Testing a Physical ModelThe three variables involved in the graph are the plasma confinement time,...

Testing a Physical Model

Part of a Series of Activities related to Plasmas and the Solar System for Middle Schools

Teachers Notes Lead Authors: Vickilyn Barnot, Assistant Professor of Education,

Director of the Early Child hood Education Program University of Pittsburgh at Greensburg Member, Contemporary Physics Education Project

Katrina Brown, Associate Professor of Physics, University of Pittsburgh at Greensburg, Member, Contemporary Physics Education Project

Todd Brown, Assistant Professor of Physics, University of Pittsburgh at Greensburg, Member, Contemporary Physics Education Project

Ted Zaleskiewicz, Professor Emeritus of Physics,

University of Pittsburgh at Greensburg, President Emeritus, Contemporary Physics Education Project

Adapted from an Activity originally authored by Robert Reiland, Shady Side Academy, Pittsburgh, PA Vice-President, Contemporary Physics Education Project G. Samuel Lightner, Professor Emeritus of Physics, Westminster college,

New Wilmington, PA, Vice-President, Contemporary Physics Education Project

Prepared with support from the Department of Energy, Office of Fusion Energy Sciences, Contract # DE-AC02-09CH11466 Copyright 2012 Contemporary Physics Education

Preface This activity, produced by the Contemporary Physics Education Project (CPEP), is intended for use in middle schools. CPEP is a non-profit organization of teachers, educators, and physicists which develops materials related to the current understanding of the nature of matter and energy, incorporating the major findings of the past three decades. CPEP also sponsors many workshops for teachers. See the homepage www.CPEPweb.org for more information on CPEP, its projects and the teaching materials available. This activity packet consists of the student activity followed by notes for the teacher. The Teacher’s Notes include background information, equipment information, expected results, and answers to the questions that are asked in the student activity. The student activity is self-contained so that it can be copied and distributed to students. Page and figure numbers in the Teacher’s Notes are labeled with a T prefix, while there are no prefixes in the student activity.

The Student Section of this Activity is structured on the BSCS 5E model for Inquiry instruction. The following description of the 5E model is excerpted from the Introduction to the BSCS text: BSCS Science: An Inquiry Approach

ENGAGE EXPLORE EXPLAIN ELABORATE EVALUATE

According to the BSCS 5E 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 (Bransford, Brown, & Cocking, 2000)

http://www.cpepweb.org/

Testing a Physical Model Page T1

Testing a Physical Model

Teacher’s Notes

Part of a Series of Activities related to Plasmas and the Solar System for Middle Schools

Introduction: This Activity has been developed to supplement the Contemporary Physics Education Project chart, Fusion: Physics of a Fundamental Energy Source. In the lower right hand corner of this chart there is a graph showing the history of fusion research and the region in which fusion reactions could be sustained. The three variables involved in the graph are the plasma confinement time, τ (the Greek letter tau), the nuclear particle density, n and the absolute temperature, T. How these three variables are related to fusion may seem like an abstract exercise to most students. This Inquiry Based Activity, Testing a Physical Model, is designed to help students visualize the kinds of reactions that take place in fusion and to make sense of how the three variables are related. This Activity uses plastic bottle tops, Velcro dots with adhesive backing, masking tape, and a closable box to produce a physical model of a fusion reactor. The bottle top cylinders (with soft Velcro attached to some, hard Velcro attached to others), simulate the nuclei and the box simulates the confinement vessel. Heating is simulated by shaking the system and fusion is simulated by the bottle top cylinders that stick together. Student activities focus on how varying the number of bottle tops and the time of shaking will influence the number (N) of fusions produced. The students should generate models of how the variables work to achieve sustained fusion in a reactor. Some thoughts on developing models along with the limitations of such models will be presented later in these Teacher’s Notes. It is important that students understand which aspects of the models are valid and which are questionable. Materials: You will need to assemble one KIT of materials for each group of three or four students in your class Materials needed for EACH KIT are: Large cardboard box (approximately 12in x 12in x 12in) Small cardboard box (approximately 5in x 5 in x 5in) 274 small plastic bottle tops (from bottles of two liters or less) 112 large plastic bottle tops (from bottles of three liters or more) 137 hard Velcro dots 56 soft Velcro dots masking tape stop watch transparent ruler pencil graph paper


Prepare for this Activity by saving the required plastic bottle tops. This can be done as part of a recycling project, or just by asking students to bring in the plastic tops from used soda bottles, water bottles, etc. The different sizes of bottle tops are necessary in order to simulate nuclei of different masses. In addition, more of the small size is needed because the number of this size will be varied in the model to investigate how variation in particle density of nuclei produces variations in fusion rates. With both sizes of tops, use the masking tape to attach two bottle tops of the same size together - hole to hole to form a closed cylinder. Affix small pieces of the Velcro with hooks (the ones with a hard feeling to them are “hooks”) to one flat side of the smaller cylinders and affix small pieces of the soft Velcro (“loops”) to one flat side of the larger tops (see Figure T1). It is important in one part of the physical model that the hooked Velcro is on the smaller bottle tops and the looped Velcro is on the larger ones. The smaller bottle tops simulate deuterons and the larger ones simulate tritons. (A deuteron is the nucleus of a deuterium atom which is sometimes called heavy hydrogen made up of a proton and a neutron. A triton is the nucleus of a tritium atom -- the most massive of the three hydrogen isotopes, consisting of a proton and two neutrons. The symbols typically used for the deuteron and triton are “D” and “T” respectively; for example the “D+T” reaction on the chart. To avoid confusion with the symbol for temperature in this activity, “T” will be used to represent triton only as part of the combination “D + T”. This is the deuteron-triton fusion reaction.) Figure T1: Bottle top nuclei details Next - - assemble the KITS each KIT will contain: Large cardboard box (approximately 12in x 12in x 12in) Small cardboard box (approximately 5in x 5 in x 5in) - - containing 6 large cylinders and 12 small cylinders Ziploc bag of 50 small cylinders 3 Ziploc bags of 25 small cylinders Ziploc bag of 50 large cylinders masking tape stop watch, transparent ruler, pencil, and graph paper NOTE: In preparing the KIT place a layer of paper over all but the small box - - so when the students open the large box to take out the small box - - they will NOT see the bags of bottle caps. NOTE: If your class periods are approximately 50 min in duration - - doing the entire Activity could well take five days - - covering one E per day.

tape holding bottle tops together

hooked Velcro

(a) A small bottle top nucleus (simulated deuteron)

tape holding bottle tops together

soft Velcro

(b) A large bottle top nucleus (simulated triton)


The BSCS 5E Model of Instruction 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) will typically include: 1) suggested instructions to the students to keep them on-track as they progress through this guided Inquiry Activity, 2) 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.) 3) description of acceptable data sets and observations, suggestions of adequate answers to questions asked in the Activity, and strategies for leading productive discussions. According to the BSCS 5E model (see the BSCS text BSCS Science: An Inquiry Approach ), 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 (Bransford, Brown, & Cocking, 2000). ENGAGE Procedure Avoid immediately telling the students that the physical model they are testing is the fusion reaction. Some will undoubtedly guess this but the ENGAGE activity might be more effective if you wait until the EXPLORE Procedure to actually confirm this guess. Organize the students into working groups of three or four. Provide each group with a KIT. Have each group open the large KIT box and remove the smaller box. Tell them NOT to open or shake the small box or peek under the paper! Prompt the students to guess “what might be in the smaller box”? Chart the “guesses” made and lead a class discussion as to why students made those ”guesses”. (Naturally no guess can be incorrect or wrong!) Now instruct the students to shake the smaller box!


Prompt the students to guess what might be in the box - - now that they have shaken it. Chart the “guesses” made and lead a class discussion as to why the students made those ”guesses". (Naturally - - again - - no guess can be incorrect or wrong!) Instruct the students to open the small box and confirm that it contains: Six large cylinders with soft Velcro on one end and twelve small cylinders with hard Velcro on one end. Have the students confirm that a small cylinder and large cylinder will pair and indeed stick together (use terms like ‘stick together’ or ‘form a pair’ rather than ‘fuse’) when the Velcro ends are pushed together. Now - - have the students place the cylinders in the small box and shake it for about 5s. Have them open the small box and count the number of pairs formed. The student groups are then asked to:

Record the number of pairs, N, which stuck together here. _________ (N= the number of cylinder pairs created.)

Have the groups share their answers with the class and propose ideas as to why their answers differ. This might be a good time to discuss with the students why the random nature of the collisions might also contribute to the range of responses (values of N) reported. One source of the random nature of the process is that all collisions do not necessarily produce pairs. See Figure T2.

Figure T2: Two of the many possible collision orientations of bottle tops

Next, instruct the students to discuss (within their groups) : things that they could do which would result in a larger N. You might suggest they perform some brief mini-experiments to confirm or refute their ideas. Chart the student responses for all to see.

(a) Bottle top nuclei on a collision path and likely to “form a pair”

(b) Bottle top nuclei on a collision path with no chance of “forming a pair”.


The list created in your class of the ways in which N could be increased will probably include many of the following

a) Shake the box for a longer period of time. b) Place more bottle top cylinders in the box. c) Shake the box harder (more vigorously). d) Replace the Velcro patches with bigger Velcro patches. e) Attach Velcro patches to both ends of the cylinders.

All of these are related to variables that you could alter in your experiment to see if they affect N:

Possible ways to increase N Variable that would be changed

a) Shake the box for a longer period of time. Shaking time = τ

b) Place more bottle top cylinders in the box. Number of cylinders = n

c) Shake the box harder (more vigorously). Vigor of shaking

d) Replace the Velcro patches with bigger Velcro patches.

Size of Velcro

e) Attach Velcro patches to both ends of the cylinders.

Amount of Velcro

To conclude the ENGAGE Procedure, lead a class discussion of the suggested ways to increase N and how each relates to the respective variables in this experiment. If the ENGAGE Procedure completes today’s activities, give students further direction by telling students that at our next meeting we will begin to explore, as scientists, the various variables that may affect the number of cylinder pairs we are able to create. EXPLORE Procedure In this section of the Activity, students will take data to show how changing the length of shaking time will change the number of cylinder pairs created (N). Student actions in the EXPLORE Procedure are very closely “guided” in that they are given explicit instructions as to how the variables should be adjusted from trial to trial. Student actions in the ELABORATE Procedure are substantially more “open” in that the students themselves are allowed to decide how the variables are to be adjusted from trial to trial. It is nevertheless important to remind the students, that when performing an experiment only ONE variable at a time should be changed. In this experiment you will be changing τ (the shaking time), so it is important to keep all the OTHER possible variables [those mentioned in b) thru e) above] constant during this first experiment. So - - do NOT

Change the number of cylinders in the box

Change the size of the Velcro patches on the cylinders

Change the amount of Velcro patches on the cylinders.


In addition stress to the students that, they must also NOT change how hard (vigorously) they shake the box. Keeping the “Vigor of shaking” constant is difficult to do. Suggestions for classroom management: •Assign specific roles to each member of each team - - for example “shaker”, pair counter, data recorder, stop watch operator, corporate spy. (Adding the role of corporate spy offers excitement and intrigue for the students while decreasing the number of questions students ask you, the teacher about procedures. The student designated as “corporate spy” is the only student from each group who may visit another group to clarify directions or to inquire as to how another group is proceeding to carry out the activities, etc.)

•It is crucial for maintaining constant vigor of shaking that the SAME student does the shaking throughout the entire Activity. Discuss with students WHY it is so important to control this variable (shaking vigor) and how changing the shaking vigor may affect the validity of this experiment.

•The noise level will be quite high - - with say 5 or 6 groups shaking randomly - - such that hearing the stop watch operator say START or STOP - - may be impossible. An alternate plan is to have you (the teacher) run the stop watch and have ALL groups shake simultaneously at your command.

•It would probably be a good idea to remind the students to shake with moderate vigor since it is unlikely they will be able to maintain a constant rate if they shake with too much vigor. •When shaking for 40 s or 50 s MANY pairs will be formed - - it might be quicker to count the UN-paired cylinders and subtract to find the number (N) of pairs that formed. •When making the graph - - always start at the 0 point – students may not understand broken scale at this time. Have the students read and follow the instructions starting with:

3) It will be important to practice shaking the box at a nearly constant rate, time after time, until you can do so reproducibly. You may use the stop watch in your KIT - - or your teacher may be in charge of the timing.

Monitor student progress in completing Data Table 1. In particular, you may need to provide guidance if the “number of pairs formed” by any single group does not become fairly consistent after six or seven trials.

Data Table 1 Trial Number N, number of pairs formed 1 2 3 4 5 6 7 8


9 Now that the students have mastered “shaking with constant vigor” it is time for them to begin taking data by varying τ (10 s, 20 s, 30 s, 40 s, and 50 s) while keeping the number of cylinders fixed (50 of each). As they start to complete Data Table 2, be sure they enter three readings for each τ and then determine the average number of pairs formed for the three trials Navg . NOTE: To save time, it would be acceptable for them to enter the data from Trials 7, 8, and 9 from Data Table1 in the10 s row of Data Table 2. (The data shown below in Data Table 2 was taken by the authors. We present it here to give you a sense of an acceptable “spread” in the data points for three trials for a specified “Time the box was shaken”.) Data Table 2 n = 100 (50 large cylinders + 50 small cylinders) Time the box was shaken (τ)

Number of pairs formed first trial

Number of pairs formed second trial

Number of pairs formed third trial

Average number of pairs formed (Navg)

10 s 20 15 16 17 20 s 23 19 26 23 30 s 28 27 32 29 40 s 35 35 33 34 50 s 36 34 34 35 Have the student groups take a sheet of graph paper and pencils from their KITs. Instruct them to label the y axis Navg and the x-axis τ. Have each group select a scale for the axis so that all their data points can be plotted on this

graph. Finally, have each group plot the ordered pairs (t, Navg ) on the coordinate plane they have

constructed. After each group fits a line to the points they should conclude: “the correlation is positive” (The authors have plotted their data below.)


If the students shake with too much vigor, they will obtain a graph more like the following: As can be seen from this graph, the data does not show a positive correlation between the number of pairs and shaking time beyond a certain time, but instead quickly reaches a saturation point (in this case around 33 pairs formed). Any shaking time beyond approximately 20 seconds produced the same number of pairs due to the fact that the shaking intensity was too great.

EXPLAIN Procedure Teacher Background Information A basic question regarding fusion is “why does it occur at all?”. What “motivates” two nuclei to fuse together? The answer to this can also be used to describe why some nuclei are prone to fragmenting on their own via a process that seems like fusion in reverse: fission. Nuclei will fuse together in a collision because it is “energetically favorable”. Systems in nature progress towards a state of the lowest possible energy: hot items cool off, and objects roll downhill. When two nuclei fuse, they may do so with conditions that make their fused state more energetic than the sum energy of their pieces. Such fusion products will break back apart. On the other hand, some fusion reactions produce a product whose net energy is lower than the energy of the pieces that went into making it up. Such nuclei will stay in this fused state in what is termed a bound (stable) nucleus. In order for these products to fuse, they must get close together. However, nuclei initially far apart are NOT energetically inclined to get closer to each other due to a force called the electrostatic force. For nuclei, this will always be a repulsive force due to the positive charged protons in the nucleus. It is shown later in this section that when the nuclei get to within a much shorter distance, an attractive force (the Strong Force) can overwhelm the electrostatic repulsive force and make it possible for a stable fusion reaction to become energetically favorable. EXPLAIN (1) The chart you give to the students shows graphics for two important fusion processes. The process on the right of the chart is reprinted below as Figure T3. This “p-p” SOLAR FUSION CHAIN, is the rather complicated process which generates the majority of energy given off by our Sun. It is NOT necessary to explain the details of the “p-p” ” SOLAR FUSION CHAIN. It MAY NOT be appropriate at the middle school level- -yet developing an initial schema of this process will be helpful for your students who may later study this process in college.


Figure T3: The “p-p” Solar Fusion Chain The process on the left in the block, reprinted below as Figure T4, is D + T = 4He + 1n

Figure T4: The D+T Reaction The D+T reaction is the process modeled in this Activity. It is the reaction that will most likely be used in the first fusion reactors to generate electricity on a commercial basis. Teacher Background Information Note that you (the teacher) may determine the depth of information discussed below as you see appropriate and relevant for your students. There are four fundamental interactions in nature: the electromagnetic interaction, the gravitational interaction, the strong interaction and the weak interaction. Students are very familiar with the gravitational interaction and have some knowledge of the electromagnetic interaction, but the other two are not part of the general knowledge of the majority of middle

Reactants Fusion Products


school students. However, a short discussion concerning the structure of the nucleus of an atom, and the electromagnetic interactions in the nucleus, necessitates the introduction of one of the two lesser known interactions. The nucleus contains only two types of particles: neutrons which carry no charge and positively charged protons. Positive charges interact predictably with one another: they repel. The nucleus is closely packed so any proton within it feels an immense electrostatic repulsive force from the neighboring positive charges. Thus, no nuclei could have more than one proton if the only force in nature were the electrostatic force since the nucleus would disintegrate as the protons tried to move away from one another. Some students might suggest that the gravitational interaction overwhelms the electrostatic interaction and is sufficient to hold the nucleus together. This is a good argument but would require the gravitational force to be stronger than the electrostatic force. In fact, the gravitational force will be very strong when the masses of the objects involved are large (e.g. Sun, planet, moon, etc.). However, the masses of the protons are so small that the gravitational force between them is very weak and is not strong enough to keep the protons together. If this discussion should arise, there are several instances that illustrate how gravity can be weaker than the electromagnetic interaction:

- Static electricity is well known to cause one’s hair to “stand up” (see Figure T5), overwhelming the gravitational force that is pulling it down.

- Static electricity causes bits of paper to be attracted to a comb that has been recently run through a person’s hair, preventing gravity from pulling the paper off.

- Static electricity is why a balloon rubbed through one’s hair can be made to stick on a wall or ceiling, overwhelming the gravitational force that tries to pull the balloon to the ground.

Figure T5: The Electrostatic Force Overwhelming the Gravitational Force

If gravity plays no significant role in keeping protons together in a nucleus, and the electrostatic force would readily destroy a nucleus with more than one proton, then there must be another force that keeps the nucleus together. In order to keep the protons near one another, this force must be stronger than the electrostatic interaction. Since it must be strong, it is called the Strong Interaction. It turns out that the Strong Interaction also works on neutrons as well as protons. So the protons and neutrons that are close to one another inside a nucleus will feel attractive strong interactions.


It is important to point out that the strong interaction must:

A. Be attractive so that it offsets the repulsive electrostatic force between protons inside the nucleus.

B. Be short range so that it can overwhelm the electrostatic force for only a very short distance or else there would be nothing to stop objects, if not the entire universe, from collapsing onto itself by the Strong Force.

Point B shows why there is a limit to the size of stable nuclei: the addition of more and more protons results in an increasing electrostatic repulsive force that can no longer be countered by the stronger, but shorter ranged, Strong Force. Protons on one side of a large nucleus would be too far from protons on the other side to experience an attractive Strong Interaction, yet they would still feel a repulsive electrostatic interaction since that interaction can act over a greater distance. Point A is the key to why the D+T reaction can produce fusion. When the D+T reaction occurs the result is a helium nucleus which, by its nature, has two protons. Although protons attract each other via the strong force, they repel each other by the electrostatic force. Neutrons do not carry a charge and are therefore not influenced by the electromagnetic interaction. Thus neutrons can attract via the strong force but are not repelled by the electromagnetic interaction. Successful fusion would therefore be easier to achieve by involving nuclei which have more neutrons in them versus those which are neutron deficient. One can think of the neutrons as acting like glue to help hold the protons together. EXPLAIN (2) Here students consider D and T. D and T represent two different types of hydrogen. Remember that hydrogen is the simplest type of atom and that a hydrogen atom will ALWAYS have only one proton but it can have three different numbers of neutrons in its nucleus: 0, 1 or 2. The most common type of hydrogen atom has a proton (p) for its nucleus and no neutrons (see Figure T6 below). This type of hydrogen is sometimes written as 1H. The ‘1’ tells us that there is one thing in the nucleus, a single proton. Another type of hydrogen, also shown in Figure T6, can have one proton as well as one neutron in the nucleus. This is called a deuteron, D, and it is sometimes written as 2H. The ‘2’ tells us that there are two things in the nucleus (one proton and one neutron). It is still a type of hydrogen since it contains only one proton. Look at the D+T graphic (Figure T4) and locate a D. A third type of hydrogen can have one proton as well as two neutrons in the nucleus. This type of hydrogen is called a triton, T, and it is sometimes written 3H. The ‘3’ tells us that there are three things in the nucleus (one proton and two neutrons). Since there is only one proton, we know that this is still a type of hydrogen. Look at the D +T graphic (Figure T4) and locate a T.


Figure T6: The three varieties (isotopes) of a hydrogen nucleus Teacher Background Information The D and T each have one proton, but they have different numbers of neutrons: D has one and T has two. When nuclei contain the same number of protons, but different numbers of neutrons they are called isotopes. The number of protons determines the type of atom, and since both the D and T have one proton they are both types of hydrogen. One final note regarding these symbols is that in the normal world, we deal with atoms. Atoms have nuclei but these nuclei are surrounded by one or more electrons. Generally, the number of electrons equals the number of protons that are contained in the nucleus. Because electrons carry a charge that is equal in magnitude to the proton’s but of the opposite sign (negative) such atoms are electrically neutral which means they carry no net charge. If the atom gains enough energy, it is then possible for one or more electrons to be freed from the atom. The atom now has an unbalanced charge (in this case positive) and is called ionized. As the atom is subjected to greater energetic collisions, it loses more and more electrons. At high enough energies, atoms lose all their electrons and the liberated electrons have too much energy to be re-captured by the nuclei. Such atoms are referred to as completely ionized and are really just bare nuclei at this point. Since temperature is a measure of the energy of a system of particles, objects with high temperatures can be expected to have more ionized atoms than those at lower temperatures. Thus, when we discuss the process of fusion among particles, we talk about the nuclei and not atoms because the latter implies electrons are orbiting the nuclei. Hence, we need to use nomenclature that differentiates an atom of hydrogen (i.e. deuterium) from a hydrogen nucleus (i.e. a deuteron). Students are also asked ‘What does the symbol 4He represent?’. He stands for helium and this is another type of atom. EVERY helium atom will have two protons. 4He is a helium nucleus and the ‘4’ tells us that it contains four things inside of the nucleus. Another name scientists use for 4He is an ɑ particle. Because a specific element can come in several varieties (isotopes) which differ in the number of neutrons, a compact nomenclature is used to describe the specific nucleus in question. The general form used in this Activity is: Atomic Mass Number (A) Chemical Abbreviation where the atomic mass number (A) is simply the number of protons plus neutrons in the nucleus. Hence, 4He has four particles in its nucleus. Because it is helium, two of these particles must be protons, leaving two remaining nucleons to be accounted for and these must be neutrons. Likewise, we could also use the symbols 1H, 2H and 3H to distinguish between, respectively, hydrogen with only a single proton in its nucleus, a deuteron and a triton. However, these different varieties of hydrogen are so important that the latter two forms are given their own special symbols: D for the deuteron and T for the triton. Using this same nomenclature, ‘1n’ stands for a neutron. So 1n represents a single neutron.


EXPLAIN (3) Students should use Figure F6 and the definitions above, to complete the table below. 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 α 2 2 no 1n 0 1 no 1H 1 0 yes EXPLAIN (4) After completing the table, there is a discussion of the energy involved in the reaction. Figure T4 for the D + T reaction shows that the α carries off 3.5 MeV of energy and the n carries off 14.1 MeV of energy. The MeV 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 the comparison of eV to J is: 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. Although the bottle top cylinder model cannot represent this portion of what is happening (energy leaving with the particles), the energy released is the important part of fusion. This energy is the reason that active research is being done to efficiently achieve fusion so that the current energy needs of our planet can be met. Before the origin of the energy can be discussed, we need to address the common unit of mass on a nuclear scale. 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 1 u = 1.661 x 10-27 kg The energy released in fusion arises from the conversion of mass to energy according to the equation, E = ∆mc2. This equation comes from Einstein’s Theory of Special Relativity.


Using the above two relations, you can state the mass in yet another way: 1 u = 931.466 MeV/c2 Although this looks cumbersome, expressing masses in terms of atomic mass units allows the energy equivalent to this mass (or as we shall see below, a mass difference) to be easily computed in MeV with the c2 dividing out using the conversion factor immediately above. NOTE: The following is an OPTIONAL exercise in the Student Activity. If you elect NOT to have your students do the calculation - - it is STRONGLY recommended that you “walk-them-through-it” - - or at minimum give a verbal description of the calculation. EXPLAIN (7) Students should be able to find the following values from the “Useful Nuclear Masses” section in the lower left hand corner of the Fusion chart. Mass of D Mass of T Mass of α Mass of 1n 2.013553 u 3.015500 u 4.001506 u 1.008665 u These masses are used to find the Mass (D + T) and the Mass (α + 1n). These values are used to calculate the change in mass, which we represent by the symbol ∆m (= the masses of the original deuteron and triton minus the masses of the helium nucleus and the neutron). Mass (D + T) Mass (α +1n) ∆m = mass of (D + T) – mass of α + 1n) 5.029053 u 5.010171 u 0.018882 u EXPLAIN (8) The students then use the calculated ∆m to find the energy released. E = ∆mc2 x 931.466MeV/uc2. E = (0.018882 u)c2 (931.466 MeV/uc2) = 17.6 MeV EXPLAIN (9) This value represents the total energy released in the fusion D+T reaction. Adding the value for the energy carried away by the neutron as shown in Figure T4 (14.1 MeV) and the energy carried away by the newly formed helium nucleus (3.5 MeV) results in exactly the same result as was calculated above. 17.6MeV is really not a lot of energy. So, how BIG is the amount of energy given off with EACH fusion? It would actually take ten million, million fusions per second to power a 30 watt fluorescent bulb.


ELABORATE Procedure In the EXPLORE section of this Activity the students investigated how N depended on τ (Shake the box for a longer period of time) holding all the other variables constant. In the ELABORATE part they will investigate how N (the number of pairs formed) depends on “place more bottle top cylinders in the box”, while holding all the other variables constant. The TOTAL number of bottle top cylinders in the box will be called n. Students should vary n while holding the following variables constant:

a) Shaking time. c) Vigor of shaking. d) Size of Velcro. e) Amount of Velcro.

‘n is sometimes called the particle concentration. In this activity, this means that n is the TOTAL of both types of bottle top cylinders (small + large). ELABORATE (3) The students are given the option to select whatever values of n they desire. A particularly useful set of n values is n = 75 (50 Ts + 25 Ds) n = 100 (50 Ts + 50 Ds) n = 125 (50 Ts + 75 Ds) n = 150 (50 Ts + 100 Ds) n = 175 (50 Ts + 125 Ds)\ A time saver would be - - if they elect to time for 10 s at each value of n - - they can use their data for n = 100, τ = 10 s from Table 2 in the EXPLORE section. ELABORATE (5) Each student group should indicate: The time for each shake of the box is _____________s.

Be sure each student group takes enough data to complete Data Table 3: Data Table 3

TOTAL number of cylinders in box (n)





75 100


ELABORATE (6) Have the students use the graph paper and pencils from their KITs. Instruct them to label the y-axis Navg and the x-axis n. Have each group select a scale for the axis so that all their data points can be plotted on this graph. Finally, have the students plot the ordered pairs (n, Navg) on the coordinate plane they have constructed. ELABORATE (7) Students are directed to fit a line to the points and describe any correlation. They should find a positive correlation between the total number of pairs formed (N) and the number of cylinders in the box (n). Sample data taken by the authors is shown below when the number Ds was varied. The shaking time was 10 s for each trial, and the number of Ts was held constant at 50. A graph of Navg vs. n where Navg is on the y-axis and n is on the x-axis is also shown. TOTAL number of cylinders in box (n)





75 14 13 15 14 100 20 15 16 17 125 31 25 21 22.3 150 26 28 22 25.3 EVALUATE Procedure EVALUATE (1) In this section of the Activity you and your students will discover how fusion is accomplished in the real world and how well their model compares to the real world situation.


EVALUATE (2) An important graph. On the lower right hand corner of the chart, FUSION: Physics of a Fundamental Energy Source, there is a box entitled: ACHIEVING FUSION CONDITIONS with a graph, Confinement Quality (nτ) vs. Ion Temperature.

Figure T7: Graph of Confinement Quality vs. Ion Temperature

Confinement Quality (nτ) is a measure of how well a plasma can achieve fusion. Note that n and τ mean the same things in the real world as they do in the model: n is the number of particles and τ is the time in which the reaction occurs. Ion Temperature is the temperature of the particles undergoing fusion. The particles are called ions because they are atoms which have been broken down into their positive nuclei and negative electrons. In other words, the electrons are no longer attached to the nuclei. The special name given to a mixture (gas) of ions is a plasma. The triangle points in Figure T7 represent the conditions which have been obtained in real world reactors using “inertial” techniques to confine the plasma sometimes called “Laser-beam-driven Fusion”. The circle points in Figure T7 represent the conditions which have been obtained in real world reactors using “magnetic” techniques to confine the plasma.


Plasmas are quite common in nature - - (See Figure T8) and make up 99% of the visible universe. Natural plasmas include: Nebula, Solar core, Lightning, Aurora, Solar wind, Solor corona, Ingterstellar Space. Manmade plasma devices include: Neon signs, Flames, Magnetic Confinement fusion devices, Inertial Confinemant fusion devices, Fluorescent lights.

Figure T8: Plasmas - - the Fourth State of matter. Physicists truly consider plasmas to be the FOURTH STATE of Matter. Unfortunately most text books discuss only three states of matter - - gas, liquid, and solid. In the real world, fusion takes place when a plasma is confined in a reactor (sometimes called a reactor vessel).


In the model of fusion used in this Activity, the bottle top cylinders (ions) are confined to the box being shaken. There are two kinds of confinement techniques commonly in use in experimental fusion research: Magnetic Confinement fusion devices and Inertial Confinemant fusion devices Teacher Background Information You may wish to share this if deemed appropriate and relevant for your students. Inertial Confinemant fusion devices, shown in Figures T9 and T10, yield the triangle data points in Figure T7. “Inertial” fusion devices are characterized by compression of the fuel (implosion driven by laser or ion beams or by X-rays from laser or ion beams) resulting in fusion reactions (mainly D+T). Laser-beam-driven Fusion

Figure T9: Graphic representing inertial” or “Laser-beam-driven Fusion

Figure T10: The NOVA laser at Lawrence Livermore National Laboratory, shortly after the laser's completion in 1984. “Inertial confinement fusion (ICF) is a process where nuclear fusion reactions are initiated by heating and compressing a fuel target, typically in the form of a pellet that most often contains a mixture of deuterium and tritium. To compress and heat the fuel, energy is delivered to the outer layer of the target using high-energy beams of laser light, electrons or ions. The heated outer layer explodes outward, producing a reaction force against the remainder of the target, accelerating it inwards and sending shock waves into the center. A sufficiently powerful set of shock waves can compress and heat the fuel at the center so much that fusion reactions occur. The energy released by these reactions will then heat the surrounding fuel, which may also begin to undergo fusion. The aim of ICF is to produce a condition known as "ignition", where this heating process causes a chain reaction that burns a significant portion of the fuel. Typical fuel

http://en.wikipedia.org/wiki/Lawrence_Livermore_National_Laboratoryhttp://en.wikipedia.org/wiki/Nuclear_fusionhttp://en.wikipedia.org/wiki/Deuteriumhttp://en.wikipedia.org/wiki/Tritiumhttp://en.wikipedia.org/wiki/Laserhttp://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Ionhttp://en.wikipedia.org/wiki/Chain_reaction


pellets are about the size of a pinhead and contain around 10 milligrams of fuel: in practice, only a small proportion of this fuel will undergo fusion, but if all this fuel were consumed it would release the energy equivalent to burning a barrel of oil.” Magnetic Confinement fusion devices (shown in Figures T11 and T12) are responsible for the circlular data points in Figure T7. “Magnetic confinement fusion” is characterized by Ohmic Heating (via electric currents) and fuel compression (by magnetic fields) resulting in primarily D+T fusion reactions.

Figure T11: Graphic representing Magnetic confinement fusion

Figure T12: Variable Configuration Tokamak (TCV): Inner view, with the graphite-claded torus, often called a tokamak. Courtesy of CRPP-EPFL, Association Suisse-Euratom.

“Magnetic confinement fusion is an approach to generating fusion power that uses magnetic fields to confine the hot fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, the other being inertial confinement fusion. The magnetic approach is more highly developed and is usually considered more promising for energy production.” Error! Bookmark not defined.

“Fusion reactions combine light atomic nuclei such as hydrogen to form heavier ones as helium. In order to overcome the electrostatic repulsion between them, the nuclei must have a temperature of several tens of millions of degrees, under which conditions they no longer form

http://en.wikipedia.org/wiki/Milligramshttp://en.wikipedia.org/wiki/Fusion_powerhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Inertial_confinement_fusionhttp://en.wikipedia.org/wiki/Atomic_nucleushttp://en.wikipedia.org/wiki/Hydrogenhttp://en.wikipedia.org/wiki/Heliumhttp://en.wikipedia.org/wiki/Coulomb_barrier


neutral atoms but exist in the plasma state. In addition, sufficient density and energy confinement are required.” Error! Bookmark not defined.

“Magnetic confinement fusion attempts to create the conditions needed for fusion energy production by using the electrical conductivity of the plasma to contain it with magnetic fields. The basic concept can be thought of in a fluid picture as a balance between magnetic pressure and plasma pressure, or in terms of individual particles spiraling along magnetic field lines.”Error! Bookmark not defined.

EVALUATE (3) Students are asked about the charges of the cylinders in their model. The small bottle caps represent deuterons and the large bottle caps represent tritons. Although the deuterons and tritons in the real world both have a charge of (+) 1, the cylinders in the model carry no electrical charge. EVALUATE (5) Students are asked “How are the bottle top cylinders (ions) confined in your model?” They will likely realize that their method of confinement is the box. Students are directed to look at the upper right hand corner of the graph. There is an orange “balloon” labeled “Expected reactor regime”. Points (representing reactors) must lie within this balloon to be considered a “successful” reactor. This is the region of the graph that represents high values of nτ and high values of temperature. EVALUATE (6) The students are asked if any current reactors (triangles or circles on the graph) are “successful”. There are no reactors shown in Figure F7 that are considered to be ‘successful” since none lie in the “Expected reactor regime”. The graph shows that the larger the value for the product of nτ (n times τ) the more likely it is to have a successful fusion reactor. Since this is a mathematical product, increasing EITHER n or τ should increase the chance of a successful reactor (more fusions - - N - - produced). EVALUATE (7) Students are asked if the data they took (and graphed) shows that N increased as τ was increased, and if it showed that N increased as n was increased. They should have found that increasing τ and increasing n resulted in an increase in N. Students are told to once again consider Figure 7. It shows that the larger the value for the Ion Temperature the more likely it is to have a successful fusion reactor (larger value for N). EVALUATE (8) Students must consider which of the variables associated with their model of fusion

a) Shaking time. b) Number of cylinders. c) Vigor of shaking. d) Size of Velcro. e) Amount of Velcro.

http://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Electrical_conductivityhttp://en.wikipedia.org/wiki/Magnetic_pressurehttp://en.wikipedia.org/wiki/Guiding_center


they think would correspond to Ion Temperature. They should realize that (vigor of shaking) would correspond to temperature: the more vigorous the shaking, the higher the Ion Temperature. EVALUATE (9) Students are directed to list the ways in which their model represents a real fusion reactor well. They may determine such things as:

•The large and small cylinders do fuse together. •N increased as τ was increased •N increased as n was increased. •The cylinders were confined - - inside the shaking box.

EVALUATE (10) Students must consider the ways in which their model represents a real fusion reactor poorly. They will likely determine that:

•There is no energy carried off by the fused cylinders. •There is no particle given off which would correspond to the n on the real D+T reaction. •There is no repulsive force between the large and small cylinders - - which would need to be overcome - -

before fusion could happen. This repulsive force does exist between Ds and Ts in the real world. Glossary of terms: α (alpha) particle: a helium nucleus that contains two protons and two neutrons. Atomic mass: The sum total of protons and neutrons in the nucleus of an atom. This is denoted by the symbol A Atomic Mass Unit: the standard unit of mass when on the scale of an atom or nucleus. The symbol for this is u. Ionized: the state of an atom which has an imbalanced of net charge from either losing or gaining electrons. MeV: Abbreviation for Mega election volt: a unit of energy that used to described nuclear reactions. Nucleons: parts of a nucleus that can be either protons or neutrons Proton: Positive charged massive particle often found in a nucleus. Neutron: uncharged massive particle often found in a nucleus. Electron; relatively light negatively charged particle often found “in orbit” around a nucleus Ion: an originally electrically neutral atom that has lost or gained electrons.


Isotopes: nuclei having the same number of protons but different number of neutrons. Deuteron (D) : isotope of hydrogen containing one proton and one neutron. Triton (T): isotope of hydrogen containing one proton and two neutrons. Ion Temperature: a measure of the energy of ions in a plasma. n: particle concentration or number of cylinders in the shake it box. 1n: a neutron - - neutral massive particle often found in a nucleus N: number of pairs formed after a shake it experiment. Magnetic confinement fusion: is an approach to generating fusion power that uses magnetic fields to confine the hot fusion fuel in the form of a plasma. Inertial confinement fusion (ICF): is a process where nuclear fusion reactions are initiated by heating and compressing a fuel target, typically in the form of a pellet that most often contains a mixture of deuterium and tritium. Confinement Quality (nτ): is a measure of how well a plasma can achieve fusion. Note that n and τ mean the same things in the real world as they do in the model: n is the number of particles and τ is the time in which the reaction occurs. τ: is the symbol used to denote shaking time. Plasma: the Fourth State of matter. Tokamak: torus shaped device used to confine the plasma in magnetic confinement fusion devices. E = mc2 : One of the most important equations in physics. Einstein’s theory of relativity equation relating mass to energy. D+T reaction: is the process modeled in this Activity. It is the reaction that will most likely be used in the first fusion reactors to generate electricity on a commercial basis. “p+p”( SOLAR FUSION CHAIN): is the rather complicated process which generates the majority of energy given off by our Sun.

http://en.wikipedia.org/wiki/Fusion_powerhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Nuclear_fusionhttp://en.wikipedia.org/wiki/Deuteriumhttp://en.wikipedia.org/wiki/Tritium

Testing a Physical ModelPart of a Series of Activities related to Plasmas and the Solar Systemfor Middle SchoolsTesting a Physical ModelTeacher’s NotesPart of a Series of Activities related to PlasmasFigure T1: Bottle top nuclei details

Testing a Physical ModelThe three variables involved in the graph are the plasma confinement time,...

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