Modeling the Interactions in a Nucleus - Page T1
Modeling the Interactions in a Nucleus
Teacher’s Notes
Part of a Series of Activities related to
Plasmas and the Solar System
for Middle Schools
Introduction:
One of the harder ideas to grasp in fusion is that nuclei, which, because of their electric charge, strongly repel at long range (compared to the size of a nucleus), can strongly attract at short range. This activity allows students to explore a similar situation in which the magnetic interaction provides the repulsion (similar to the electric interaction within the nucleus) and Velcro provides an attractive force at short range (similar to the nuclear strong interaction).
This activity can be used directly in a unit on plasmas and the solar system, or at any time when plasmas, nuclear science, or fusion are being discussed. Students also have the opportunity to review basic features of magnetic poles.
You may wish to use this activity in conjunction with another CPEP inquiry based activity, Testing a Physical Model. It is designed to help students visualize the kinds of reactions that take place in fusion and what variables they depend upon by simulating a nuclear fusion reaction within a confinement vessel. Both activities introduce the students to the idea of using models as a valuableway to understand physical phenomena.
Materials (the following list is for one lab group, typically 2-3 students):
6 Ceramic Ring Magnets[*]with poles painted, N one color & S another4 of the 6 painted magnets should have Velcro glued to similar sides (for example, only glued to N poles). Two of the magnets should have soft Velcro and two should have hooked Velcro.
1 unsharpened pencil (to be the support for two of the magnets for the “magnetic rod assembly”)
2 cap erasers, one to be placed on each end of the pencil to keep the magnets from
coming off
Set #1: 2 ring magnets with poles painted
Set #2: 2 ring magnets with poles painted & Velcro (1 soft & 1 hooked) on similar sides
Set #3: 2 ring magnets with poles painted & Velcro (1 soft & 1 hooked) on similar sides,
arranged on an unsharpened pencil with similar sides (with Velcro) facing each other. Erasers should be placed on ends to keep magnets from sliding off.
In the Elaborate section, students are asked to use refer the CPEP chart, Fusion: Physics of a Fundamental Energy Source. This chart presents a great deal of information on plasma physics and fusion reactions, including examples of solar and terrestrial fusion reactions. This chart is available for purchase in 30 packs of a notebook (placemat) size, a poster size and a large wall chart size.The notebook size charts can be distributed to the individual students for reference. Alternatively, the poster size or large wall size can be displayed for student reference. Please see the website for ordering information.
The BSCS 5E Model of Instruction
The student activity is organized using the BSCS 5E model (see the BSCS text BSCS Science: An Inquiry Approach, Bransford, Brown, & Cocking, 2000). In this model each “E” represents an important part of the sequence through which students progress to develop their understanding. First, students are engaged by an event or a question related to a concept, and they have opportunities to express their current understanding. Then they participate in one or more activities to explore the concept and share ideas with others before beginning to construct an explanation. Following the initial development of an explanation, students have the opportunity to elaborate and deepen their understanding of the concept in a new situation. Finally, students evaluate their growing understanding of the concept before encountering a new one. The combination of the 5E model with a strong assessment-oriented design provides opportunities for learning and conceptual change in students, which leads to an improved understanding of science.
The remainder of these Teacher’s Notes will be organized into five sections, one section for each of the 5E’s: Engage, Explore, Explain, Elaborate, Evaluate. Each section (ENGAGE for example) may include:
- suggested instructions to the students to keep them on-track as they progress through this guided inquiry activity,
- additional background material so the teacher can acquire an appropriate “comfort zone” in guiding this activity, (The amount of this material to be shared with the students should be determined by their prior knowledge and the specific goals set by the teacher.)
- description of acceptable data sets and observations, suggestions of adequate answers to questions asked in the activity, and strategies for leading productive discussions.
ENGAGE Procedure – using the set of magnets with poles marked(set # 1)
In this part students will be working with the basic features of magnetic poles. They will get a hands-on sense of the interaction between like poles and opposite poles. The term interaction (rather than force) is used in this activity since interactions of a particle more generally include all the forces that affect it along with decays and annihilations that the particle might go through. Students will also note how distance between poles affects the interactions.
The following are suggested answers to the questions in this part.
- When do the magnet ends repel?
Answer: When ends of magnets marked with the same color (like poles) are brought toward each other, they repel.
- When do the magnet ends attract?
Answer: When ends of magnets marked with different colors (unlike or “opposite” poles) are brought toward each other, they attract.
- When is the push/pull the strongest?
Answer: The push/pull is the strongest when the ends of the magnets are closest. When the magnet ends are repelling (push), it can be very difficult to get the ends to touch. When the magnet ends are attracting (pull), it is most difficult to move them apart when they are touching one another.
- When is the push/pull the weakest?
Answer: Both the push and the pull between ends of magnets are weaker as the distance between the ends of the magnets increases. This means that the push and the pull are weakest when the ends of the magnets are far apart.
Once all of the student groups have answered the above questions, they can share their observations and answers to the questions one at a time, with one spokesperson per group or with group whiteboard presentations. Once it is clear that all students have a good understanding of how ends or poles of magnets affect one another, begin the next part.
EXPLORE Procedure – using the set of magnets with Velcro sides (set # 2)
This part of the activity introduces a second interaction. In the previous part the magnetic poles represented electrical charges(to be "discovered" by the students in the Explain section). But in the nucleus the only electrical charge is the positive charge of protons. This means that there are only repulsive electrical forces in the nucleus, and if there are no other forces the nucleus should fly apart. This is contradicted by the fact that there are many stable atoms with stable nuclei. Forces between Velcro on the surfaces of the ends of the magnets can be attractive at short range. This represents the short-range nuclear interaction that holds nuclei together.
The following are suggested answers to the questions in this part.
- Do the magnets with Velcro still repel? When?
Answer: Yes. When ends of magnets marked with the same color (like poles) are brought toward each other, they still repel.
- Do the magnets with Velcro still attract? When?
Answer: When the ends of the magnets being moved toward each other with have different colors, they still attract as before. Having Velcro on the ends doesn’t change this.
- Are there any differences in the attraction or repulsion compared to the plain (without Velcro) magnets?
Answer: When the magnets are too far away for contact between the Velcro parts, there is no difference. When end of magnets of the same color are brought close enough to each other that the Velcro parts make good contact, the magnets now often stay together.
- What can happen now because of the Velcro?
Answer: Ends of magnets that repelled each other when not touching can now stick together.
During a class discussion, share your answers with your class.
EXPLAIN Procedure
When you create a model you are representing a situation with something else that has similar characteristics. The physical situation you are modeling is the interactions in an atomic nucleus.
You may know some things about the structure of an atom. Fill in the blanks below with the appropriate answers using previous knowledge or research the answers if needed.
- An atom has a positively charged, dense center portion called the nucleus, which is surrounded by negatively charged particles called electrons.
- In the nucleus are two types of particles called protons and neutrons.
- The protons have a positive electric charge.
- The neutrons are neutral.
- Objects that have opposite electric charge attract each other.
- Objects that have the same electric charge repel each other.
- So…protons repel other protons.
Now consider the following questions:
Question: Since a nucleus consists of neutrons and protons, explain why a nucleus should not stay together.
Answer: The protons repel each other and so they should "fly apart".
Question: But a nucleus does stay together. How might this happen?
Answer: There must be some other interaction providing the force to hold them together.
Question: With this activity, you have tried to model what happens in the nucleus of an atom. Think back to your observations with the magnets with Velcro. When you brought the similar sides (poles) of the magnets together, did you still feel repulsion?
Answer: Yes, until they got really close together.
Question: When you brought the similar sides (poles) of the magnets together,could you get them to stick together? If so, when?
Answer: As you brought the magnets together there was a repulsive force that got stronger the closer they got to each other. But, when they were close enough for the Velcro the "grab", this was strong enough to hold the magnets together.
There were actually two interactions at work with the Velcro magnets: the magnetic interaction (part of the electromagnetic interaction) and the Velcro interaction. Inside the nucleus of an atom, there are also two interactions at work. One is the electric interaction and one is the strong nuclear interaction.
Question: In our model, which interaction (magnetic or Velcro) represented the electric repulsion of protons in the nucleus?
Answer: The magnetic interaction.
Question: In our model, which interaction (magnetic or Velcro) represented the strong nuclear attraction of protons in the nucleus?
Answer: The Velcro interaction.
Question: According to your model, which interaction in the nucleus (electric or strong nuclear) acts over larger distances?
Answer: The electrical interaction.
Question: According to your model, which interaction in the nucleus (electric or strong nuclear) only acts when the objects are very close together?
Answer: The strong nuclear interaction.
ELABORATE Procedure
Question: Using our magnets, we can also model what might happen when two separate nuclei interact. Recall that a nucleus is made up of protons and neutrons. Does a nucleus have an electric charge? If so, is it positive or negative?
Answer: Because of the protons, the nucleus has a positive electric charge.
Question: In the Explain section, you observed that even though protons repel, the nucleus stayed together because of a second interaction, the strong nuclear interaction. Would you expect that you could get two nuclei to "stick together"? Why or why not?
Answer: Because of the repulsion of the positively charged nuclei, you would expect that they would fly apart if you tried to put them together. They would only stay together if there is a second interaction. The same strong nuclear interaction that held protons together could keep the nuclei stuck together.
Question: Observe the “magnets on a rod” assembly. The similar sides(poles) of the magnets have Velcro glued to them. Do the similar sides attract or repel?
Answer: They repel.
Question: Is this consistent with the observations you made earlier in the explore procedure?
Answer: Yes. The ends of the magnets marked with the same color always repelled. These are the sides with similar poles.
Question: Now shake the rod back and forth. Can you get the pieces to attract and stay together?
Answer: Yes. Sometimes two of the magnets move toward each other because of the shaking. Whenever they got close enough that the Velcro parts were pushed together, the Velcro caused the pieces to stay together.
Question: In your model for this exercise, what do the repelling magnets represent? How is this similar and how is this different from what they represented in the model of the nucleus in the Explain section?
Answer: The repelling magnets represent the electrical repulsion interaction of the nuclei. This is the same as in the previous model, except that now the positive charge of the nuclei may be due to more than one proton.
Question: In your model for this exercise, what does the Velcro interaction represent? How is this similar and how is this different from what it represented in the model of the nucleus in the Explain section?
Answer: Again, the Velcro represents the strong nuclear interaction. This time it is between different nuclei and can keep them together (fuse). In the first model, this interaction was used to keep the nucleus together.
Question: Why did you need to shake the magnets in order to get the magnets to stick together?? What might the shaking represent in your model?
Answer: Themoving magnets repel and you need to get them moving toward each other to get them close enough for the Velcro parts to connect and keep the magnets together. Shaking the magnets got them moving fast enough that they could get close enough. The same is true for the nuclei. The magnets represent positively charged nuclei, which can’t get close enough for the nuclear interaction to act unless the nuclei are moving fast enough toward one another. You get the magnets and nuclei moving faster by adding energy (by shaking with the magnets).
Fusion Energy
(Note: Much of the material in this part of the student activity and in these Teachers Notes was originally prepared for the Testing a Physical Model activity)
Question: Using the pictures from the Fusion: Physics of a Fundamental Energy Source chart, Figure 3, and the definitions above, fill out the following table:
Symbol / Number of protons / Number of neutrons / Is this a type of hydrogen?D / 1 / 1 / yes
T / 1 / 2 / yes
2H / 1 / 1 / yes
3H / 1 / 2 / yes
4He / 2 / 2 / no
/ 2 / 2 / no
1n / 0 / 1 / no
1H / 1 / 0 / yes
Question: This presents another problem. If the nuclei are heated enough to get them moving this fast, it is hard to keep the nuclei together. They want to fly all over the place. You must have some way to keep them together, to confine them. In our model, how did you confine the "nuclei"?
Answer: The rod and the cap erasers kept the magnets confined.
Optional Calculation of Energy Released in the D + T reaction:
It is possible to calculate the energy released in the D + T reaction using data from the Fusion: Physics of a Fundamental Energy Source chart and simple arithmetic. You may want to give this as an extra credit or use it as a challenge work for your better students. Or, you might want to walk the class through this calculation.
Some notes on this calculation:
Energy units: The energy is given in MeV, which stands for Mega electron volt. The suffix “mega” means there are one million electron volts. Although “one million” sounds large, the unit is actually quite small compared to what is generally seen in the everyday world. In the metric system, the unit of energy is the Joule. But 1 Joule represents an enormous amount of energy compared to that released in a single fusion reaction. The energy released by a single fusion reaction is much too small to be given in everyday units. In numerical form:
1 eV = 1.6022 x 10-19 J = 0.00000000000000000016022 J
Even at the MeV level (one million eV), the amount is much too small to be represented easily by everyday energy units.
Mass units: As was the case with the standard unit of energy, the Joule, being much too large for the processes involved, the standard unit of mass is also too large. A more realistic unit of mass is used: the atomic mass unit (u) where