Suggested Exercises

Biographical references

The following sources can be used as references for most of the scientists appearing in the exhibit. Many are available in public libraries. There are also biographical materials available on the Web.

1. Ernest Rutherford left New Zealand for England and studied with J. J. Thomson. Niels Bohr and Otto Hahn went to England to study with Ernest Rutherford. Strassmann studied with Hahn, and Frisch with Bohr.

Using biographical sources investigate other student-teacher relationships among illustrious scientists.

  • Do all famous scientists have successful students?
  • Must one have a great teacher to be a great scientist?
  • How important is the student-teacher relationship in terms of your own achievement?

2. On his 1939 voyage by ship to the U.S., Niels Bohr had a blackboard in his stateroom.

  • What would you expect a physicist of Bohr's stature to request today if he were to cross the Atlantic?
  • Would a physicist take a ship, a jet, the Concorde—or simply use the Internet?
  • What difference would it make?
  • How would the story of the spread of the news of fission have changed if the discovery had taken place last year?

3. George Gamow, a noted physicist, said that "the fission of the uranium nucleus can be considered a very interesting paragraph (but only a paragraph) in the story of physics." Fission has taken on an importance beyond this because of the technological applications which are derived from its discovery.

  • How has the discovery of fission and its byproducts, nuclear power and the atomic bomb, influenced the way our society views science?
4. Write an essay contrasting science as it would be if society took no interest in its technological applications and science as it is today.
  • If people did not apply science to practical uses, how would its role in our society change?
  • What other field of study would it most resemble?
  • Would governments support scientific research?
  • Would the same type of person pursue science as a career?
5. Lise Meitner lived in Germany from 1907. She headed a research unit and became respected as a scientist throughout the world. In the 1930s, she was protected from Nazi persecution in spite of being Jewish because she was still an Austrian citizen. After Hitler took control of Austria, Meitner was no longer protected and, in 1938, was forced to flee Germany. She never again found a job in a major research center.

Imagine that you are Meitner and write a letter to a cousin, or to a respected scientist, or to a government official of Germany. In this letter or letters, express your feelings about science, politics, religion and the situation you find yourself in. (Incidentally, such letters from Meitner have been preserved in archives.)

6. Enrico Fermi and Emilio Segrè did not discover uranium fission although fission did indeed occur during their 1934 experiments. Segrè is quoted as saying, "The whole story of our failure is a mystery to me. I keep thinking of a passage from Dante: 'O crucified Jove, do you turn your just eyes away from us or is there here prepared a purpose secret and beyond our comprehension?"

  • What is Segrè implying by this quote?
  • How might world history have been altered if the discovery of fission occured before the emigration of physicists to the U.S. and well before the start of World War II?
  • What does this suggest about the role of chance in history?

7. It is not hard to follow the reasoning Frisch and Meitner used to calculate the energy released in fission. One method they used relied on Einstein's discovery that energy released (E) is equal to a loss of mass (m) times the speed of light (c = 3 X 108 meters/sec) squared.

Consider a typical fission reaction:
235U+ ln —> 140Xe + 94Sr + 2ln

The Xe rapidly decays into l40Ce, and the Sr into 94Zr, with the emission of electrons of negligible mass. We know now that—
mass of 235U = 235.044 atomic mass units (amu)
mass of 1n = 1.009
mass of 140Ce = 139.905
mass of 94Zr = 93.906

  1. Find the sum of the masses of the initial nuclei.
  2. Find the sum of the masses of the final nuclei, and subtract from the mass you found in Step 1.
  3. Calculate the energy released, using E = mc2. 1 amu = 1.657 X 10-24 grams. (Check: directly in terms of energy, with c2 already multiplied in, 1 amu = 931 Mev = 1.49 X 10-3 ergs.)
8. (This problem uses the results of the preceding exercise.) A typical nuclear reactor generates 1000 Megawatts (109 Watts) of thermal energy. If it operates for 100 days, what mass of uranium-235 does it consume?

9. The discovery and exploitation of fission did not require knowledge of the famous equation E = mc2. In fact, at the time the masses of the radioactive daughter nuclei were not known well enough to make a good calculation. Frisch and Meitner calculated the energy release by a second method (which was the only method Joliot used).

  1. Note the fission reaction in exercise 7. The radius R of a nucleus is related to its atomic number A by the approximate equation

    R = KA l/3 where K = 1.07 X 10 -15 m.

    Calculate the radii of the Ce and Zr nuclei.
  2. Assume that at the moment the uranium breaks into these fragments, the distance between the centers of the two fragments is equal to the sum of their radii. Calculate the electrostatic force of repulsion between them. (The charge of each nucleus is equal to the number of protons in it.)
  3. The kinetic energy of the two fragments after they have moved far apart must be equal to the electrostatic potential energy they have before they separate. The electrostatic potential is equal to the work done in moving the two nuclei in from a great distance to a distance equal to the sum of their radii. An equation for this is derived in your textbook:

    work = U = the quantity of [(Kq1 times Kq2) divided by r]
  • What is the sum of the kinetic energies?
  • Where did this energy come from?
  • Compare with the energy calculated using E = mc2. Why are the two numbers not exactly equal?

(Note for the teacher: we presume the above equation is derived in the textbook you use. But the symbols may not be the same; modify the exercise if necessary to bring into line with your textbook. (For the last part of the exercise, we assume that you also assigned exercise 7.)

10. One typical fission reaction is: 235U + ln —> l44Ba + 89Kr + 3 ln

Using a table of stable nuclides, estimate what is the number of excess neutrons in the Ba and Kr fission products? How many neutrons would you expect to be given off as these nuclides decay, according to your arithmetic?

In fact, after the initial three neutrons, seven beta particles are emitted. The Ba undergoes four successive beta emissions to become l44Nd; the Kr after three beta decays becomes 89Y. Write down the seven disintegration equations for these processes. The various elements that turn up will be part of the "fallout" from a nuclear weapon or the "wastes" of a nuclear reactor. Extra credit: look up the half-lives of all these fission products.
11. In the fission reaction of the preceding exercise, the two main fragments repel one another strongly because both are positively charged. Newton's Second Law shows that the smaller fragment will have the larger acceleration. Assuming both nuclei are initially at rest and using conservation of momentum, find the ratio of their velocities and the ratio of their kinetic energies.

In a nuclear reactor, the fragments strike nearby atoms and knock them out of place, gradually damaging the metal that holds the fuel. If you were designing a fuel element for maximum lifetime, would you expect Ba or Kr fragments to be a greater problem? Why? (Remember that a fragment's mass, velocity, and electric charge will all play a role when it hits an atom.)
12. In the late 1930s, scientists knew of three possible outcomes when a nucleus was bombarded with a neutron.

(i) a proton might be emitted,
(ii) an alpha particle might be emitted, or
(iii) a beta particle might be emitted.

(a) Write the nuclear equations showing what would happen in each of these three possible reactions if aluminum was bombarded:

27A1 + ln —> ?

(b) Write an equation that will show why Fermi, Hahn, and others believed that bombarding uranium with a neutron produces radium.
13. Why is the number of neutrons emitted per fission important for the creation of a chain reaction?
14. ACTIVITY: Size of the nucleus. A nucleus is much too small to measure with ordinary tools, and indirect means are needed. One method is to shoot particles through a thin foil. By calculating the ratio of particles that bounce off a nucleus and those that miss and go through the foil, the cross-section (roughly speaking, the area) of the nuclei can be calculated. An experiment simulating this is suggested by R. D. Edge in The Physics Teacher (March 1978):

Take about 40 United States pennies or marbles and scatter them fairly uniformly over a sheet of paper. Drop a pencil, point first, from four or five feet onto the paper, without aiming. Count the shots that hit a penny, keeping track of the total number of shots but neglecting those that miss the paper entirely. Thirty or so shots should be enough. The probability that the pencil hits a penny is proportional to the ratio of the area of all the pennies to the area of the paper, which for an ordinary sheet of 8.5 X 11" paper is 603 cm2. Let the area of one penny be A. Then the area of 40 pennies is 40A. If the total number of shots is N and the number hitting pennies is n, then

little n divided by big N = (40A divided by 603)

and the area of one penny is A = (15) (n/N).

In fact the area of one penny is 2.83 cm2. How close is your answer? What are the sources of inaccuracy in the answer you got? How could you get a more accurate answer using more or less the same method?

15. ACTIVITY: Radioactive decay. Objective: to determine the half-life of a sample from experimental data.

Half-life experiments are best done with a radioactive sample and a radioactivity detector. But the experiment can be simulated in various straightforward ways.

Method 1: Dice
The student has one hundred dice (or sugar cubes with a dot placed on one side of each with a felt marker), and one hundred beans. The number six on a die (or a dot on a sugar cube) is chosen as the "decay event." Prepare a chart to record the number of each toss, the number of dice, and the number of beans. The cubes are tossed on a table. Each die with a six is removed and a bean is left in its place on the table. Record the "toss number" (for the first toss this is 1), the number of cubes remaining, and the number of beans placed on the table. Repeat for the second toss, and continue until less than ten dice remain.

Plot a graph of the number of remaining dice vs. the "toss number." Also plot the number of beans placed on the table. From the graph, determine the half-life of the sample.

Method 2:
If a computer is available, the teacher or student can wite a program to do the tossing. One hundred "X"s are displayed on the screen. The computer assigns a random number to each position, and if that is less than a number chosen to represent decay, the "X" on the screen becomes an "O". A summary chart keeps a tally of the parent nuclei (X) and their daughter nuclei (O) along with a running clock. Students record the number of parent nuclei every 30 seconds. The analysis proceeds as in method 1.

A second set of data is taken where the "X"s are not displayed, and their initial number is 10,000. The graph of this sample is compared with the one with a smaller number of parent nuclei. (Hahn and Strassmann were working with numbers of radioactive nuclei that gave, typically, hundreds of observed decays per hour, and with halflives ranging from minutes to days.)

16. ACTIVITY: Some analogies to the fission chain reaction:

(a) Set up a chain of wooden matches on a fireproof surface in such a way that each match-head lies underneath the wooden end of two other matches. (See diagram; it helps to break the matches so they are very short.)
What happens when the left-most match is lit? How is this like an explosive fission chain reaction?


(b) Set up a board with thirty mousetraps, each cocked and loaded with masses, for example corks or small rubber balls, which can spring into the air and trigger other mousetraps. What happens when a mass is thrown to trigger a first mousetrap? Try it with a smaller number of mousetraps. Try it with two corks per mousetrap. In what way does this simulate an explosive fission chain reaction?


(c) Each student is given a ping pong ball (or a piece of tightly crumpled paper). The students are told to throw their ball (or paper) high up in the air if another ball (or paper) falls on their desk. The teacher throws a ball in the general direction of a student. What happens? Try it with two or three balls per student, all to be thrown up together. Try it with fewer students. How does this simulate an explosive fission chain reaction? Try the same exercise with students handing one another the balls rather than throwing them. Now what happens? In this similar to a non-explosive chain reaction, that is, a nuclear pile such as Fermi built?

(Note for the teacher: See Richard M. Sutton, "A Mousetrap Atomic Bomb," American Journal of Physics 15 (1947), pp. 427-28.)
17. An exercise similar to the following was carried out by Otto Frisch and Rudolf Peierls in 1940. Their answer led them to recommend that the British government attempt to build atomic bombs. The British in turn spurred the U.S. to faster action.

(a) Suppose that you could assemble one kilogram of the fissionable form of uranium (U-235). If it all split at once, how much energy would be released?

(b) Assume that 10% of this energy could be used to move a pile of dirt. How much energy is needed to move one shovelful of dirt to a height of one meter? How many shovelfuls should the uranium have moved? (Make a rough assumption for the mass of a "shovelful".)

(c) If the bomb was used to move dirt and form a hemispherical crater, the dirt at the bottom would have to be moved considerably more than the dirt at the top. Calculate, very approximately, the radius of a crater that could be blasted out by the fission of one kilogram of U-235.

(Note for the teacher: We assume you have assigned exercise 7 or done such an exercise in class.

(Fermi made such a calculation already in 1939—estimating the size of a crater a uranium bomb might make in Manhattan. Frisch and Peierls developed more elaborate calculations to find the strength of a shock wave from a bomb. S. Glasstone, The Effects of Nuclear Weapons, contains information which can be used to write exercises covering many fields of physics.)
18. At the conclusion of the exhibit, there are two very different reactions to the first controlled release of nuclear energy. Crawford Greenewalt, a young American engineer and executive, was excited by hopes of a better world through atomic energy; Leo Szilard was fearful of the uses of atomic bombs. If you had been there, knowing only what they knew then, what would your feelings have been? How much of such reactions depends upon individual personality, and how much upon the historical experience of successful American engineers, refugee Jews, or contemporary students like yourself? I
19. When Niels Bohr was told of fission by Frisch, Bohr exclaimed, "Oh, what idiots we have been that we haven't seen that before. Of course, this is exactly as it must be." This "Aha!" feeling is basic to science. A mental barrier suddenly falls, and what had seemed impossible becomes simple.

Consider the following puzzle: "Name a 4 letter word that ends in -eny." What is the answer? Why do many people have a hard time finding the answer?

Unscramble the following sets of letters to discover the names of scientists connected with the discovery of fission (for example, ERFIM = Fermi). While you do this, keep track of your own mental processes. Write a short essay on the difficulties you run into and the different techniques you use to solve the puzzles. Relate your search for a solution to Bohr's exclamation. Are there similarities between the way scientists work and the way you solve important problems in your life?

20. A decay by alpha emission is often followed by b decay. Why is it b- rather than b+? Specifically, why is there n —> p + e- + v rather than n —> p + e++ v? S
21. Find descriptions of a recent scientific advance in a popular newsstand science magazine and in a more professional journal (Science, Nature). One way to do this is to search a popular magazine for an item which the magazine says was "recently reported" in a professional journal. You may also look for items in a newspaper (try the New York Times Index) or science news you have seen on television. Discuss the way the news was reported in the different places, with attention to any misrepresentation or sensationalism. Compare different perceptions of the event.

Look for a description of the same event in Scientific American and in Science News. What role do these magazines play?

If you wished to keep up with science events and you were to devote one hour per week to this, which of the above sources of information would you subscribe to? Can you find similar information on the Web?
22. Watch a television science program, and then search for information on the same subject in some of the magazines listed in the preceding exercise. If you have Internet access, do a Web search too. Which gives you a more complete and accurate understanding of the subject? What different kinds of understanding can you get from different media? Which comes closest to a scientist's form of understanding?
23. The exhibit quoted newspaper articles with sensational claims about the release of vast energy, claims quickly denied by some of the top physicists of the day. Discuss the role of the press and of the scientists in this dialogue. Read carefully Rutherford's statement: was he more or less accurate than the reporters? Were the reporters operating under different concerns than the physicists? Would your response to this question be different if there were no atomic power or atomic weapons today? (In fact fission is a delicately balanced phenomenon, which almost fails to be possible.) D
24. Some physicists describe the year 1932 as their "year of wonders." In that year Chadwick discovered the neutron, Urey discovered deuterium, Lawrence and Livingston invented the cyclotron, Cockcroft and Walton experimentally verified that E = mc2 for lithium, and Heisenberg published a paper on the theory of the nucleus. Do library research and write a report on one of the discoveries listed and the people involved with that discovery. I,R
25. The year 1932 was also a year of wonders in world politics. What was happening worldwide in 1932? Contrast the general situation with that of physicists. Specifically, what was happening that year to the economy, politics, etc. in the United States, Germany, Italy, Britain, and Japan? How were physicists affected by these events? I,R
26. Identify some current scientific-technical developments in their infancy today (genetic engineering, biotechnology, fusion, string theory). Use news magazines, newspapers, the Web, and science magazines. What do you think the future holds for these fields? Specifically, will these fields bring us solutions to some of our problems, or create new problems of their own, or some combination? Discuss this using the remarks of scientists, politicians, and public interest groups. Include a comparison with nuclear physics events of 1932-1942. How is the present the same? How is it different? How successful are predictions of the future likely to be? I,R
27. In the exhibit, the chemist Otto Hahn implies that a hierarchy exists within the sciences when he asks his audience, "Are you also afraid of these physicists?" Who is Hahn's audience here? A second example of this implied hierarchy is in a story told by Robert Wilson: "As the director of the Fermi National Laboratory, I was entertaining Professor Bogolyubov, who is director of the Dubna Laboratory. We began to converse, and at a slow moment in the conversation, to keep it going, I traced his career from that of a pure mathematician, to a theoretical physicist, to an administrator, and finally to director of Dubna. I asked him when his fall to a director occurred... and he answered without hesitation: 'Once I had descended from mathematics to theoretical physics, I could do anything!' "

Why is there a hierarchy in science? What other hierarchies exist in our culture? Whom do you respect more than physicists, and whom less? What historical forces or events might lead to a change in the way most people rank physicists?
28. Read the chapter "Departure" by Laura Fermi from her book Atoms in the Family.

(a) How was the immigration of Fermi to the United States affected because of his status as a scientist? How has immigration policy of the U.S. changed since 1939?

(b) A wife of one of Fermi's associates in Italy said, "Enrico's departure is a betrayal of the young people who have come to study with him and who have trusted in him for guidance." Laura Fermi asks herself the following questions in response. "Of contradicting duties, which should one choose? Should the responsibilities toward one's family or those toward one's students come first?" How would you answer this question?

Suppose instead of "toward one's students," the question read, "toward one's country." Would this change your answer?
29. Consider the sources used in this exhibit. What problems exist in interpreting history from these excerpts (some of which were recorded decades after the event they describe)? How could an oral history be made more valid? What advantages do audio recordings have over the written page? What disadvantages? In your answer, take into account both questions of human memory, and questions of authenticity.

(Note to the teacher: As mentioned in the acknowledgments on the script, voices have been heavily edited and rearranged. For example, the Anderson excerpts interweave sentences from talks made on two different occasions; the Szilard excerpt has five "cuts" where an interviewer's questions were removed and Szilard's replies were rearranged.)
30. Interview your grandparents or neighbors to find out what recollections they have of this period 1932-1942. Describe what similarities and differences exist between their memories and the audio recording you have just heard. R
31. Ernest Rutherford said, "our interest is purely scientific." Interpret what he meant by this and comment on whether it is possible to have scientific interests independent of the rest of the world. Is a scientist responsible for what others do with scientific discoveries? Does a scientist have more responsibility than any other citizen? D
32.Leo Szilard says that he feared for the future because he had read H. G. Wells' novel of 1913, The World Set Free. Find and read this book (you may need to use inter-library loan), or some other science fiction novel dealing with atomic bombs and written more than thirty years ago, for example: Nevil Shute, On the Beach; Pat Frank, Alas, Babylon. Compare the author's insights with your knowledge of today. How prophetic are these books? What role do novels like these play in shaping public knowledge and sentiment? R
33. Using library sources, find out what happened in 1939-1945 to Frisch, Joliot, Fermi and Bohr. How might their lives, and their work on nuclear physics, have been different if there had never been any likelihood of a Second World War? R
34. Read the original article excerpts from (a) Hahn and Strassmann's first "fission" paper; (b) Frisch and Meitner's paper; and (c) Bohr's paper.

Why do Hahn and Strassmann state that they publish their latest experiments hesitantly? Why, at the close of the paper, are they reluctant to state that they have discovered fission? Is the same sort of hesitancy found in the Frisch and Meitner paper?

Why do Hahn and Strassmann show more confidence in their results in their February, 1939 summary?

If you knew nothing about Niels Bohr, could you infer from his paper that he was a highly respected scientist? Give instances of how his paper is different in "personality" from the others.
35. Consider Rutherford's statement that "fundamental things have got to be fairly simple."

(a) What does he mean by "simple"? Has science moved toward this goal of simplicity? How?

Do all the problems you have in life have simple solutions? Does "simple" used in this context mean the same as in Rutherford's statement? From what point of view is nuclear fission simple?

(b) Scientists often connect simplicity with beauty. The mathematician and physicist Henri Poincare once wrote:

The scientist does not study nature because it is useful to do so. He studies it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living... I mean the intimate beauty which comes from the harmonious order of its parts and which a pure intelligence can grasp...

The physicist Werner Heisenberg recalled that he once told Einstein:

If nature leads us to mathematical forms of great simplicity and beauty... that no one has previously encountered, we cannot help thinking that they are 'true,' that they reveal a genuine feature of nature... You must have felt this too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us...

Is there a viewpoint from which nuclear fission could be called beautiful? Have you ever experienced the type of beauty that the quotes refer to? Describe an event or understanding that made you realize how beautiful something is that people do not easily recognize as beautiful. How could your education be improved so that you can experience some of the beauty that people in special fields of work recognize?
36. Draw a scientist or write a description of a scientist. Compare your image of the scientist with those of other students, and identify stereotypes which many people share.

Why do you think people have these stereotypes? Is it worthwhile to have stereotypes? Do stereotypes cause some people to turn toward or away from a career in science? Does an existing stereotype influence what courses you choose to study?

(Note to the teacher: After students have made their drawings, they may be helped by considering the following composite portrait reported by Mead and Metraux in Science vol.126, p.384-390 (1957). "The scientist is a man, who wears a white coat and works in laboratory. He is elderly or middle aged and wears glasses... he may wear a beard... he is surrounded by equipment: test tubes, bunsen burners, flasks and bottles... he writes neatly in black notebooks... One day he may straighten up and shout: 'I've found it!'... Through his work people will have new and better products... he has to keep dangerous secrets...")
37. Consider how the media present the image of a scientist. Is the presentation different in magazines, novels, movies and cartoons? Do scientists have their own stereotype of what a scientist is like? Is this stereotype different from the one that non-scientists hold? I,R

38. There are "visible scientists" in our society—ones that you see on television and read about in magazines, and who always seem to be in the public eye. Identify some of these visible scientists and find out what their field of research has been. Have these visible scientists won the Nobel Prize or other awards given by scientists? How did they become so well known? Do they have a specific cause or are they only identified as scientists?

A larger project for an advanced student or student team can be made from four Web exhibits which all describe "moments of discovery:" nuclear fission, an optical pulsar, the electron, and the transistor. The student(s) should study all four exhibits and discuss similarities and differences -- socially in terms of individuals, scientific institutions, and communication, and scientifically in terms of technologies and thought processes. Students can review the lists of questions in the Teachers' Guides for ideas on directions to follow (perhaps too many!). The students should conclude with general statements about things that seem necessary for all discoveries, at least in modern physical science.