are caused by:
Cosmic rays hitting nuclei in our atmosphere
Natural radioactivity
Nuclear power plants
Accelerator laboratories like NSCL
Because nuclei are SO small and they’re usually SO far apart, the chances of a reaction are VERY unlikely. Even “solid” objects like your hand have a lot of empty space between their nuclei!
Thus, nuclear reactions are hard to accomplish, though some important ones do happen here (cosmic rays hitting our atmosphere create high-energy neutrons, which hit N-14 in the air and knock out one proton to create C-14). While decay and fission do occur on earth, fragmentation and fusion/capture require two or more nuclei to get close enough to interact. For this reason, unstable isotopes are mostly very rare on our planet. We have to make our own to study them, like researchers do at National Superconducting Cyclotron Laboratory using fragmentation! The Fragmentation Box activity in “Marble Nuclei hands-on activities” demonstrates this.

29. 3a: Advanced Binding Energy
“Binding energy” is the amount of energy that is necessary to break a nucleus completely apart (to protons and neutrons)
Binding energy is measured in MeV, which is a really small amount
More binding energy
more tightly bound nucleus
longer-lasting/more stable

30. 3a: Radioactivity
Nuclei can minimize their overall energy (i.e. become more tightly bound) through radioactive decay
The steeper the drop in energy, the faster that process will go (shorter half-life)

31. 3a: Magic Numbers
The lowest-energy nuclei are the stable isotopes.
Isotopes with just enough protons or neutrons to close a quantum energy shell (the “magic number”) are the lowest.
A nucleus is considered “magic” if it has this many protons or neutrons (or even “doubly-magic” if both):

32. 3a: Binding by Element
To change a nucleus to one that is less bound (moving down the graph) requires you to put energy in.
Thus, changing a nucleus so that it moves up the graph means that energy comes out!
Do these reactions release or consume energy?
H fuses (combines) to He
Three He-4 fuse to C-12
U fissions (breaks) into lighter elements
Fe fuses or fissions
Which one releases the most energy?

33. What nuclear scientists study
Worksheet Part 4

34. Isotopes: many shapes and sizes
Nuclei don’t have to be round. Scientists have discovered nuclei that are oblong like a football or even flat like a Frisbee. See what shapes you can make with your marble nucleus! Although not all shapes of nuclei can exist, many oddly-shaped ones do. Scientists at NSCL have learned much about some very rare and unusual nuclei. For instance, they are currently studying the structure of lithium-11, which has two neutrons in a large “halo” around its other particles. This “halo” makes the Li-11 nucleus as big as lead-208, a nucleus that contains almost 20 times as many particles!
The S800 spectrograph at NSCL measures nuclear size and shape

35. Limits of stability How far can nuclei go? … UNBOUND
Proton “dripline”?
Neutron“dripline”?
UNBOUND

36. Black boxes are stable isotopes
Making the Elements
Black boxes are stable isotopes
Protons (Elements)
Iron
common rare
Neutrons (Isotopes)
Nuclei are bombarded with neutrons, forming rare isotopes that will decay into stable heavy elements

37. Marble nuclei activities
Fragmentation box
Isotope BINGO
You can learn more about the chart of the nuclides and nuclear reactions with the marble nuclei activities!
Nucleosynthesis Game