two 45 minute class periods

This will be one of the last lessons in the unit on Atomic Structure and Nuclear Chemistry.  By this time students should be familiar with basic atomic structure, and the concept of isotopes, and have an understanding of radioactivity and the various processes of radioactive decay.  Specifically, students should be able to identify the major subatomic particles (proton, neutron, electron) in the modern atomic model and explain how they interact, as well as the three main types of radioactive decay (alpha, beta, and gamma).

Students will be presented with the concepts of nuclear binding energy, nuclear fusion and nuclear fission, and the concept that in these reactions matter is transformed into energy, as related in the equation, e = mc2.  Nuclear fusion will be explored further as the means by which elements heavier than hydrogen are created in the cores of stars.

Students will gain an understanding of the fundamental ideas behind fusion and fission, the “iron limit” (which states that fusion reactions are no longer energetically favorable in producing nuclei heaver than that of iron), the concept of nuclear binding energy.  They should also gain a general understanding that mass and energy may be interconverted in certain processes, as represented in Einstein’s famous equation.  Furthermore, students should gain an appreciation for the awe-inspiring fact that all of the elements on earth and inside their bodies (except hydrogen) were fused in the cores of stars.

Procedure

Opener

Engage:

• Show students the closing sequence of Orson Welles’s “Dr. Strangelove”, depicting a series of atomic bomb explosions.  At the end of the clip, ask them to describe what they saw.  With guidance, students should eventually conclude that large amounts of energy, light, and heat were being released by the explosions.  Tell them that power behind the explosion is a process called nuclear fission.
• Show students a picture of the Sun.  Ask them what they see.  With guidance, students should eventually conclude that large amounts of energy, light, and heat were being released, just as in the case of the atomic bomb explosions.  Tell them that the process behind the power of the sun is a process called nuclear fusion.
• In both cases, ask students to think about where this huge amount of energy comes from, and accept all responses.  Remind them of the concept of conservation of energy, and ask how it applies or seemingly does not apply in this case.  Ask them to think about conventional explosions (involving chemical, as opposed to nuclear reactions) and where the energy comes from in such cases.  Students should conclude that in conventional exothermic processes, energy is released because starting material has greater energy than products.  Guide them to reaching the same conclusion in the case of the nuclear explosions.  Ask them to think about what is changing energy in these nuclear reactions.  They should conclude, if only from the name of the reactions, that it is the nuclei of the material involved that is changing energy.

 

Discrepant Event:

• Tell the students that the process occurring in the sun is the nuclear fusion reaction that essentially converts two atoms of deuterium (2H) into one atom of helium (4He).  Using their list of isotope masses, have them break into pairs and try and verify that the conservation of mass upholds in this reaction.  After a few minutes, ask for their findings.  They should report that the mass of two deuterium atoms is actually slightly larger than the mass of the one helium atom that is formed in the reaction. 
• Explain to them that another process that occurs in the Sun is the fusion of 3 4He nuclei to form one 12C atom.  Again, have them break up into their pairs to use their isotope list to try and verify that the conservation of mass upholds in this reaction.  Again, they will find that the mass of the reacting nuclei is greater than the product nucleus. 
• Ask them to try and explain where this “missing mass” has gone, and if it might have any relationship to the vast amounts of energy that are known to be released in these fusion reactions. 
• Repeat this protocol for the reaction that is occurring in the “Dr. Strangelove” atomic bomb sequence, namely the fission of 235U to produce 90Rb, 143Cs, and two neutrons.   Again, they should find that the combined mass of the product nuclei is slightly less than the mass of the starting Uranium.

 

 

Development

• Briefly introduce and define the concept of nuclear binding energy and Einstein’s equation, e = mc2, and have the students break up into groups of 3 and discuss the phenomena that has been introduced to them.  Namely: what is the source of the large amounts of energy released by the Sun (nuclear fusion) and atomic bombs (nuclear fission), why does the conservation of mass not seem to hold for these types of reactions, and what role does the loss of mass in the process of these reactions play in the release of the enormous quantities of energy?  Also, how can it be possible that energy is lost in both fusion and fission reactions, which appear to be reverse processes, and are these processes always energy yielding?
• Ask the students to calculate the change in mass in going in the reverse direction of the fusion and fission reactions that were introduced to them.  The students should find that mass is gained in a hypothetical fission reaction in which helium splits into two deuterium nuclei.  Similarly, mass is gained in fusing 90Rb, 143Cs, and two neutrons to form 235U.  Tell them that these processes do not actually occur, and ask them why they think this is so.

Closure

• Return to the essential questions asked in the development phase of the lesson.  Ask each group to report on their hypotheses for the phenomena described above. 
• Explain that the “missing mass” in fusion and fission reactions is transformed into energy, as described by e = mc2, and that this is the source of the vast amounts of energy released in nuclear reactions.  The exothermicity of nuclear reactions can be explained by the fact that product nuclei are less energetic (and thus less massive) than reactant nuclei, which can be explained by nuclear binding energy. 
• Explain the “Iron Limit”, i.e.: the point at which fission reactions become favored over fusion reactions, due to the fact that elements in the “Iron group” have the greatest binding energies of all elements.  Explain that this is the reason that fusion reactions are energetically favored (mass is lost) when producing elements lighter than Iron, and disfavored (mass is gained) when producing elements heavier than Iron, and vice versa for fission reactions. 

Use student feedback to improve the lesson, or make it more or less difficult.  At all points in the lesson where students are asked to break into groups and discuss important questions, ask them to record their thoughts/hypothesis and turn them in at the end of class. Have the students fill out the following worksheet during the course of the lesson:

Nuclear Reactions, e = mc2

1.  Describe as best you can what is occurring in the atomic bomb explosions in Orson Welles’s movie, “Dr. Strangelove”?  What is the name of the process that provides the power behind these explosions?  What occurs during this type of reaction?

2.  Describe what you see occurring in the photograph of the Sun.  What is the name of the process that powers the Sun and other stars?  What occurs during this type of reaction?

3.  What do the two processes described above have in common?  Where do you think this huge amount of energy comes from?

4.  In order for a reaction to release energy, what needs to happen (what characteristics do the products have in relation to the reactants)?  Keeping this in mind, what do you think is changing energy in “nuclear” reactions?

5.  The process that occurs in the Sun fuses two atoms of 2H (deuterium) into one atom of helium (4He).  Write the reaction, and verify that the Law of Conservation of Mass applies in this reaction, given the isotope masses discussed in class.  What are your findings?  Are you surprised by these findings?

6.  Another process that occurs in the Sun is the fusion of 3 4He nuclei to form one 12C atom.  Again, write the reaction and please verify that the Law of Conservation of Mass applies in this reaction, given the isotope masses discussed in class.  What are your findings?  Are you surprised?

7.  Where do you think this “missing mass” has gone?  Do you think it might have any relationship to the huge amount of energy released in these types of reactions?

8.  Try to verify the Law of Conservation of Mass for the fission reactions in the atomic explosions in “Dr. Strangelove.”  The reaction involved is the splitting of 235U to produce 90Rb, 143Cs, and two neutrons.  As you did with the two fusion reactions above, write this reaction, and verify that the Law of Conservation of Mass applies, given the isotope masses discussed in class.

9.  Write the definition of Nuclear Binding Energy.

10.  Write Einstein’s famous equation, and explain in a few words what it means.

11.  Use your answers to questions 9 and 10 to try and explain where the large amounts of energy released by the Sun (nuclear fusion) and atomic bombs (nuclear fission) comes from.  Why does the Law of Conservation of Mass not seem to hold for these reactions?  What role does the loss of mass play in the release of energy in these reactions?

12.  Calculate the change in mass for the reverse reactions of those mentioned in questions 5, 6, and 8.  Is mass being produced or consumed in these reactions?  Why do you think these reactions do not actually occur?

13.  After the class discussion, explain what happens to the “missing mass” in the fusion and fission reactions we talked about today.  Was this what you had originally hypothesized?

14.  Explain what the “Iron limit” means, and why the fission of 4He not favorable, while the fission of 235U is favorable.

15.  Given the “Iron limit”, how is it possible for stars to create elements heavier than Iron?

Discuss the “Iron limit” and ask students to think about this question: if all elements are created by fusion reactions in stars, given the “Iron limit”, how can elements heavier than Iron be produced?  Ask them to propose hypotheses, and guide them to realize that, while unfavorable, these reactions can and do occur.  Ask them to think about what conditions these unfavorable fusion reactions might occur.  Finally, explain to them that in the extreme energy released by a supernova explosion at the end of a star’s life, there is adequate energy for fusion processes to occur that produce elements heavier than Iron.