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Nuclear Energy Mail to Me   
Nuclear Energy is energy released by the splitting (fission) or merging together (fusion) of the nuclei of atom(s). Nuclear energy is the energy that is trapped inside each atom. The ancient Greeks believed that the smallest part of nature is an atom. But they did not know 2000 years ago that atoms are made up of further smaller particles—a nucleus of protons and neutrons, surrounded by electrons, which swirl around the nucleus much like the earth revolves around the sun.
One of the laws of the universe is that matter and energy can neither be created nor destroyed. But they can be changed in form. Matter can be changed into energy. Albert Einstein’s famous mathematical formula E = mc2 explains this. The equation says: E [energy] equals m [mass] times c2 [c stands for the speed or velocity of light]. This means that it is mass multiplied by the square of the velocity of light. nuclear-1.jpg (7162 bytes)

Scientists used Einstein’s equation as the key to unlock atomic energy and to create atomic bombs.

An atom's nucleus can be split apart. This is known as fission. When this is done, a tremendous amount of energy in the form of both heat and light is released by the initiation of a chain reaction. This energy, when slowly released, can be harnessed to generate electricity. When it is released all at once, it results in a tremendous explosion as in an atomic bomb.

nuclear-2.jpg (14610 bytes)

Nuclear energy can also be harnessed by fusion. A fusion reaction occurs when two hydrogen atoms combine to produce one helium atom. This reaction takes place at all times in the sun, which provides us with the solar energy. This technology is still at the experimental stage and may become viable in future.

Uranium is the main element required to run a nuclear reactor where energy is extracted. Uranium is mined from many places around the world. It is processed (to get enriched uranium, i.e. the radioactive isotope) into tiny pellets. These pellets are loaded into long rods that are put into the power plant's reactor. Inside the reactor of an atomic power plant, uranium atoms are split apart in controlled chain reaction. Other fissile material includes plutonium and thorium.

In a chain reaction, particles released by the splitting of the atom strike other uranium atoms and split them. The particles released by this further split other atoms in a chain process. In nuclear power plants, control rods are used to keep the splitting regulated, so that it does not occur too fast. These are called moderators.

The chain reaction gives off heat energy. This heat energy is used to boil heavy water in the core of the reactor. So, instead of burning a fuel, nuclear power plants use the energy released by the chain reaction to change the energy of atoms into heat energy. The heavy water from around the nuclear core is sent to another section of the power plant. Here it heats another set of pipes filled with water to make steam. The steam in this second set of pipes rotates a turbine to generate electricity. If the reaction is not controlled, you could have an atomic bomb.

But in atomic bombs, almost pure pieces of uranium-235 or plutonium, of a precise mass and shape, must be brought together and held together with great force. These conditions are not present in a nuclear reactor.

The reaction also creates radioactive material. This material could hurt people if released, so it is kept in a solid form. A strong concrete dome is built around the reactor to prevent this material from escaping in case of an accident.

Experiences with nuclear programmes differ and the future of nuclear power remains uncertain because of public reaction. But in the past few years the capacity of operating nuclear plants has increased more than twenty fold. There are more than 400 nuclear power plants providing about 7% of the world's primary energy and about 25% of the electric power in industrialized nations.

The growth of nuclear power combined with the shift from carbon-heavy fuels such as coal and oil to carbon-light gas contribute to the gradual ‘de-carbonization’ of the world energy system.

Chernobyl, Three Mile Island, and other nuclear accidents have increased the fear of harnessing nuclear energy. Another issue with international and local implications is the storage and disposal of radioactive wastes: both from nuclear reactors making electricity and from the production of military weapons. Earlier disposal practices, such as dumping of nuclear waste at sea, have been completely stopped by formal treaty because of environmental concerns (and by cessation of furtive scuttling of nuclear submarines). Regimes for transport and temporary storage of civil and defense nuclear wastes now function, although sites and designs for permanent disposal have yet to be accepted.

People are concerned about both low- and high-level radioactive wastes; the latter, though smaller in volume is more technically problematic. With the rise of nuclear electrification, the volume of spent fuel and other wastes has risen substantially; but is still small. In some countries such as the US, the volume of high-level waste from commercial power plants has now reached hundreds of millions of tones.

Nuclear energy is released by three exoenergetic (or exothermic) processes:

  • Radioactive decay: Were a neutron or proton in the radioactive nucleus decays spontaneously by emitting either particles, electromagnetic radiation (gamma rays), neutrinos (or all of them).
  • Fusion: Two atomic nuclei fuse together to form a heavier nucleus.
  • Fission: The breaking of a heavy nucleus into two (or more rarely three) lighter nuclei.

Nuclear Fission: Basics

When a nucleus fissions, it splits into several smaller fragments. These fragments, or fission products, are about equal to half the original mass. Two or three neutrons are also emitted.

Nuclear Fission

The sum of the masses of these fragments is less than the original mass. This 'missing' mass (about 0.1 percent of the original mass) has been converted into energy according to Einstein's equation.

Fission can occur when a nucleus of a heavy atom captures a neutron, or it can happen spontaneously.

Nuclear Chain Reactions

A chain reaction refers to a process in which neutrons released in fission produce an additional fission in at least one further nucleus. This nucleus in turn produces neutrons, and the process repeats. The process may be controlled (nuclear power) or uncontrolled (nuclear weapons).

Nuclear Chain Reaction

235 + n -› fission + 2 or 3 n + 200 MeV


If each neutron releases two more neutrons, then the number of fissions doubles each generation. In that case, in 10 generations there are 1,024 fissions and in 80 generations about 6 x 10
23 (a mole) fissions.

Energy Released From Each Fission

165 MeV
7 MeV
6 MeV
7 MeV
6 MeV
9 MeV

200 MeV

~ kinetic energy of fission products
~ gamma rays
~ kinetic energy of the neutrons
~ energy from fission products
~ gamma rays from fission products
~ anti-neutrinos from fission products

1 MeV (million electron volts) = 1.609 x 10 -13 joules

Critical Mass

Although two to three neutrons are produced for every fission, not all of these neutrons are available for continuing the fission reaction. If the conditions are such that the neutrons are lost at a faster rate than they are formed by fission, the chain reaction will not be self-sustaining.

At the point where the chain reaction can become self-sustaining, this is referred to as critical mass.

In an atomic bomb, a mass of fissile material greater than the critical mass must be assembled instantaneously and held together for about a millionth of a second to permit the chain reaction to propagate before the bomb explodes

The amount of a fissionable material's critical mass depends on several factors; the shape of the material, its composition and density, and the level of purity.

A sphere has the minimum possible surface area for a given mass, and hence minimizes the leakage of neutrons. By surrounding the fissionable material with a suitable neutron "reflector", the loss of neutrons can reduced and the critical mass can be reduced.

By using a neutron reflector, only about 11 pounds (5 kilograms) of nearly pure or weapon's grade plutonium 239 or about 33 pounds (15 kilograms) uranium 235 is needed to achieve critical mass.

Controlled Nuclear Fission

Controlled Nuclear Chain Reaction

To maintain a sustained controlled nuclear reaction, for every 2 or 3 neutrons released, only one must be allowed to strike another uranium nucleus. If this ratio is less than one then the reaction will die out; if it is greater than one it will grow uncontrolled (an atomic explosion). A neutron absorbing element must be present to control the amount of free neutrons in the reaction space. Most reactors are controlled by means of control rods that are made of a strongly neutron-absorbent material such as boron or cadmium.

In addition to the need to capture neturons, the neutrons often have too much kinetic energy. These fast neutrons are slowed through the use of a moderator such as heavy water and ordinary water. Some reactors use graphite as a moderator, but this design has several problems. Once the fast neutrons have been slowed, they are more likely to produce further nuclear fissions or be absorbed by the control rod.

Why Uranium and Plutonium?

Scientists knew that the most common isotope, uranium 238, was not suitable for a nuclear weapon. There is a fairly high probability that an incident neutron would be captured to form uranium 239 instead of causing a fission. However, uranium 235 has a high fission probability.

Of natural uranium, only 0.7% is uranium 235. This meant that a large amount of uranium was needed to obtain the necessary quantities of uranium 235. Also, uranium 235 cannot be separated chemically from uranium 238, since the isotopes are chemically similar.

Alternative methods had to be developed to separate the isotopes. This was another problem for the Manhattan Project scientists to solve before a bomb could be built.

Research had also predicted that plutonium 239 would have a high fission probability. However, plutonium 239 is not a naturally occurring element and would have to be made. The reactors at Hanford, Washington were built to produce plutonium.

Spontaneous Nuclear Fission

Spontaneous Nuclear Fission

Spontaneous Fission

The spontaneous nuclear fission rate is the probability per second that a given atom will fission spontaneously--that is, without any external intervention. If a spontaneous fission occurs before the bomb is fully ready, it could fizzle. Plutonium 239 has a very high spontaneous fission rate compared to the spontaneous fission rate of uranium 235. Scientists had to consider the spontaneous fission rate of each material when designing nuclear weapons.

Little Boy: A Gun-Type Bomb

Little Boy: A Gun-Type Bomb 3D cut-away

In essence, the Little Boy design consisted of a gun that fired one mass of uranium 235 at another mass of uranium 235, thus creating a supercritical mass. A crucial requirement was that the pieces be brought together in a time shorter than the time between spontaneous fissions. Once the two pieces of uranium are brought together, the initiator introduces a burst of neutrons and the chain reaction begins, continuing until the energy released becomes so great that the bomb simply blows itself apart.

Time of Reaction

The released neutron travels at speeds of about 10 million meters per second, or about 3% the speed of light. The characteristic time for a generation is roughly the time required to cross the diameter of the sphere of fissionable material.

A critical mass of uranium is about the size of a baseball (0.1 meters). The time, T, the neutron would take to cross the sphere is:

T =

0.1 meters

1 x 107 meters/second


1 x 10-8 seconds

The complete process of a bomb explosion is about 80 times this number, or about a microsecond.

This time was informally known as a 'shake' ("as fast as the shake of a lamb's tail") by the physicists at Los Alamos.

Fat Man: Implosion-Type Bomb

Fat Man: Implosion-Type Bomb 3D cut-away

The initial design for the plutonium bomb was also based on using a simple gun design (known as the "Thin Man") like the uranium bomb. As the plutonium was produced in the nuclear reactors at Hanford, Washington, it was discovered that the plutonium was not as pure as the initial samples from Lawrence's Radiation Laboratory. The plutonium contained amounts of plutonium 240, an isotope with a rapid spontaneous fission rate. This necessitated that a different type of bomb be designed. A gun-type bomb would not be fast enough to work. Before the bomb could be assembled, a few stray neutrons would have been emitted from the spontaneous fissions, and these would start a premature chain reaction, leading to a great reduction in the energy released.

Seth Neddermeyer, a scientist at Los Alamos, developed the idea of using explosive charges to compress a sphere of plutonium very rapidly to a density sufficient to make it go critical and produce a nuclear explosion.

Implosion-Type Bomb: Detonation Sequence

Explosive Lens Diagram

    • The high explosive surrounding the fissile material is ignited.
    • A compress ional shock wave begins to move inward. The shock wave moves faster than the speed of sound and creates a large increase in pressure. The shock wave impinges on all points on the surface of the sphere of the fissile material in the bomb core at the same instant. This starts the compression process.
    • As the core density increases, the mass becomes critical, and then supercritical (where the chain reactions grows exponentially).
    • Now the initiator is released, producing many neutrons, so that many early generations are bypassed.
    • The chain reaction continues until the energy generated inside the bomb becomes so great that the internal pressure due to the energy of the fission fragments exceed the implosion pressure due to the shock wave.
    • As the bomb disassembles, the energy released in the fission process is transferred to the surroundings.


Nuclear Fusion


Fusion powers the sun and stars as hydrogen atoms fuse together to form helium, and matter is converted into energy. Hydrogen, heated to very high temperatures changes from a gas to a plasma in which the negatively charged electrons are separated from the positively charged atomic nuclei (ions). Normally, fusion is not possible because the positively charged nuclei naturally repel each other. But as the temperature increases the ions move faster, and they collide at speeds high enough to overcome the normal repulsion. The nuclei can then fuse, causing a release of energy.

In the sun, massive gravitational forces create the right conditions for this, but on Earth they are much harder to achieve. Fusion fuel - different isotopes of hydrogen - must be heated to extreme temperatures of over ten million degrees Celsius, and must be kept dense enough, and confined for long enough (at least one second) to trigger the energy release. The aim of the controlled fusion research program is to achieve "ignition" which occurs when enough fusion reactions take place for the process to become self-sustaining, with fresh fuel then being added to continue it.

Basic fusion technology


With current technology, the reaction most readily feasible is between the nuclei of the two heavy forms (isotopes) of hydrogen - deuterium (D) and tritium (T). Each D-T fusion event releases 17.6 MeV (2.8 x 10-12 joule, compared with 200 MeV for a U-235 fission). Deuterium occurs naturally in sea water (30 grams per cubic metre), which makes it very abundant relative to other energy resources. Tritium does not occur naturally and is radioactive, with a half-life of around 12 years. It can be made in a conventional nuclear reactor, or in the present context, bred in a fusion system from lithium. Lithium is found in large quantities (30 parts per million) in the Earth's crust and in weaker concentrations in the sea. While the D-T reaction is the main focus of attention, long term hopes are for a D-D reaction, but this requires much higher temperatures.

In a fusion reactor, the concept is that neutrons will be absorbed in a blanket containing lithium which surrounds the core. The lithium is then transformed into tritium and helium. The blanket must be thick enough (about 1 metre) to slow down the neutrons. This heats the blanket and a coolant flowing through it then transfers the heat away to produce steam which can be used to generate electricity by conventional methods. The difficulty has been to develop a device that can heat the D-T fuel to a high enough temperature and confine it long enough so that more energy is released through fusion reactions than is used to get the reaction going.

At present, two different experimental approaches are being studied: fusion energy by magnetic confinement (MFE) and fusion by inertial confinement (ICF). The first method uses strong magnetic fields to trap the hot plasma. The second involves compressing a hydrogen pellet by smashing it with strong lasers or particle beams.

Nuclear fusion separates stars and brown dwarfs from Jupiter-like objects. Nuclear fusion is the process of light nuclei combining to form heavier nuclei. For elements lighter than iron, this process liberates energy. The fusion of elements heavier than iron takes energy rather than gives energy. Stars are therefore powered by the fusion of elements lighter than iron, particularly of hydrogen.

Recall how an atom is constituted: an atom has a nucleus composed of protons and neutrons, collectively known as nucleons, around which electrons orbit. In nuclear fusion, the total number of protons and neutrons is conserved, but some protons are converted into neutrons in the process. A proton becomes a neutron by emitting a positron, the antiparticle of the electron, and a neutrino in an exothermic process that releases 0.8 MeV of energy. A neutron becomes a proton by emitting an electron and a neutrino in an endothermic process.

Available Energy and Abundances

How much energy can be released through fusion? This is found by looking at the mass per nucleon in an atom. The energy released in nuclear fusion is substantial enough that it appears in the atom's rest mass. An examination of the excess rest mass energy per nucleon for all isotopes shows that the nucleus with the greatest available energy is hydrogen, which has an 7.3 MeV energy excess relative to carbon-12. Helium, on the other hand, has only 0.6 MeV energy excess relative to carbon-12, so fusion that takes hydrogen to helium releases a total of 26.7 MeV for each helium nucleus that is created. Helium itself fuses to create carbon, but this process releases a more modest 7.2 MeV per created carbon atom. Other stable atoms that are created through nuclear fusion are oxygen-16, with an energy excess of -0.3 MeV per nucleon relative to carbon, neon-20, with -0.4 MeV, and magnesium, with -0.6 MeV. The lowest value of excess energy per nucleon is found for iron-56 at -1.1 MeV relative to carbon. Most of a star's nuclear energy is therefore released in the conversion of hydrogen into helium.

The impact of stellar nuclear fusion on the elements in our universe is apparent. The most abundant elements after hydrogen and helium, which were created in the early expanding universe, are oxygen, an end product of helium fusion, neon, another end product of helium fusion, nitrogen, an element created from oxygen and carbon during hydrogen fusion, and carbon, the initial end product of helium fusion. This observational result is a consequence of the expulsion of gases by stars as they evolve. These fusion products mixed into the interstellar gasses influences the subsequent evolution of stars created from these gases. In this way, each generation of star influences the next generation. The fusion products created by the first stellar generation prepared the universe for life by creating carbon and oxygen.

Thermal Equilibrium in Nuclear Fusion

A star's core is badly out of thermal equilibrium. For a fixed temperature the constituents of an isolated system are determined solely by the temperature. For the relatively low temperature at the core of a solar mass star, a cool 15 million degrees (1 keV), the equilibrium state is composed primarily of iron-56 and other elements with similar numbers of nucleons it their nuclei. An equilibrium state that is predominately hydrogen requires a much higher temperature, one of order 100 billion degrees (9 MeV). A stellar core therefore attempts through nuclear fusion to bring its elemental composition into thermal equilibrium. The stumbling block to this is the low reaction rates for the various nuclear reactions. The reactions that occur first are the reactions that become most rapid at low temperatures, and rapid in this case means rapid enough to replenish the energy lost by the star's core through the propagation of radiation and the conduction of heat.

The first reactions that can counteract the transport of radiation out of the star as gravitational collapse raises the core's temperature and density are the reactions that convert hydrogen into helium. The next set of reactions that can occur as the temperature rises converts helium into carbon and other light elements with nuclei composed of multiple helium nuclei. Further increases in temperature initiate carbon fusion, and then oxygen fusion. These reactions continue until either the core becomes gravitationally stable from the degeneracy pressure of electrons, after which it is a cooling degenerate dwarf star, or until the core collapses into either a neutron star, which has a high-density equilibrium configuration radically different from the iron equilibrium that characterizes lower-density cores, or a black hole, in which the core configuration is unobservable and the subject of very speculative and esoteric research.

Uncertainty in Nuclear Fusion

Nuclear fusion rates are expressed in terms of cross sections. The cross section can be thought of as a disk of a particular area centered on one of the two nuclei involved in a fusion process. If the other nucleuses´ moving in a strait line perpendicular to this disk hits the disk, then a reaction occurs. If it does not, then no reaction occurs. This is a convenient abstract representation of the interactions among nuclei that allow a simple calculation of the reaction rate for a given density and temperature. The cross section for a reaction is a function of both temperature and density.

Hydrogen Fusion

The fusion of hydrogen into helium takes place through a somewhat complex network of reactions involving many isotopes that are intermediate in weight between hydrogen and helium and involving several elements that are heavier than helium. When one examines these numerous reactions, however, one finds that the conversion of hydrogen into helium predominately follows one of five paths.

The five different fusion paths can be divided into two sets of processes: the Proton-Proton (PP) process, which depends only on the amount of hydrogen and helium in the star, and the Carbon-Nitrogen-Oxygen (CNO) process, which depends on the amount of carbon, nitrogen, and oxygen in addition to the amount of hydrogen and helium in the star. The amount of carbon, nitrogen, and oxygen in a star is set by the composition of the interstellar gas at the time of the star's birth. But most of the metals (elements other than hydrogen and helium) in the interstellar gas are created and expelled by stars, so the history of star creation and evolution within a galaxy determines the effectiveness of the CNO process in a star. Because the universe had a low metal content early in its history, the first-born stars fuse hydrogen predominately through the PP process. This is one of three ways that the structure and evolution of a star depends on the age of the universe (The other two are through the influence of metals on the strength of the stellar wind in massive stars and on the transport of radiation out of a star).

The Proton-Proton Process


There are three branches to the PP process of convert hydrogen (H1) into helium (He4). The first branch does the conversion without creating any nuclei heavier than helium. The remaining two branches go through a step that creates beryllium.

The first PP branch takes hydrogen to deuterium (H2) to helium-3 (He3) to helium-4 (He4). In a chemistry-style notation with γ representing the gamma-ray and v representing the electron neutrino, the fusion chain is as follows:

H1 + H1


H2 + e+ + v

H2 + H1


He3 + Y

He3 + He3


He4 + 2 H1

The second and third branches of the PP chain involve the creation of beryllium-7 (Be7) and its subsequent destruction. The second branch splits from the first branch after the creation of helium-3. Helium-3 combines with helium-4 to create beryllium-7. Beryllium-7 combines with a free electron to give lithium-7 (Li7). Lithium-7 combines with hydrogen to give two helium-4 nuclei, returning the helium atom destroyed at the beginning of the offshoot.

He3 + He4


Be7 + Y

Be7 + e-


Li7 + v

Li7 + H1


He4 + He4

The third branch splits from the second branch after the creation of beryllium-7. In it, beryllium-7 combines with hydrogen to become boron-8 (B8). Boron-8 is unstable and decays into beryllium-8 (Be8), which rapidly decays into two hydrogen nuclei.

Be7 + H1


B8 + Y



Be8 + e+ + v



2 He4

Helium is present in substantial quantities at the birth of every star, so the initial composition of the star is never an impediment to the PP process proceeding along the second and third branches. As a star converts its hydrogen to helium, increasing the density of helium in the core, these branches becomes more common.

The core temperature determines which of these branches is dominant. The first PP process branch dominates in the production of helium for core temperatures below roughly 15 million degrees (1.3 keV), the second branch dominates between 15 and 25 million degrees (1.3 to 2.2 keV), and the third branch dominates above 25 million degrees.

The total energy released in converting four hydrogen nuclei into a single Helium nucleus is the same for each of the three branches, 26.7 MeV. Much of this energy, however, is carried by the neutrino, and because neutrinos interact weakly with other particles, most of them escape from a star's core without loss of energy. The fractions of the energy lost from the core through direct emission of neutrinos for the first, second, and third branches are 2%, 4%, and 28%. The third branch produces a substantial energy output in neutrinos, making it an import source of energy loss. Neutrinos from this branch were the focus of the first experiments that measured the sun's neutrino flux and found it to be lower than expected.

The Carbon, Nitrogen, Oxygen Process

The contamination of a star by metals gives rise to the CNO process, where hydrogen nuclei are converted into helium nuclei by combining with carbon, nitrogen, and oxygen, the C, N, and O of the process's acronym. The two branches of this process cycle through a sequence that converts the elements carbon, nitrogen, and oxygen into each other's isotopes. The first cycle starts and ends with carbon-12.

C12 + H1


N13 + Y



C13 + e+ + v

C13 + H1


N14 + Y

N14 + H1


O15 + Y



N15 + e+ + v

N15 + H1


C12 + He4

The second branch is a similar type of cycle, and it joins onto the first. Starting with nitrogen-14, the process steps through two of the last-three reactions given above until nitrogen-15 are produced. It then proceeds as follows to convert nitrogen-15 back into nitrogen-14, with the production of fluorine-17 (F17) occurring in one of the steps:

N15 + H1


O16 + Y

O16 + H1


F17 + Y



O17 + e+ + v

O17 + H1


N14 + He4

For abundances characteristic of the Sun, the CNO process becomes important for core temperatures of roughly 15 million degrees (1.3 keV), and it provides virtually all of the conversion of hydrogen into helium above 25 million degrees (2.2 keV). The fractions of the nuclear energy loss from the core through neutrino emission in the first and second branches of the CNO process are 6% and 4%.

Hydrogen Fusion in Main-Sequence Stars

The core temperature of a star rises with its mass, so the PP process is dominate at low masses, and the CNO process is dominate at high masses. For main-sequence stars with elemental abundances similar to the Sun, the conversion of hydrogen into helium is equal for the two processes when a star is about 2 solar masses. Below about 1.2 solar masses, the contribution to the energy production from the CNO process is insignificant; this means that the Sun is powered only by the PP process. Above about 3 solar masses, virtually all of the energy generated in a star comes from the CNO process.

The minimum mass of a star is about 0.075 solar masses. Below this mass, the core of a gravitationally-collapsing gas sphere never rises high enough for hydrogen fusion to begin. These objects are giant, cooling Jupiter´s that eventually get lost in space (another danger for Will Robinson). By the way, the planet Jupiter is 0.001 solar masses, so it is far below the nuclear fusion threshold.

Radioactive Decays


The three types of nuclear radioactive decay are alpha, beta and gamma emission.

  1. An alpha particle is a Helium 4 nucleus (two protons and two neutrons). It is produced by nuclear fission in which a massive nucleus breaks apart into two less-massive nuclei (one of them the alpha particle). This is a strong interaction process.
  2. A beta particle is an electron. It emerges from a weak decay process in which one of the neutrons inside an atom decays to produce a proton, the beta electron and an anti-electron-type neutrino. Some nuclei instead undergo beta plus decay, in which a proton decays to become a neutron plus a positron (anti-electron or beta-plus particle) and an electron-type neutrino.
  3. A gamma particle is a photon. It is produced as a step in a radioactive decay chain when a massive nucleus produced by fission relaxes from the excited state in which it first formed towards its lowest energy or ground-state configuration.

Stability and Instability in Nuclei

Why are some nuclei stable while others decay radioactively?

The answer lies in conservation of energy. A nucleus will decay if there is a set of particles with lower total mass that can be reached by any of the above types of decay process or simply by fission, a process in which a massive nucleus splits into two less massive ones.  Alpha decay is also a type of fission, common because the alpha particle is a particularly low energy arrangement of two protons and two neutrons.

The mass of a nucleus is determined by the sum of the energies of all its constituents. The energies of the constituents depend on their masses, their motion, and their interactions.

In chemistry we talk of the energy levels, or states of electrons, in an atom. Electrons fill energy levels because there is a rule of electron behavior (derivable from the quantum theory) known as the Pauli Exclusion Principle. This principle applies to all fermions. The principle states that only one electron can occupy any possible state in an atom. Each energy level has only a fixed number of states in it -- and can contain no more than that number of electrons.

Example -- Helium 4

Let us consider a Helium 4 nucleus. The two protons occupy the two lowest possible energy states for protons and the two neutrons occupy the two lowest energy states for neutrons. This fills the lowest energy levels for both types of particles.

Their interactions are such that the mass of this nucleus is less than the mass of a helium three nucleus plus a free neutron, so it cannot decay into that combination.

If one of the neutrons could beta decay it would produce a Lithium 4 nucleus (3 protons and one neutron) plus an electron and an anti-electron type neutrino. But the sum of these masses is greater than the Helium 4 mass so this decay is forbidden too.

But why is Lithium 4 more massive than Helium 4 even though a free neutron is more massive than a free proton?

The reason is that a third proton cannot be put into as low an energy state in the nucleus as occupied by the second neutron.  Just as for electrons in an atom, the lowest energy level in the nucleus has only two states for protons and two states for neutrons.

The pattern of stable nuclides thus consists of nuclei with roughly equal numbers of protons and neutrons (or a few extra neutrons because electrical repulsion between protons makes the energy levels for protons slightly higher than the equivalent levels for neutrons).  Nuclei with excess protons decay via beta-plus emission while nuclei with too many neutrons decay by beta-minus or electron emission.

Beta  decay and gamma decay  often occur as steps in a chain of radioactive decays that begins with the fission of some heavy element. The fragments which appear after this fission have the right number of neutrons and protons to be some nucleus, but they are not arranged in the right energy levels because they just split off in whatever arrangement they happened to find themselves in.  Secondary transitions in which a proton moves from a higher level to a lower one with emission of a photon are then common, as are beta-emission  transitions in which  either a proton or a neutron moves to lower energy level (and changes type). Only when all the fragments have settled down to their lowest mass (energy) forms does the decay chain end. Different steps in the chain may have very different half-lives.




0.164 second


2 minutes


60.5 minutes


15 hours


8 days


14.3 days


5.3 years


5,730 years


24,110 years


4.5 billion years




How nuclear reactors work

The basics

The principle behind generating electricity in a nuclear reactor is relatively simple.  Atoms in the nuclear fuel undergo a chain reaction, and these reactions generate heat.  The heat is used to turn water into steam. The steam turns turbines. When the turbines rotate, the power generators produce the electricity that is eventually fed into your home.  It's a process that´s very similar to generating electricity from burning fossil fuels. What makes nuclear power technically complex is the safety aspect.  The system must regulate the rate of the nuclear reaction and it must minimize the emission of radiation into the environment.

The reactor


To describe the reactor's set-up, Whitlock uses the analogy of a tin can that is set on its side and has its top and bottom punctured by hundreds of straws.  The tin can represents the calandria, the reactor's inner shell, and the straws represent the pressure tubes that the fuel bundles are loaded into.  The pressure tubes and fuel bundles are made of a zirconium alloy that is mechanically durable but allows neutrons from the fuel to pass through. 

The pressure tubes also carry coolant through the reactor.  The coolant transfers the heat away from the reactor to eventually generate steam.  In current reactors, heavy water is used as the coolant. 
Heavy water serves another purpose in the design. It's the moderator used to slow the neutrons down.  If the calandria is a tin can, the moderator sits in the can filling the spaces between the straws.  There are benefits to using heavy water instead of light water as the moderator in a nuclear reactor.

"The neutrons don't slow down quite as much (in heavy water), but the advantage is they will not be absorbed by the water," says Whitlock. "Light water is much better at slowing down neutrons, but it will also absorb half of them." 

Because fewer neutrons are absorbed by the moderator, a reactor can use fuel with a much lower percentage of the fissible isotope of uranium.

The whole reactor is enclosed in within thick concrete walls to prevent the release of radiation. 

The fuel bundles are put into the reactor by remotely-operated loading machines.  The efficiency of reactors is further increased by the fact that fuel bundles can be replaced while the reactor is still running.  The more time the reactor spends in operation, the more electricity is produced. So, not having to shut the reactor down to refuel is a big advantage.

The reaction

Heat is generated by capturing the energy released from the nuclear fission of an isotope of uranium, U-235.  However, the reaction doesn't occur spontaneously when the fuel is loaded into the reactor.  It needs another isotope to kick-start the process.

Nuclear fission: a neutron hits U-235 nucleus, which then splits into two smaller nuclei.

More neutrons and energy are released in the process.

"You find an isotope that will give off some neutrons.  Californium-252 is an isotope that will just emit neutrons, so you put some of this into a canister and you lower it into the core and things get going," said Whitlock.

Pressurized water nuclear reactors like the ones at Prairie Island use a three-loop water system to produce electricity and nuclear waste. mindfiesta
mindfiesta Heat in the reactor core comes from a chain-reaction of exploding uranium atoms. In the core, primary water is heated above 600 degrees Fahrenheit.
Hot primary water is pumped through steam generators, mindfiesta
mindfiesta Where heat is transferred to secondary water that flashes into steam.

Primary water returns to the core for reheating.

Very high pressure
keeps primary
water from boiling.


Q. What are the details on nuclear energy?

A. It is somewhat complicated and depends on facts about nuclear physics and nuclear engineering.

  • Nuclear power can come from the fission of uranium, plutonium or thorium or the fusion of hydrogen into helium. Today it is almost all uranium. The basic energy fact is that the fission of an atom of uranium produces 10 million times the energy produced by the combustion of an atom of carbon from coal.
  • Natural uranium is almost entirely a mixture of two isotopes, U-235 and U-238. U-235 can fission in a reactor, and U-238 can't to a significant extent. Natural uranium is 99.3 percent U-238 and 0.7 percent U-235.
  • Most nuclear power plants today use enriched uranium in which the concentration of U-235 is increased from 0.7 percent U-235 to (nowadays) about 4 to 5 percent U-235. This is done in an expensive separation plant of which there are several kinds. The U-238 "tails" are left over for eventual use in "breeder reactors". The Canadian CANDU reactors don't require enriched fuel, but since they use expensive heavy water instead of ordinary water, their energy cost is about the same.
  • In 1993 there were 109 licensed power reactors in the U.S. and about 400 in the world. They generated about 20 percent of the U.S. electricity. (There are also a large number of naval power reactors.) The expansion of nuclear power depends substantially on politics, and this politics has come out differently in different countries. Very likely, after some time, the countries whose policies turn out badly will copy the countries whose policies turn out well. There are only 104 operating reactors in 2007 and the percent of electricity that was nuclear was about 17.
  • In 2007 five applications were made to the Nuclear Regulatory Commission to construct and operate new nuclear power plants.
  • For how long will nuclear power be available? Present reactors that use only the U-235 in natural uranium are very likely good for some hundreds of years. Bernard Cohen has shown that with breeder reactors, we can have plenty of energy for some billions of year.

Cohen's argument is based on using uranium from sea water. Other people have pointed out that there is more energy in the uranium impurity in coal than could come from burning the coal. There is also plenty of uranium in granite. None of these sources is likely to be used in the next thousand years, because there is plenty of much more cheaply extracted uranium in conventional uranium ores.

  • A power reactor contains a core with a large number of fuel rods. Each rod is full of pellets of uranium oxide. An atom of U-235 fissions when it absorbs a neutron. The fission produces two fission fragments and other particles that fly off at high velocity. When they stop the kinetic energy is converted to heat - 10 million times as much heat as is produced by burning an atom of the carbon in coal. See the supplement for some interesting nuclear details.
  • Besides the fission fragments several neutrons are produced. Most of these neutrons are absorbed by something other than U-235, but in the steady-state operation of the reactor exactly one is absorbed by another U-235 atom causing another fission. The steam withdrawn and run through the turbines controls the power level of the reactor. Control rods that absorb neutrons can also be moved in and out to control the nuclear reaction. The power level that can be used is limited to avoid letting the fuel rods get too hot.
  • The heat from the fuel rods is absorbed by water which is used to generate steam to drive the turbines that generate the electricity.
  • A large plant generates about a million kilowatts of electricity - some more, some less.
  • After about two years, enough of the U-235 has been converted to fission products and the fission products have built up enough so that the fuel rods must be removed and replaced by new ones.
  • What to do with the spent fuel rods is what causes most of the fuss concerning nuclear power.

Q. What about the plutonium?

A. Besides fission products, spent fuel rods contain some plutonium produced by the U-238 in the reactor absorbing a neutron. This plutonium and leftover uranium can be separated in a reprocessing plant and used as reactor fuel. The Japanese had their spent fuel rods reprocessed in Europe and shipped the plutonium back home for use in reactors. This is what Greenpeace was fussing about.

Q. How much plutonium is produced?

A. In terms of nuclear fuel, about 1/4 as much as the U-235 that was in the fuel rods in the first place. Thus running a reactor for four years produces enough plutonium to run it for one more year provided the plutonium is extracted and put into new fuel rods. Newer designs with higher "burnup ratios" get more of their energy from plutonium.

Q. What if you don't reprocess?

A. You lose the economic benefit of the plutonium; the spent fuel remains radioactive longer and has to be better guarded, because it contains plutonium. However, there is plenty of uranium for now, so it may not be economic to reprocess at present provided the spent fuel remains available for later reprocessing.

Q. What about breeder reactors?

A. If the reactor design is much more economical of neutrons, enough U-238 can be converted to plutonium so that after a fuel cycle there is more fissionable material than there was in the original fuel rods in the reactor. Such a design is called a breeder reactor. Breeder reactors essentially use U-238 as fuel, and there is 140 times as much of it as there is U-235. The billion year estimates for fuel resources depend on breeder reactors. The French built two of them, the U.S. has a small one, the British built one, the Russians built one and the Japanese are building one.

Breeder reactors seem to be a resource rather than a reserve. They are more expensive than present reactors and maybe will wait for large scale deployment until uranium gets more expensive. This is unlikely to be soon, because large uranium reserves have been discovered in recent years.

Q. What about the Integral Fast Reactor (IFR)?

This was a breeder reactor with reprocessing on site, so no plutonium ever became externally available. It was hoped that it would address the proliferation concerns of the anti-nukes, i.e. it was hoped that they would be appeased. However, as soon as the Clinton Administration came to power, its anti-nukes got the IFR cancelled. Appeasement didn't work this time either. The IFR still has its enthusiasts, and maybe it will be revived.

Here's another page on the integral fast reactor..

Q. Can a nuclear plant blow up like a bomb?

A. No. A bomb converts a large part of its U-235 or plutonium into fission fragments in about 10^-8 seconds and then flies apart. This depends on the fact that a bomb is a very compact object, so the neutrons don't have far to go to hit another fissionable atom. A power plant is much too big to convert an important part of its fissionable material before it has generated enough heat to fly apart. This fact is based on the fundamental physics of how fast fission neutrons travel. Therefore, it doesn't depend on the particular design of the plant.

Q. Can a nuclear plant blow up to a lesser extent?

A. Yes, if it is sufficiently badly designed and operated. The Chernobyl plant reached 150 times its normal power level before its water turned to high pressure steam and blew the plant apart, thus extinguishing the nuclear reaction. This only took a few seconds.

Q. How much of a disaster was that?

A. In terms of immediate deaths it was a rather small disaster. 31 people died. Cave-ins in coal mines often kill hundreds.

However, about 20 square miles of land became uninhabitable for a long time. This isn't a lot.

Fall-out from the Chernobyl explosion will contribute an increase to the incidence of cancer all over Europe. How much of an increase is disputed. Since the increase will be very small in proportion to the amount of cancer, we probably won't know from experience.

The largest estimates are in the low thousands which would make Chernobyl a disaster comparable to the Bhopal chemical plant or the Texas City explosion of a shipload of ammonium nitrate or the Halifax disaster during World War I. On the other hand these large estimates are small compared to the numbers who have died in each of several recent large earthquakes in countries using stone or adobe or sod houses.

It is comparable to the number killed in coal mining accidents in the Soviet Union over the years Chernobyl was operating.

The large estimates depend on the linear hypothesis which is almost certainly wrong but which is used for regulatory purposes because it is so conservative. The estimates are probably too high by a substantial factor, maybe 10, maybe 100.

However, a recent survey indicates a greatly increased rate of thyroid cancer in children (including three deaths)j in Belarus since the accident. I don't know the total number of cases which would permit comparing Chernobyl with other accidents. Here is more on the Chernobyl accident including links to British, Ukrainian and Russian accounts of the accident and its effects.

Q. Are nuclear power plants perfectly safe?

A. No. Nothing is perfectly safe, but they are safe enough to be relied upon as a source of energy.

Q. What about nuclear waste?

A. The waste consists of the fission products. They are highly radioactive at first, but the most radioactive isotopes decay the fastest. (That's what being most radioactive amounts to). About one cubic meter of waste per year is generated by a power plant. It needs to be kept away from people. After 10 years, the fission products are 1,000 times less radioactive, and after 500 years, the fission products will be less radioactive than the uranium ore they are originally derived from. The cubic meter estimate assumes reprocessing, unfortunately not being done in the U.S.

Q. What about diversion of material from power plants to countries wanting to make bombs?

A. Every country wanting to make bombs has succeeded as far as is known. None have used material produced in power reactors. (Plutonium produced in RBMK reactors may have been used in Soviet weapons. The RBMK was designed as a dual-purpose reactor suitable both for power production and bomb production. For this it was necessary to be able to replace fuel rods while the reactor was operating, and this made the reactor too big for a containment structure, and this is what allowed the radioactivity to spread.)

If the fuel rods are kept in the reactor for the two years or so required for economical power generation, much of the Pu-239 atoms produced absorb another neutron and become Pu-240. It is more expensive to separate the Pu-240 from the Pu-239 than to get Pu-239 from a special purpose reactor in which the fuel rods are removed after a short time. The Pu-240 makes the bomb fizzle if there is very much of it. For more details see the article by Myers.

It seems that some of the Russian PU-239 of which samples were sold in Germany was pure enough so that some isotope separation process was probably used after the plutonium was extracted from the fuel rods.

Q. Are the reserves of uranium adequate for the long term?

A. In the very long term, breeder reactors will be used. These get about 100 times as much energy from a kilogram of uranium as do present reactors. This makes the present stock of uranium go much farther. Indeed all the enriched uranium used in nuclear reactors and all the U-235 used in nuclear weapons have been separated from U-238, and the leftover U-238 is still available. If this U-238 were used to generate energy in breeder reactors and the electricity were sold at present prices, the present American stock of depleted uranium would generate $20 trillion worth of electricity. [Doubtless this number has changed one way or the other since the above was first written. I haven't time to keep updating it.]

Q. What about power from nuclear fusion.

A. Since the 1930s it has been understood that the sun gets its energy by combining hydrogen atoms to get helium. It was immediately apparent that if we could use these nuclear reactions we would have energy for billions of years. At first the problems of getting this energy on earth seemed insuperable, because of the millions of degrees of temperature required to get hydrogen atoms to combine.

In the 1950s it was discovered how to do this in hydrogen bombs by using ordinary nuclear fission bombs to set off the fusion of the hydrogen isotopes of deuterium and tritium. Projects were promptly started for doing this under less violent conditions. After 50 years, fusion reactors may be close to getting more fusion energy out of the reaction that has to be put in. Present proposals use deuterium and lithium-6, as do present hydrogen bombs. The Princeton Plasma Physics Laboratory has an FAQ about magnetic and inertial fusion. The US Department of Energy has a Fusion energy research site, and there is also a UK fusion energy site.

None of the projects is close to designing a plant.

Fusion power has the following possible advantages if it can be made to work.

  • The fuel supply is potentially larger. However, the uranium supply seems to be large enough.
  • Fission products are not produced, although there will be induced radioactivity in the structures of the plants.
  • No material useful for bombs is produced.

Q. Are we ever likely to have nuclear powered cars?

Alas, no, if present nuclear physics is all there is to say about the possibility. A nuclear reactor engine that would provide the right amount of energy for a car could be built and would run fine and would require refueling only every 5 or 10 years. The only problem is that it would kill the driver, the passengers, and perhaps bystanders. Nuclear reactors, as described above, produce neutrons, which are very penetrating particles and give people radiation sickness if the exposure is substantial. (All our bodies are penetrated all the time by small numbers of neutrons.) Power reactors have several feet of concrete shielding between the active part of the reactor and the operators. A big enough vehicle like an aircraft carrier or a big submarine can afford the shielding. In the 1950s some thought that nuclear aircraft were feasible. Maybe they were, but the projects were abandoned.

Q. What are the arguments against nuclear energy?

A. There are many arguments, some related specifically to nuclear energy and others stemming from more general ideas about society. I have labeled the unrelated arguments and made a few comments to be answered more fully later.

  • The problem of disposal of nuclear wastes hasn't been solved. There are several good technical solutions, but the political problem hasn't been solved in the U.S. [2003: Now the political problem has been solved, but lawsuits will be filed and may hold up the solution for a while. 2010 is now predicted as the time when waste will start being stored in Nevada.]
  • Nuclear energy is uneconomical compared to other sources of energy. It is doing ok.
  • The energy required to build nuclear plants, operate them, and mine and process the uranium may be so large as to cause a net energy deficit. Here's a thorough Energy Analysis of Power Systems including nuclear energy and its competitors. The basic fact about nuclear energy is that the input energy is 4.8 percent of output energy if gaseous diffusion is used to enrich uranium and 1.7 percent if the newer centrifuge technology is used. Another way of looking at the same facts is that if gaseous diffusion is used for enrichment, the energy invested in building the plant is paid back in 5 months, whereas if centrifuges are used the payback time is 4 months.
  • It is bad for humanity to have plenty of energy. - Unrelated.
  • Nuclear reactors produce plutonium, and plutonium is terrible because it can be used to make bombs. Safeguards are indeed needed.
    • Plutonium is the most poisonous substance known. No it isn't.
    • Plutonium symbolizes nuclear war. — Unrelated.
  • Nuclear reactors are likely to have accidents with severe consequences for humanity. See above.
  • Radiation from operating nuclear reactors and other activities involved in nuclear energy is dangerous.
  • Energy should be generated locally, even by individual households, rather than by centralized power stations. —unrelated
  • The risk to an individual of harm from a nuclear accident is an involuntary risk, as compared to the much larger risk from driving a car, which is voluntary.

This comparison ignores much larger involuntary risks, e.g. the risk of emphysema from coal burning, the risk of an airplane hitting your house, and the risk of a flood when a dam breaks. Each of these risks is larger and comes from a human activity. There are other large risks, such as that of a flu epidemic, which are only partly caused by human activities - such as allowing international travel or having pre-schools where children transmit infections to each other.

The decision to incur such involuntary risks is a collective decision, made in accordance with laws.

Here are some answers to all the arguments listed (even the ones I have labeled unrelated) and any more that people suggest. Some will be answered by reference to the literature.

Q. Is the use of nuclear absolutely essential to the sustainability of progress?

A. Probably not. Solar energy would also work, but at considerably greater cost if relied upon for most of the world's energy.

Q. Then what about giving up on nuclear energy because of the danger of nuclear war?

A. Giving up on nuclear energy is unlikely to reduce the danger of nuclear wars. In fact it is likely to increase the danger, because of the advantage it would give to whoever would first reintroduce nuclear weapons. Also the poorer world that would result from the abandonment of nuclear energy would be more likely to have wars.

Q. What if all energy generated were nuclear?

A. A preliminary page discusses this eventuality. When I get a chance to look up more relevant facts, it will be improved.

Q. Is the opposition to nuclear power strong enough to prevent its use?

A. Not when and if refusing to build nuclear plants results in a substantial loss of a country's standard of living. Politicians seem to believe that mentioning nuclear energy is political poison at present. They may be right or it may be just one more superstition prevalent among politicians and their consultants. Recently a taboo against mentioning nuclear energy has developed among scientists - especially those specializing in energy. None of the articles in the recent special issue of Science devoted to energy mentioned nuclear energy - pro or con - even though nuclear energy provides 17 percent of American electricity. Perhaps energy scientists feel that mentioning nuclear energy will have an adverse effect on their grants. Perhaps there is some other reason. To some extent "hydrogen" in the energy literature is a code word for nuclear energy, since many articles promoting hydrogen don't say how else it can be generated economically in the quantities required to run an economy. Recent waves of ideology are strongly involved.

Q. Is nuclear energy sustainable?

A. Yes. In the short term, probably the next hundred years, there is so much uranium that no-one can profitably prospect for more. In the medium term breeder reactors will extend the energy obtained per kilogram of uranium by a factor of about 100. In the very long term, Bernard Cohen has shown that plenty of uranium can be extracted from seawater for a few billion years. I suppose extraction of uranium from low grade ores is likely to be better than extracting it from seawater, but Cohen's seawater argument provides a strong proof that uranium will remain available in the very long term. Here's Cohen's own web page.


- Editorial Team,
Evolution of Life SWINE FLU