Nuclear Processes and Energy Changes by Steve Marsden

Chemical reactions involve outer or valence electrons. Atoms rearrange, bonds are broken and formed, energy is exchanged with the surroundings, and new substances result. But the constituent atoms remain the same. This is characteristic of the behavior we call "chemical".

There is another category of processes that involve the atom that differs fundamentally from chemical behavior. In it, atoms become different atoms, often being broken apart into smaller pieces. Sub-atomic particles are ejected as massive amounts of energy are released to the surroundings. Mass "disappears". These describe just some of the characteristics of behaviors that are nuclear in nature, involving the inner part of the atom (the nucleus) instead of the outer electrons. [nucleus] [Nuclear Reactions]

Because the nucleus is involved in these changes it is important to distinguish among different isotopes of an element that will not have the same behaviors. [isotopes] [isotopic symbols]

Although the proton and neutron on the atomic mass scale have masses of "1", their exact masses differ a little and the sum of the individual masses of particles in an atom is greater than the measured mass of the assembled atom. For those reasons, the atomic masses found on the periodic table that indicate average isotopic mass adjusted for abundance in nature cannot be determined with simple integer sums of the protons and neutrons in a nucleus. [average atomic mass]

This "missing" mass is one of the first puzzles we encounter when we try to understand nuclear processes. Understanding its significance sheds some light on the whole question of why there is radioactivity in the first place, i.e., why are some nuclei unstable?

On the simplest level, a nucleus is unstable if the repulsive forces in the nucleus are greater than the attractive forces in the nucleus. The nature of both of these forces is different. The strong nuclear force exists between all nucleons. But this force only acts at very small distances. The weaker electrostatic force exists among the protons with their like charges.

For a partial look into the strong nuclear force we can examine how much energy is needed to break apart a nucleus. [Nuclear Binding Energy]

The binding energy is not only the energy needed to break apart an existing nucleus into separate nucleons, it is also the energy which is released when a nucleus is formed from separate nucleons. This is the result of the mass which "disappears", generally called the mass defect (Dm). Inserted into Einstein's mass-energy equation, the mass defect gives the binding energy of the nucleus.

Comparing the binding energy per nucleon for known isotopes reveals a steep increase in stability in the light elements (He-4 is exceptionally high) until Fe-56. Then there is a gradual decline in binding energy as nuclei become heavier. [Binding energy trend]

To an extent, the conclusions drawn from a comparison of binding energies contradict ordinary experience. Uranium--which has no non-radioactive isotopes at all--has a relatively high binding energy. Why does it fall apart?

Because there are still many unknowns in a likely structure of the nucleus, this question cannot be completely answered. There are some clues: elements with an even number of protons tend to have more stable isotopes AND by far the majority of stable nuclides have both even numbers of neutrons and protons. [odds of stability]

One model of nuclear structure suggests that protons and neutrons exist in "nucleon shells" or energy levels. In this model pairing like nucleons gives added stability. The model suggests "magic numbers" (analogous to the noble gas electron totals) which are equivalent to filled nucleon energy levels: N or Z = 2, 8, 20, 28, 50, 82 (and N = 126).

Isotopes of elements which are either not found on this planet or else are extremely rare and short-lived seem to support this model: Tc-98 (odd/odd), At-210 (odd/odd), Fr-223 (odd/odd), Pm-145 (odd/even), Po-209 (even/odd). Other extremely stable nuclides have double magic numbers: He-4, O-16, Ca-40, Pb-208.

The recent synthesis of elements 114, 116, and 118 appears to lend validity to another model of nuclear stability which suggests that the magic numbers are arranged over a mappable "seascape" which includes narrow islands of special stability. If this model is correct in at least some of its aspects, still heavier nucleons could well turn out to have ordinary stability (i.e., be non-radioactive).

When a nucleus is unstable it either splits apart spontaneously into fragments or else ejects small particles. The end result of this "decay" is either a more stable nucleus or a completely stable (non-radioactive) nucleus. [Atomic Decay]

The emission of the small particles and any energy that accompanies them is called radioactivity. The phenomenon was first described by the French scientist Henri Becquerel and the general characteristics of the small particles given off during decay were determined through experiment by Rutherford. [What is it that Comes out of Radioactive Materials?]

Radiation Units: Apart from the normal measures of mass and volume, the amount of radioactive material is given in becquerel (Bq), a measure that enables us to compare the typical radioactivity of some natural and other materials. A becquerel is one atomic decay per second *.

* A former unit of (radio) activity is the Curie - 1 Bq is 27 x 10^-12 curies.

The common pathways for nuclear decay include the following:

type of decay	alpha	beta	positron	electron capture	gamma
particle involved					none
symbol

In all of these processes--except gamma--elements are transformed into other elements and a significant amount of energy is released. The source of the energy is the small mass loss, Dm, which must occur for any spontaneous nuclear process.

Alpha decay or alpha particle emission is the release of a small particle, generally from a heavy nucleus. The particle consists of 2 neutrons and 2 protons but no electrons. This gives it the same nuclear structure as a helium-4 ion with a charge of +2. Alpha emission is an efficient way for a nucleus to shed excess mass quickly but it alters the neutron : proton ratio only very gradually. The effect of alpha emission is to move the element two spaces back on the periodic table with a mass loss of 4. [Cloud/Bubble Chambers]

Beta decay or beta particle emission is the release of an electron from the nucleus. Of course we do not expect electrons to be in the nucleus! By observing the effect of beta decay on a nuclide we can infer the mechanism behind it. Every time a beta particle is ejected the element advances one space on the periodic table with no change in mass. The conversion of a neutron into a proton would accomplish this:

This proposed mechanism is supported by the relatively short lifetime of a neutron when knocked out of the nucleus. It rapidly breaks up into a proton, an electron and a smaller high energy particle. Beta decay is therefore a good way to reduce the neutron: proton ratio in a nucleus. [Neutrinos ]

Gamma radiation is electromagnetic radiation of very short wavelengths (shorter than x-rays). The short wavelengths mean high energy and gamma rays tend to pass right through most solid objects. Since there is no particle associated with gamma radiation there is no identity change in the nuclide undergoing gamma decay. Gamma decay is a mechanism for ridding the nucleus of excess energy and generally accompanies other types of decay. It is not, however, random. The wavelengths of gamma rays emitted during various decays are predictable and spectroscopic methods are based on their detection.

Electron capture decay does not result in the emission of a particle. Instead, an electron from the inner energy level is drawn into the nucleus. The vacancy created by this event initiates a cascade of electrons dropping from higher energy levels and is accompanied by the release of electromagnetic energy, typically x-rays or gamma rays. The result of electron capture is an element with one less proton and one additional neutron so this appears to be the mechanism:

Positron decay or positron emission has the same net effect on a nucleus as electron capture: the element moves back one space on the periodic table without a mass change. But in this case a particle is ejected from the nucleus. And an odd particle it is!

A positron is a piece of science fiction come true: antimatter. It is the antiparticle of the electron, with an equal mass but opposite charge. When electrons and positrons meet they annihilate one another with a burst of energy. As exciting as that sounds it makes for a very edgy natural world and so it is not surprising that positrons are quite rare. Positron emission is only observed in some artificially created nuclides. Because of the net result of positron decay this is thought to be the mechanism:

With so many options to choose from, is it possible to predict what kind of decay will occur for a given nucleus? Yes and no. Comparing the mass number of a nucleus with the average mass given on the periodic table (or the known mass of a stable isotope) gives some information based on the mechanisms already mentioned. The heaviest stable nuclide has a mass of 209. Nuclides with more mass than this tend to decay by alpha particle emission in order to shed excess mass quickly.

If a nucleus has a mass less than 209 but "too many" neutrons compared to the average atomic mass or a known stable isotope, it is likely to decay by beta emission since that process converts neutrons into protons. An isotope with "too few" neutrons is likely to decay by either positron emission or electron capture since these decays convert protons into neutrons.

The "goal" of any of these decay processes is to create a nucleus which is more stable--eventually non-radioactive. Sometimes this cannot be achieved in a single step. There are several decay processes in the natural world involving the slow transformation of very heavy elements like uranium and thorium into stable isotopes of metals like lead. These gradual transformations are in large measure responsible for what we call "background radiation". [Decay Series]

Radioactivity can be detected in a variety of ways. Becquerel accidentally found that photographic film could be exposed by it (as Roentgen before him had found with x-rays). The most common instrument for measuring radiation is the geiger counter, invented by Hans Geiger, who worked with Rutherford on the alpha particle scattering experiment that led to the nuclear model of the atom. [Geiger counter] [Rutherford’s further studies]

The biological effects of radiation are feared by just about everyone, and with some justification. The principal potential damaging effects of radiation exposure run the gamut from cellular disruption to the destruction or altering of genetic material in cells. [Estimate Your Annual Radiation Dose ]

Alpha particles are generally the least penetrating type of radiation due to their size and charge. They are typically deflected by skin but may be absorbed into the very top layers if they have sufficient energy. It is possible for them to break some molecules into fragments if they collide with them but their general damaging effect is to ionize molecules by stealing electrons from them to become neutral helium atoms.

Decay Rates

When an unstable nucleus "decays" it does so with a particular rate that is characteristic of that nucleus and the amount of sample present. That fact that the rate depends on the amount of sample present means that it is following first order kinetics. We can represent the rate in equation form as:

rate = k N where the rate is measured at a given time, t, k is the rate constant for that particular isotope, and N is the amount of sample present (or some quantity proportional to the amount of sample). As with any chemical rate, these rates change over time as less reactant remains. There is an alternative way to represent the rate of a reaction which takes this into account (and resorts to calculus to do it):

This is known as the integrated rate law equation. N_o is the original amount of sample while N is the amount remaining at time t. This equation allows us to determine the decay rate of a sample at any given time AND to predict how much of a given sample will remain at any given time. It also shows that the rate behavior is logarithmic in nature. [Decay Rate] [Examples]

Nuclear scientists often refer to the decay rate in terms of a quantity called half-life. This is simply the time it takes for half of a sample to decay into something else. The half-life can be related to the rate constant using the integrated rate law and recognizing that the ratio N_o/N will be 2/1 when t is the half-life:

The rates of radioactive decay vary a lot. Some are expressed in milliseconds while others, like that of U-238, run into the billions of years. How can the half-life of such a long-lived isotope be determined?

Clearly no one can wait around for half of a sample of U-238 to decay. And the changes in a sample even within a human lifetime would be difficult to measure. Fortunately it is not necessary to do so. Because the rate of decay is proportional to the amount of sample, a geiger counter (or more sensitive detector) and the rate equation can be used to determine the half-life of an isotope. [Half Life]

A more typical use of the rate equation is to determine the amount of sample that might remain at a given time or to estimate how long it will take a sample to decay to a certain amount. [Nuclear Decay Rate Example – click for solutions]

The presence of long-lived radioactive materials in the natural world also offers the opportunity to determine the approximate ages of geologic formations, glacial ice, archaeological artifacts, and so on.

Inorganic materials in the natural environment often contain small amounts parent/daughter isotope pairs. Some isotope pairs which have proven useful in geologic dating are shown below. [Dating]

parent	daughter	half-life
U-238	Pb-206	4.5 x 10⁹ yr
K-40	Ar-40	1.28 x 10⁹ yr
Rb-87	Sr-87	4.9 x 10¹¹ yr

For organic material or artifacts composed of organic material, a different parent/daughter pair is used. Organic materials are based on hydrocarbon compounds. In 1955 a scientist at Caltech, W. F. Libby, proposed that dating of such material could be done by measuring the ratio of C-12, the most abundant isotope of carbon, to C-14, a radioactive isotope of carbon with a half-life of about 5300 yrs.

Carbon-14 occurs in nature but not in the same way as carbon-12. The supply of carbon-14 is the result of nuclear reactions in the upper atmosphere. In the stream of particles and EMR that constantly bombard the planet, neutrons occasionally collide with nitrogen atoms:

The carbon-14 formed by this mechanism gradually becomes incorporated into atmospheric carbon dioxide. The CO₂ is taken up by plants during photosynthesis and animals eat the plants for food. Some animals also eat other animals for food. In the long run, according to Libby, living organisms develop a "steady state" concentration of C-14 in them. Measurements of the ratio of C-14/C-12 place it at 1 in 10¹² atoms. So there's not very much.

Once an organism dies, its carbon cycle with the environment stops. As the carbon-14 slowly decays (by beta emission) it is not replaced. Thus the 1/10¹² ratio gradually decreases. By carefully measuring the current ratio in a sample and comparing it to the "steady-state" ratio in a living organism scientists can estimate when the organism died. For plant material used in artifacts, such as cloth or canvas, this gives an approximate "age". [Nuclear Decay Rate Example]

The accuracy of carbon-14 dating depends on a variety of factors. Obtaining a good sample is one. Artifacts are easily contaminated with "current" carbon from the environment. Several samples need to be examined. The method also relies on the assumption that the rate of cosmic ray bombardment has not varied much over the useful range of C-14 dating. [Shroud of Turin Dating]

This used to be a major bone of contention among critics of the process. Studies of tree growth-rings have revealed uneven cosmic ray bombardments during some periods of the time frame accessible to C-14 dating (about 24,000 years). This is now taken into account in current work.

Fission

In addition to the spontaneous decay of radioactive materials by emission of
sub-atomic particles and energy, there is another way for unstable atoms to achieve nuclear structures which are stable.

A few elements undergo a process known as fission. One nucleus splits into two smaller nuclei and typically a few neutrons. Energy is also released based on the mass loss during the transformation.

U-235 is the only naturally occurring nuclide that fissions. [U-235 fission clip]

However, both U-238 and Th-232 can be converted by neutron capture and subsequent beta decay into fissile isotopes: Pu-239 and U-233.

A great deal of data exists on the fission of U-235 due to research during World War II and also because of later nuclear power research. Perhaps the most impressive datum of all is the amount of energy that can be released when U-235 fissions.

One gram of U-235 can release enough energy during fission to raise the temperature of 66 million gallons of water from 25^oC to 100^oC! By contrast, to accomplish the same sort of feat by burning pure octane would require 1.65 million gallons of the fuel. [Characteristics/Facts about Fission]

Obtaining such quantities of energy from fission depends on sustaining the splitting of atoms, not a one-time event. The neutrons, which are a by-product of the fission process, are important in this respect. At least one neutron per fission event must remain within the sample and initiate another fission event in order for the rate of fission to grow. The sample size and geometry needed for this is known as the critical mass.

In sub-critical masses the capture ratio for neutrons is less than 1 per fission event and the rate of the process does not grow. Energy output is low. With a critical mass a chain reaction begins which rapidly reaches explosive proportions. [Critical Mass Interactive Animation]

An understanding of these principles and their manipulation is the basis for the design of both weapons and power plants. [Research problems]

Nuclear power reactors are designed to use the controlled fission of enriched uranium to heat water which will produce steam. The steam is used to turn turbines just as it would be in a coal- or gas-fired power plant. The turbines are attached to generators which produce electricity. [What Does a Nuclear Reactor Actually Do? ] [Nuclear Reactor Poster]

The fuel core of a power plant contains more than a critical mass of 3% enriched U-235. Moderator or control rods containing cadmium (which absorb neutrons) are inserted among the fuel rods until the neutron capture ratio is 1. In U.S. commercial power plants ordinary water is also used as a moderator and heat exchanger. Slowing neutrons down means that a smaller critical mass is needed.

In some Canadian reactors heavy water (²H₂O or D₂O) is used as a moderator. Heavy water is not as good a moderator but the reactors run on unenriched uranium. An advantage of this design is that no manufacturing process takes place which could produce weapons-grade material. However, the cost of heavy water is high. [WWII and Heavy Water]

Because the usual enriched U-235 fuel contains a large portion of U-238, a side reaction takes place during fission. Slow neutrons may be captured by the non-fissile U-238. [Making Pu-239]

Pu-239 is fissionable. It is also highly radioactive and a potent biological toxin. Current U.S. law forbids reprocessing of plutonium wastes and up until the end of the Cold War the government stockpiled Pu-239, produced at special facilities such as Hanford in the state of Washington, for use in weapons (the critical mass of Pu-239 is smaller than for U-235).

It is possible to actually design fission reactors to efficiently "breed" Pu-239 fuel while "burning" U-235. Such reactors in essence create nuclear fuel as they consume it. Although a number of experimental breeder reactors were built in this country they were plagued by problems, not the least of which were concerns regarding the safety of using highly toxic plutonium in commercial settings. Currently breeder technology is not in use in the United States. There are a few operating commercial breeder power reactors abroad.

Transmutation and Fusion

Most of the elements present on this planet have few or no naturally occurring unstable isotopes, except for the very long-lived ones like uranium and thorium isotopes and an interesting pair of isotopes which illustrate how elements may be transformed into other elements by "building up" rather than decay processes.

Carbon-14 and Hydrogen-3 (tritium) are both formed in the upper atmosphere as a result of collisions with neutrons from solar radiation which reaches the earth:

In general neutrons make good projectiles for penetrating the electron cloud and entering the nucleus because there are no electrostatic repulsive forces to deal with. Unfortunately those properties also make them difficult to accelerate and direct.

The first evidence for transmutation of elements came from Rutherford's observation that some alpha particles released by the decay of radium interacted with the nitrogen in the air to produce O-17:

Further evidence of transmutation led to the discovery of the neutron in 1932 by James Chadwick after observers noted that when some light elements were bombarded with alpha particles they emitted highly penetrating, neutral particles.

In 1933 the first artificial radioisotope was created by Irene Curie and her husband Frederic Joliot by bombarding aluminum foil with alpha particles:

The basic principles upon which the creation of the transuranium elements (and the few "missing" elements such as Tc and Pm) are contained in this early work: choose a target material close to the atomic number you want and select and appropriate projectile. The projectile is accelerated and allowed to bombard the target.

Accelerators are designed to move charged particles at faster and faster speeds until they are directed toward a target for impact and (hopefully) reaction. There are three basic types of accelerators: linear, circular [cyclotrons] and the synchrotron. [Accelerator]

The linear accelerator is the type at Stanford University. The voltage of each tubular section is alternated so that the charged particle is repelled from the section it is leaving and attracted to the section it is entering. [linear accelerator]

The cylcotron was invented by Lawrence (element 103 is named after him) in 1930 and operates on the same principles as the linear accelerator but includes electromagnets to force the charged particles to follow a curved path. This saves space.

The synchrotron is similar but uses a varying magnetic field to make the particles travel in a circle rather than a spiral. The particles can be "spun out" to the target when they reach sufficient speeds by changing the magnetic field.

Often the bombardment is repeated over and over for days or weeks. [Making elements]

The transmutation of elements mimics a natural process by which all of the elements are "built up": fusion. Fusion is the opposite of fission. The process is ongoing in all stars. In the early stages of stellar fusion hydrogen and helium isotopes are the typical reactants. But as a star ages and the amounts of hydrogen and helium are depleted fusion of heavier nuclei such as lithium and carbon (and eventually even heavier ones) may occur.

·         the activation energy is extremely high [Too hot]
·         the products are most often stable [Stable He]
·         the energy yield per gram of fuel is greater for hydrogen/helium fusion [Fusion Yields]

If not for the first of these, fusion would seem to be an attractive process for meeting energy needs. The fuel is abundant (based on the water available on the earth and its deuterium content the estimate is 5 x 10¹⁵ tonnes of H-2) and the "waste" generated is certainly less than for comparable fission processes.

We are able to produce fusion reactions but not in a form that is of much use: hydrogen bombs. In these thermonuclear weapons the activation energy for the fusion reaction is supplied by a fission reaction! Clearly such technology is not going to run anyone's toaster any time soon.

There are competing experimental fusion reactor designs but so far results have been disappointing.

One basic design for a fusion reactor is known as the tokamak. In this reactor atoms are stripped of their electrons at very high temperatures to form plasma. This is too hot for any container so a helical magnetic field is used to confine the plasma and keep it away from the walls of the reactor. Some success has been obtained with this design, but generally no more energy out than in and reactions are not self-sustaining.

Another approach involves targeting a fuel pellet with many high powered laser beams from all sides. Like the tokamak approach, this design uses an incredible amount of energy on a tiny amount of fuel and so far the yields have been very disappointing. [Reactor Design]

The extremely high energy input required to overcome the electrostatic repulsive forces of the nuclei, containment problems and difficulties making the reaction self-sustaining have proven to be formidable challenges. Funding for research is, as always, another serious problem.