Nuclear Fission energy for war and peace

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Chapter 8

Nuclear Fission
energy for war and peace

Soon after the neutron induced radioactivity was discovered, several groups of researchers bombarded uranium by neutrons and analyzed the radioactive products formed thereof. However, results were not what they expected, and they misinterpreted of their results due to their expectations. The German group eventually interpreted their results in terms of fission, and fission was discovered in the midst of World War II.

Nuclear fission is a process, by which a heavy nuclide splits into two or more pieces. From masses of nuclides, scientists knew that such a process would release a lot of energy. Thus, research on nuclear fission became the top secret in Germany, England, France, the former U.S.S.R., and the United States. It was obvious that a weapon employing the nuclear fission would be so powerful that whoever had developed it would win. Such a weapon would destroy the enemy in such a way that even the winner will be scared.

.... For in the development of this organization (the United Nations) rests the only true alternative to war, and war appears no longer as a rational alternative. Unconditional war can no longer lead to unconditional victory. It can no longer serve to settle disputes. It can no longer be of concern to great powers alone. For a nuclear disaster, spread by winds and waters and fear, could well engulf the great and the small, the rich and the poor, the committed and the uncommitted alike. Mankind must put an end to war or war will put an end to mankind.
John F. Kennedy

September 25, 1961, Address to the United Nations.

Soon after the discovery of nuclear fission, the technology was employed to make bombs. The desire to win the war sped up the development of atomic bombs. Two such bombs were used in the war. The destruction was so massive and horrified that no additional nuclear bomb has been deployed in wars.

Political will and public pressure have diverted human effort to develop peaceful applications of nuclear energy. As a result, nuclear power reactors have supplied energy for our need for decades and they continue to do so. Yet, reactor accidents have changed the public opinion and about nuclear energy. The future of nuclear reactors became uncertain. However, energy demand is always on the increase, and at some point, the public opinion may shift again.

Nuclear Fission Reactions

Soon after their discovery, neutrons were used to bombard all kinds of material to induce radioactivity. Neutron bombardment of uranium produced complicated radioactivity. Because researchers were looking for heavier nuclides, they took a long time to discover that neutron bombardment actually split uranium into two light nuclides, and such a process is called nuclear fission.

The Discovery of Fission Reactions

No doubt, you have heard of the term nuclear fission because of the infamous atomic bombs and power producing nuclear reactors. Because a new concept is required to recognize fission, the story leading to the discovery of fission is particularly interesting.

  • Why did researchers bombarding uranium with neutrons?
    What were researchers looking for?
    What did the radioactivity indicate?
    How was nuclear fission discovered?
    Why did neutron bombardment produce many products, and what are the products?
    Which isotope undergoes fission?
    Are neutron released in the fission process?

After their discovery, neutrons were used to bombard all elements including uranium. At that time, three prominent research groups separately led by Enrico Fermi (1901-1954) in Rome, F. Joliot (1900-1958) and I. Curie in Paris, and Otto Hahn (1879-1968), Lise Meitner, and Fritz Strassmann in Berlin diligently bombarded uranium with neutrons, hoping to produce transuranium elements (elements heavier than uranium).

After bombardment by neutrons, uranium samples became radioactive. Beta particle emission was particularly noticeable. The three groups competed with one another to identify the products in these experiments. Since they worked in three different countries, the competition was an international race for the first to identify the nuclide(s) produced. They expected neutron capture reactions followed by  emission to produce elements 93 (E93) and 94 (E94), which were unknown at that time. They expected these reactions:

238U (n, ) 239U92 (, ) 239E93 (, ) 239E94.

They published papers offering various interpretations and attacked each other for misinterpretations. The arguments went on for some time while the war intensified in Europe. The French group precipitated a  emitter with half-life 3.5 d together with lanthanum, and they interpreted it as an isotope of actinium (Z = 89), which drew criticism from Hahn who argued that  and proton emissions were not possible.

Hahn, a chemist, Strassmann, an analytical chemist, and Meitner, a physicist, worked together to make transuranium elements. Meitner was very excited when she detected a great increase in radioactivity after uranium was irradiated with neutrons. Strassmann, applied analytical chemistry skills to precipitate the radioactive products. He understood that hydrogen sulfide (H2S) would not precipitate uranium radioactive decay daughters, but after neutron irradiation, he precipitated most of the radioactive products using H2S. The half-life measurements indicated to them that not one but many elements were produced (Shea, 1983).

How could one reaction give rise to so many different products? The three groups struggled over this question for many years, and eventually Hahn's group, including Meitner on exile, came to the conclusion that the neutron bombardment caused 235U to split into small fragments whose mass numbers are slightly more or less than half the mass number of uranium. Products, which they earlier thought to be the radioactive as isotopes eka rhenium, eka osmium, eka iridium and eka platinum, co precipitated with rhenium, osmium, irridium etc, were later identified as fission products not transuranium elements. The nucleons in a nucleus form a liquid drop, and the fission process is very much like splitting a drop into two, often unevenly.

The Official History of the Manhattan Project (US, 1977) gives the following story. The discovery of neutron induced fission was first brought to Copenhagen by Dr. Meitner, who, as a non-Aryan, was exiled from Germany in 1938. She used barium ions, Ba2+, as a carrier and precipitated the radioactive products from the neutron bombardment. None of the chemical methods could separate the radioactive ingredient from the barium ion, and she concluded that the isotope 238U must have split into two fragments. The atomic weight of barium, 137, is a little more than half of 238. When she arrived at Copenhagen, she communicated her thought to Dr. Frisch, who communicated the information to his friend N. Bohr, who was in the United States at the time. Bohr conveyed Meitner’s insight to Fermi who immediately changed his strategy of research. In March, 1940, Fermi's group (working in Columbia University) found that only the less abundant (0.7%) isotope 235U underwent fission.

When Fermi (1901-1954), Szilard (1898 1964), and F. Joliot (1900-1958) learned of the fission of uranium, they were anxious to find out which isotope underwent fission and if neutrons were released in the fission process. If neutrons are released, they had envisioned a chain fission reaction because the newly released neutrons induce more fission reactions. Almost at the same time and independently, researchers in various groups discovered that only 235U underwent fission and neutrons were indeed released. The release of neutron made the fission reactions candidates for a very powerful weapon known as the atomic bomb, which was eventually built and used.

During the lecture, a movie on the life of Lise Meitner called "The Missing Link" will be shown. The title was derived from her isolation of the isotope protactinium, 231Pa91, an element unknown until that time. Elements thorium, Th90, and uranium U92 were well known, but the element between them will missing. The movie is a very good video essay that addresses several issues including politics and power.

Skill Building Questions

  1. What is the lesson learned from the story leading to the discovery of neutron induced fission? (New concepts are required to recognize new phenomena. Concepts are important tools in research. New phenomena create new concepts, and new concepts give new interpretation to old phenomena. Many concepts became theory, and we take some of them for granted.)

  2. Why are reactions induced by neutron bombardment of uranium so difficult to explain? How can uranium fission products be identified and confirmed? (The neutron bombardment caused 235U to split into small fragments whose mass numbers are slightly more or less than half the mass number of uranium. Thus, many products were produced. We will discuss this further in the next few sections.)

The Fission Nuclear Energy

The discoveries that one of the uranium isotopes 235U underwent nuclear fission reactions, and that neutrons were released opened a new frontier for research and development. The discoveries were so important that they were treated as top secret because of the its potential applications in war. Furthermore, these discoveries were made at a time when the entire world was at war, and the war sped up the research and development.

  • How much energy is released per fission reaction?
    How can the amount be estimated or calculated?
    What are the applications of fission energy in war and peace?

A strategist asks many questions about a new discovery, and a philosopher plans for the future. The questions and plans are seeds for further research and development.

We concentrate on the fission process and the energy aspect in this section. A spontaneous reaction releases energy. Neutron induced nuclear fission reactions are spontaneous reactions and they release energy. This quantity is important, because it affects fission research and development. Both theoretical considerations and practical measurements have been carried out to give estimates of the amount of energy released in fission reactions. Some examples showing how estimates can be made are given here.

You have learned that when nucleons bind together to form a nuclide, energy is released. The energy so released is called binding energy. The average binding energy is the largest for nuclides with mass number around 56. Thus, splitting up a heavy nuclide such as uranium to give nuclides with mass number about 117 releases energy. A rough estimate is to consider an even split of 235U to give two nuclides of mass numbers 117 and 118. A search of stable nuclides with mass numbers 117 and 118 are 117Sn50, and 118Sn50, their masses being 116.902956 and 117.901609 amu respectively. The mass of 235U92 is 235.043924 amu. The difference in mass

E = m c2

35.043924 - (116.902956 + 117.901609)
= 0.2394 amu (931.5 MeV/1 amu)
= 223 MeV.

In reality, a fission reaction usually gives two unequal fragments, plus 2 to 3 neutrons. These neutron-rich fragments are beta () emitters. As a more realistic example to calculate the energy of a fission reaction, let the two fragments be isotopes of rubidium and cesium plus three neutrons. The reaction can be represented by

235U + n  142Cs55 + 90Rb35 + 4n + Q.

where Q is the mass equivalence of energy released. The neutron-rich cesium and rubidium isotopes are not stable, and they undergo radioactive decays:

142Cs  142Ba +  (~1 m) 90Rb  90Sr +  (half-life, 15.4 m)

142Ba  142La +  (11 m) 90Sr  90Y +  (27.7 y)

142La  142Ce +  (58 m) 90Y  90Zr (stable) +  (64 h)

142Ce  142Pr +  (51015 y)

142Pr  142Nd (stable) +  (19 h)

The total energy can be calculated from the measured masses of 235U, 90Zr, 142Nd, and neutron but some of the energy will not be released during the operation of the reactor due to the very long half-lives (in this case of 90Sr, 142Ce). However, a calculation to estimate the energy may proceed in the following way:

Reaction 235U9290Rb37 + 142Cs55 + 3n + Q.
Mass /amu 235.04924 = 89.904703 + 141.907719 + 3 x 1.008665 + Q

Q = (235.043924 - 89.904703 - 141.907719 - 3 x 1.008665)(931.4812 MeV/1 amu)
= 191.4 MeV per fission

The energy of 191.4 MeV is equivalent to 0.0000307 J or 307 erg, which is released per fission of 235U nucleus. Fission of one kilogram (1000 g) of uranium-235 will release 7.861019 J

= 7.861013 J

This amount of energy is equivalent to 2.2×1010 kilowatt-hour, 22000 megawatt-hour, or
22 giga-watt-hour. This amount of energy keeps a 100-watt light bulb lit for 25,000 years.

Energy (MeV) distribution in fission reactions

Kinetic energy of fission fragments

167 MeV

Prompt (< 10–6 s) gamma () ray energy


Kinetic energy of fission neutrons


Gamma () ray energy from fission products


Beta () decay energy of fission products


Energy as antineutrinos (ve)


In the fission process, the fragments and neutrons move away at high speed carrying with them large amounts of kinetic energy. The neutrons released during the fission process are called fast neutrons because of their high speed. Neutrons and fission fragments fly apart instantaneously in a fission process. No delayed liberation of neutrons was ever observed. Gamma rays (photons) equivalent to 8 MeV of energy are released within a microsecond of fission. As mentioned earlier, the two fragments are beta emitters. Recall that beta decays are accompanied by antineutrino emissions, and the two types of particles carry away approximately equal amounts of energy. Beta decays often leave the nuclei at excited states, and gamma emission follows. Estimated average values of various energies are given in a table here.

Skill Building Questions

  1. Give an example to show how the amount of energy released in a nuclear fission can be estimated.

  2. Assume 235U splits into two fragments with masses 100 and 132 and three neutrons. Find the masses of stable nuclides with these masses. What is the fission energy in this cases?

  3. How is the fission energy distributed among the various forms?

  4. Calculate the speed of a neutron which has kinetic energies of 1 and 2 MeV respectively.

The Cyclotron and Fission Research

The machine built by Cockroft and Walton accelerated protons, which smashed 7Li nuclei. Any machine that speeds up the velocity of particles are called particle accelerators. Particles from accelerators induced many nuclear reactions, and the value of accelerators in the study of nuclear reactions was soon realized.

  • How can particles be accelerated?
    How to build particle accelerators?
    What are the purposes of particle accelerators?
    How can particle accelerators be used to study fission reactions?

Various types of particle accelerators have been built, using electric potentials or electromagnetic forces. Linear particle accelerators made particles moving faster along a straight line; whereas cyclotrons accelerated them as they travel along circular path. The cyclotrons built by Ernest O. Lawrence in Berkeley, California belong to the latter type, and they have given useful results.

A cyclotron has two hollow D-shaped (Dee) sections assembled together with a small space in between. A magnetic field deflects the particles into spiral motion. By applying alternated voltages between the Dees, the cyclotron accelerates charged particles to desirable energies. By changing the strength of the magnetic field, particles of various energies are made available. The first such cyclotron has a diameter of only 13 cm, and it accelerated protons to a maximum energy of 13 keV. Cyclotrons built later with larger diameter accelerated particles to energies between 10 and 100 MeV.

Accelerated particles are used to induce nuclear reactions as discussed in the last Chapter. Reactions between accelerated charged particles from cyclotrons and light nuclides produced neutrons of variable energy. The following are some of the reactions:

7Li (p, n) 7Be
3T (p, n) 3He
1H (t, n) 3He
2D (d, n) 3He
2D (t, n) 4He
3T (d, n) 4He.

Reactions between tritium (3T or t) and deuterium (2D or d) are particularly important, because these are fusion reactions. Furthermore, they release neutrons of various energies.

Cyclotron induced nuclear reactions provide neutrons of controlled energy for the study of fission. For example, some reactions of protons with medium-weight nuclides are listed below together with their threshold energy and neutron energy range.

Threshold* Energy range (keV)

Reaction energy (MeV) of narrow-energy neutron
51V (p, n) 51Cr 2.909 5.6-52

45Sc (p, n) 45Ti 1.564 2.36-786

57Fe (p, n) 57Co 1.648 2-1425


* The threshold energy is the minimum energy of proton required for the reaction.

Energy from the neutron source 27Al (, 1n) 30P mentioned earlier can not be varied. Neutron sources from the cyclotron have an advantage over neutron sources induced by natural radiation, because neutron energy can be varied. This enables the study of energy dependence of neutron induced fission reactions. The variation of cross sections for neutron-induced fission as a function of neutron energy is a vital piece of information for nuclear reactor design. The study showed that fast neutrons (energy ranges from 10 MeV to 10 KeV) are not effective to induce fission, but slow neutrons (0.03 to 0.001 eV) are very effective. Slow neutrons are also called thermal neutrons, because their energy corresponds to room temperatures.

Skill Building Questions

  1. What are particle accelerators? What are cyclotrons? How do they accelerate charged particles?

  2. What are the applications of particle accelerators?

  3. What are the advantages of neutron sources from nuclear reactions induced by particle accelerators? (They provide neutron sources of variable but definite energy for experiments.)

The Synthesis of Plutonium

The intention to synthesize transuranium elements by neutron bombardment of uranium split 235U nuclei.

  • Can transuranium elements be made by neutron capture reactions of uranium?
    If so, why are tranuranium elements not detected?
    How can plutonium be dynthesized?
    What are the properties of plutonium?
    Why is plutonium a strategic material?

Experiments to produce elements 93 and 94 by the (n, ) reaction are sound, but so much fission products were produced that they impaired the detection of transuranium elements. The cyclotron, however, provided high intensity neutrons of definite energy, and it gave a chance for success.

The cyclotron provided neutrons for E. M. McMillan (1907-) and P. H. Abelson (1913-), to bombard uranium. In the summer of 1940, they confirmed one product as element 93, and named it neptunium, Np, after the planet Neptune. They inferred that Np would decay by emitting a  particle converting itself into element 94, named plutonium after the planet Pluto. These reactions are summarized bellow:

238U + n  239U + 
239U (half life 23.5 m)  239Np + 
239Np (half life 2.35 d)  239Pu + 

or in short notations:

238U (n, ) 239U ( , ) 239Np ( , ) 239Pu
238U (n, 2) 239Pu

Actually, the neutrons with high kinetic energies are used to produce transuranium elements. The fission theory by Bohr and Wheeler suggested that 239Pu would undergo fission. Thus, the cyclotron in Berkeley was put to work to produce enough plutonium for experiments. By mid-1941, the fission characteristic of plutonium was well established.

Plutonium was first detected (1940) by Glenn T. Seaborg, Joseph W. Kennedy, and Arthur C. Wahl, from the reaction 238U (d, b) 240Np using deuterium from the 60-inch cyclotron at Berkeley, California. The most important isotope is 239Pu, because it has a long half-life (24,400 y) and it is a fission fuel. This isotope can easily be produced using a breeder reactor, which shall be described later in this Chapter.

Plutonium has a very high electrical resistivity and a density of 19.84 g cm-3. It is chemically reactive, dissolving in acids and forming various ions of characteristic colour in water: Pu3+, blue-lavender; Pu4+, yellow-brown; and PuO+2, pink. Many compounds of plutonium have been prepared, often starting from the dioxide, PuO2), the first compound of any synthetic element to be separated in pure form and in weighable amounts (1942). Isotope 244Pu gives a melting point of 912 K, boiling point 3,508 K. The concept of critical mass will be introduced later, and you may be interested in knowing that the critical mass of 239Pu is only 300 grams.

Skill Building Questions

  1. Describe the neutron capture reaction of uranium leading to the formation of neptunium and plutonium.

  2. What is the significance of the synthesis of neptunium and plutonium?

  3. Why is 239Pu the most important isotope of plutonium?

Uniting Political and Nuclear Powers

Neutron induced fission reactions release energy and neutrons. The amount of energy in fission reactions is alarmingly large and the liberation of neutrons in the fission process gives the possibility of an explosive chain reaction, which releases a tremendous amount of energy. At that time, the scientists already foresaw the danger of nuclear power, especially if the technology falls in the wrong hand.

Since securing the presidency of Germany in 1933, Hitler became a dictator, and many top scientists in Austria, Hungary, Italy and Germany felt uncomfortable. Scientists with ethnic backgrounds other than German felt threatened. Many European scientists had escaped the Hitler regime and come to the United States. At the time fission was discovered, Hitler invaded Poland, Hungary, Slovak and other European countries. Many scientists were concerned that Hitler would make use of fission to build bombs. Such a move is a threat to the entire world.

  • Why scientists feared the danger of nuclear power?
    What was the political situation when fission was discovered?
    Why were so many scientists felt threatened?
    Who took the initiative to bring the issue to the most powerful political leader and why?
    What did they do individually and collectively and why?
    What would you do if you were afraid of the nuclear power falling into the wrong hand?
    What is an effective strategy to prevent a disaster from happening?

Among the concerned people were three Hungarian refugee scientists Leo Szilard, Eugene Wigner, and Edward Teller, who thought the time has come to unite political force with nuclear power. They thought Hitler had the potential and possibility of developing atomic bombs. This matter should be brought to the immediate attention of the President of the United States, Roosevelt. To achieve this, they needed someone with a reputation. They convinced Albert Einstein that such an action was a necessity. Szilar, Wigner and Teller composed a letter for Einstein, and Einstein signed the letter* as the sender. They took the matter so serious that they convinced the economist Alexander Sachs to personally deliver the letter to the White House. (Use Einstein and letter and Roosevelt as keys to search the Internet will get many sites containing this letter)

Refugee scientists from Hungary, Germany and Italy (L. Fermi, 1955) have worked under a totalitarian political system, in which totalitarian leaders controlled everything including universities and researchers. The governments knew whatever went on in university laboratories. They were fearful of Germany being the first to develop the atomic bomb. Thus, they took the initiative to bring the issue to the president of the United States. Most American scientists at that time were usually unfamiliar with this type of political control, and they felt less threatened.

The likelihood that Germany might develop an atomic bomb caused President Roosevelt to act and he decided immediately to create an Advisory Committee on Uranium that would give financial assistance to universities engaged in uranium research. The sum of $300,000 (remember these are 1940’s dollars) was immediately allocated to Columbia, Princeton, MIT, Chicago, California, Virginia etc. Research on uranium and fission is complicated, and information on many aspects of uranium and of fission is required. Each group worked on one or more aspects of fission, and nuclear research was intensely carried out by many young and old scientists.

The Chicago group worked on uranium, and the California group worked on plutonium. Soon they realized that enriched 235U or pure 239Pu would be required for the construction of an atomic bomb. For building an atomic bomb, production of enough fissionable material is the most important task. However, other information such as identification of fission products, accurate cross section for neutrons as functions of energies, moderating neutron motion, and percentages of neutrons that induce fission are all required.

Review Questions

  1. What is power? What do high political positions, reputation, money, science and knowledge have in common? (Each of these represents a form of power. Agree or not agree, elaborate your view.)

  2. Comment on the action taken by Szilard, Wigner, and Teller. (Political and economical forces do influence scientific development. The objective of this question is to raise the awareness of the impact of science on politics and vice versa.)

  3. Comment on the reaction of President Roosevelt.

Thermal Neutrons

Fermi's group irradiated uranium samples with neutrons. They surrounded the samples with different materials at various times and found samples surrounded by water, wood, and paraffin more radioactive.

  • Why surrounding the samples with water, wood, and paraffin increased their radioactivity?
    What happens to neutrons when they collide with atoms and molecules in a medium?
    Which one is more effective in slowing neutrons, heavy nuclides or light ones? Why?
    What are the energies of neutrons after they have scattered many times with atoms?
    How do these energies depend on the temperature of the medium?

After Fermi's group has learned of nuclear fission, they attributed the fission radioactivity increase to the moderation (slowing down) of neutrons by hydrogen and light elements in water, wood, and paraffin. They thought that neutrons are slowed quickly by collision with protons, because the two particles have comparable mass. Neutrons can transfer almost all their kinetic energy to proton in a collision.

Materials used to slow down fast neutrons are called moderators. On the average, 20 collisions with protons are sufficient for neutrons to reach an equilibrium state that further collisions will no longer change their average kinetic energy. The average kinetic energy of neutrons depends on the temperature of the medium, in which they are in thermal equilibrium with. These neutrons are called thermal neutrons. In the following paragraphs, we further describe how energy of the molecules depends on the temperature.

Molecules in a medium are constantly in motion: vibration, rotation, and translation. The average kinetic energy of molecules is directly proportional to the temperature in K. At room temperature (293 K) the average kinetic energy of all molecules is 0.025 eV. Of course, some molecules have higher and some have lower kinetic energies than 0.025 eV. In fact, the kinetic energies of the molecules have a Maxwellian distribution. This skewed distribution is depicted here, and it is different from the normal or bell shaped distribution. As the temperature changes, the skewed distribution shifts slightly to give a higher average kinetic energy.

The neutrons collide with molecules and atoms in the medium constantly, and their energies have the same distribution as those of the molecules.

Neutrons are often classified as fast, thermal, and cold neutrons according to their kinetic energies. Fast neutrons have a kinetic energy exceeding some threshold, typically 0.1 or MeV. Neutrons just released from the fission reactions are fast neutrons. After some collisions with atoms in the medium, they become thermal neutrons and their typical average kinetic energy is 0.025 eV. The average kinetic energy of cold neutrons is less than 0.01 eV. Slightly different boundaries of division may be given in other literature due to differences in view points or definition of room temperatures, but these are typical values. Cold neutrons are either from super cold hydrogen moderated experimental reactors or selected by diffraction from crystals. There are some special applications for this type of neutrons.

Skill Developing Questions

  1. Explain the following terms: moderator, fast neutrons, thermal neutrons and cold neutrons.

  2. Sketch a distribution for kinetic energies of thermal neutrons.

  3. Estimate the velocities of a neutron whose kinetic energies are 0.1 MeV, 0.025 eV, and 0.01 eV respectively.

Thermal Neutron Cross Sections

Cross section () is a measure of the probability of a given reaction, as we have discussed elsewhere. Cross sections are further classified according to types and reactions. Since thermal neutrons are readily available thermal neutron cross sections (c), are important nuclear data. They are usually given for each nuclide to indicate its probability of thermal neutron capture. For possible fission material, the thermal neutron cross section for fission (f) is also given.

  • How do you look for a suitable fission material for nuclear reactor from a nuclear data source?
    What parameters indicate the suitability of fission material?
    What materials are suitable for the construction of fission reactors and bombs?
    What are the thermal neutron cross sections (c) of some key elements that are useful for the construction of atomic bombs and for nuclear reactors?

Thermal neutrons are much better than fast neutrons at inducing nuclear fission. Thus, thermal neutron cross sections for all nuclides have been studied, because many materials are required for fission device (bombs and reactors) constructions.

Around 1940, the Uranium Research Program measured thermal neutron cross sections for various reactions of almost all nuclides. In the following list, thermal neutron (capture) cross sections () and thermal neutron fission cross sections (f) are given for some key nuclides. Half-lives (t1/2) of the radioactive nuclides are also given, because they are important properties of the nuclides regarding fission device.

1H 2H 12C 14N 16O 113Cd 233U 235U 238U

c /b 0.33 0.00052 0.0034 1.82 0.0002 19,820 46 98 2.7

f /b 530 580 2.7×10-6

t1/2 /y 1.6×105 7×108 4.5×109
Note the large difference in cross sections between hydrogen, 1H, and deuterium, 2H, given above. The difference warrants the extraction of heavy water (2H2O or D2O) from natural water for fission device applications. Since the cross section for deuterium is small, heavy water, D2O, does not absorb many neutrons, and using it as moderator for reactors gives sufficient neutrons for using natural uranium as a fuel. If pure water is used as a moderator, hydrogen atoms absorb to many neutrons and 235U enriched uranium is required as fuel. Carbon and oxygen have very small thermal neutron cross sections compared to nitrogen. When Fermi built the first nuclear reactor, he used carbon (graphite) as the moderator, and he put the graphite (moderator) in cans to reduce nitrogen in reactor.

The extremely large thermal neutron cross section of 113Cd makes cadmium a good neutron absorber or eliminator. The element cadmium contains many isotopes. The abundance (in %) and thermal neutron cross sections (b) are listed below:

106Cd 108Cd 110Cd 111Cd 112Cd 113Cd 114Cd

c / b 1 1 0.1 24 2.2 19,820 0.3

Abundance /% 1.25 0.89 12.45 12.80 24.13 12.22 28.37
The abundance of 113Cd is moderate but adequate. Furthermore, the neutron-capture reaction 113Cd (n, ) 114Cd leads to a stable isotope. These properties made cadmium a very desirable material for the nuclear technology industry.

The thermal neutron cross section of fission of 235U is 160,000 times larger that that of 238U. Fission of 238U is negligible. This difference made it necessary to enrich 235U for nuclear energy and atomic bomb material. Research in the 1940s revealed another important fissionable isotope of plutonium 239Pu. Even though other isotopes of plutonium had higher cross sections than 239Pu, their half-lives are very short. The half lives and thermal fission cross sections of plutonium isotopes are given below for your reference:

236Pu 237Pu 238Pu 239Pu 240Pu 241Pu 242Pu

f 150 2100 17 742 0.08 1010 0.2

t1/2 2.9 y 45 d 88 y 24131 y 6570 y 14 y 3.8×105y
Other factors in nuclear energy considerations were methods and costs of production. All these factors led to the conclusion that only the production of 235U and 239Pu are feasible and practical. Production of 233U was not worth considering.

Review Questions

  1. What is the significance of thermal neutron cross sections and thermal neutron cross section for fission?

  2. Compare the difference in thermal neutron cross section for hydrogen and deuterium. Describe the implication of the difference.

  3. What are the thermal neutron cross sections for isotopes of the following elements: boron, zirconium, and cadmium? What are the products of neutron capture reaction for the stable cadmium isotopes? What are the consequences of the capture reaction?

  4. What are the abundances of uranium isotopes in natural occurring uranium? From the thermal neutron cross sections and abundance, discuss work required for using uranium as a fuel for nuclear energy generation. (Consult a hand book for the required data)

Fission Products

Fission products are nuclides produced in fission reactions. As suggested earlier, rubidium and cesium as two of the possible fission products. Finding out fission products is certainly a strategic project the fission research.

  • What are the fragments produced in nuclear fission?
    What rays are emitted from the fission product, and why?
    How does radioactivity of fission products vary over time after fission?
    What is the distribution of the nuclides in terms of mass numbers?
    What is the impact of fission products on the applications of fission reactions?

After capturing neutrons, the compound nuclei 236U are at excited states with excess energy. The 236U nuclei undergo fission;  or  emission. The half-life for fission is much shorter (10 14 s) than those of  and  emissions (half-life for  decay is 2.3107 y). Fission is the preferred process.

Since many nuclides are produced in the fission process, the study of fission products requires the separation, identification, and quantitative determination of various elements and isotopes. Since heavy nuclides contain more percentages of neutrons than light nuclides do, fission products from the fission of heavy nuclides are too rich in neutrons. Thus, fission products emit  particles until they are stable. This aspect has been illustrated when we estimated the energy of fission reactions.

Since the nuclei usually split into two pieces of different masses, the mass numbers of fission products range between 40 and 170. In terms of elements, they range from potassium, to tungsten, nearly all the elements in the 4th, 5th, and 6th periods, including the lanthanides*. They include alkali metals (K, Rb, Cs), alkaline earth metals (Ca, Sr, Ba), all the transition metals from scandium to tungsten, metalloids (Ge, Sb, Te, Se, etc) halogens (Br, I) and inert gases (Kr and Xe). Thus, separation of fission products into various elements is a complicated operation.

Sketch of Slow neutron Fission Yields from 235U as a Function of Mass Number.
log(Fission yield)


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60 90 110 140 170

Mass no.
Some (2 to 4) neutrons are released per fission reaction. The atomic numbers of fission products are difficult to determine, because they rapidly undergo  decay. Studies have revealed that most fission events are asymmetrical, with heavy and light fragments, rather than symmetric (with two equal fragments). Relative amounts (in percentage of total nuclides produced) of nuclides formed are called fission yields. The plot of fission yields from 235U against mass number gives two peaks, one between mass 80 and 110 and the other between 120 and 160. Between the two peaks is a low yield region, the center of which corresponds to a mass number 113. A symmetric fission produces two fragments of mass number 113 if no neutron is emitted. The yield distribution depends on the kinetic energy of the neutrons, but all plots have the general feature of two peaks in similar area. The two peaks have slightly different shapes when kinetic energies of the neutrons are different.

Atomic bombs and nuclear reactors are two types of fission application. Fission-product data and their behavior are of fundamental importance, because they have a great impact on the environment and society. Fission products are left following bomb explosions and reactor accidents. For example, some typical long-lived fission products such as 90Sr and 129I are used for monitoring nuclear explosions and accidents. These data are also essential for reprocessing used nuclear fuels and nuclear waste management.

Management of used or irradiated fuels also depends on radioactivity of fission products. Most fission nuclides have very short half lives. After a decade, few nuclides remain radioactive. A very low yield nuclide 85K has a half life of 10.7 years, and two other nuclides, 90Sr and 137Cs have half lives of 29 and 30 years respectively. There are no fission nuclides whose half-life lies between 30 and 105 years. Fission products with half lives greater than 100 years with yields greater than 10–4 are 126Sn (1105 y), 126Tc (2.1105 y), 91Tc (1.9106 y), 135Cs (3106 y), 107Pd (6.5106 y), and 129Tc (1.6107 y).

Fission products affect the operation of reactors in many ways, one of which is the absorption of neutrons by fission products. The high-yield fission product 135Xe has a c of 2,640,000 b, and a half-life of 9.2 hours. The presence of this product lowers the level of fission, and this effect is often referred to as xenon poisoning. The chain reaction of the atomic pile in Hanford suddenly stopped in July, 1944. John Wheeler, the poisoning expert, was consulted. After checking the control parameters of the reactor before the interruption, he concluded that it was the xenon. A few hours later, the reactor resumed function, and this is consistent with the half-life of 135Xe.

Skill Building Questions

  1. Assume two neutrons and 133Xe are produced in a fission reaction, what is the other fragment? Work out the decay scheme and show the half lives of the fission products. (Consult a handbook for required data).

  2. Both 129I and 131I nuclides are produced in nuclear fission. Suggest a method for their isolation. What are the half-lives of these nuclides? What are the daughter nuclides in the decays of these fission nuclides?

The First Fission Nuclear Reactor

Research on uranium has been divided into several tasks. With strong financial support from President Roosevelt, some facts are well known to the inner circle of researchers involved with the uranium project. Neutrons are released in nuclear fission of 235U. Thermal neutron cross sections for many elements have been measured.

  • Will uranium undergo a chain fission reaction?
    Will the chain reactions lead to a runaway explosion?
    Can a chain fission reaction be controlled?
    How to control a chain reaction to sustain for a long period of time?

Since neutrons are released, uranium undergoes a chain fission reaction, when the neutrons are moderated, and sufficient number of them will cause the next generations of reaction. Firmly believed in this, Fermi’s group assembled uranium into an atomic pile to test the feasibility of a sustained chain fission reaction. They used natural uranium with graphite as moderator, cadmium in the control rod, and boron in the neutron detector. These are the key requirements for nuclear reactors.

Because this was the first atomic pile, only the trial and error method was available to them. They experimented with various materials as they assembled the atomic pile. They used water as the moderator at the beginning, and it did not work. They thought water absorbed too many neutrons. They switched to graphite, still not working. They attributed the failure to the impurity in graphite, so they purified graphite, and made it into bricks. Due to high thermal neutron cross section for nitrogen (1.82 b), they put graphite and uranium into cans and removed the air from them. Step by step, they identified and solved many problems. They placed alternate layers of graphite bricks and pieces of natural uranium and constructed an atomic pile in a racquet court at Stagg Field at the University of Chicago.

Another major problem for the first nuclear reactor was the size of the atomic pile. Various calculations have given an estimate of the amount of required uranium, but experiments give the ultimate test. Fermi’s group built up the pile, and tested the operation as the size grew.

After years of effort, the atomic pile had a sustained chain reaction of a fission nuclear reactor on December 2, 1942 (Fermi, 1955). This was the beginning of the controlled fission reaction. Its success not only provide the pile as a tool for other research, the reactor became a research tool for future reactor design. Its operation provides data for the construction of larger and more sophisticated reactors. It was indeed a great event.

The way they built the first reactor was risky and dangerous in today’s standards. For example, control rods were manually handled. When the reactor was powered up for testing, the emergency measures were solutions of boron and cadmium compounds ready to be poured on to the pile by people standing on guard. On the other hand, every step was handled carefully, and the reactor operation did not have any major problems.

In 1946 the first controlled nuclear chain reaction in Russia was achieved at the Kurchatov Institute, four years following Fermi's in Chicago.

As of 17 August 1995 there were 425 nuclear power reactors in operation worldwide. At that time, the U.S.A. had 107 nuclear reactors in operation, generating the most nuclear power, more than twice that of France, the world second largest. According to the Uranium Institute information, (, Belgium, France, Lithuania, and Sweden, had more than 50% power supplied by nuclear reactors in 1996, whereas the U.S.A., Canada and Japan had 22, 16, and 33% respectively.

Skill Building Questions

  1. What is a chain reaction? In the fission reactions, what is the chain carrier? What is the principle of a fission reactor? How can a chain reaction be controlled from a runaway explosion?

  2. What method was used to build and test the first nuclear reactor? (Trial and error is a powerful method for problem solving).

  3. Why was water not a suitable moderator for Fermi’s first nuclear reactor? What are desirable properties for a material used as moderator? (light mass, low thermal neutron cross section, low cost of production, and desirable engineering properties)

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