9.8.D - Artificial Transmutations

In nuclear physics, nuclear fission is the most common type of artificial transmutation and is either a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei), often producing free neutrons and photons (in the form of gamma rays) and releasing a very large amount of energy. The two nuclei produced are most often of comparable but slightly different sizes, typically with a mass ratio of products of about 3 to 2, for common fissile isotopes. Fission as encountered in the modern world is usually a deliberately-produced manmade nuclear reaction induced by a neutron.

Nuclear fusion reactions typically occur inparticle accelerators where charged nuclei are accelerated to high speeds over long distances in order to overcome the repulsive force of the postively charged protons in the nucleus. Particle accelerators are used to study matter as well as to synthesise elements that do not occur naturally. Uranium is the naturally occuring element with the highest atomic number (92) and all elements above it have been synthesised.

In this unit you will:

  • Explain how the neutron was discovered using conservation laws
  • Outline how neutrons are used to probe matter
  • Describe artificially induced fission processes and write nuclear equations
  • Explain the function of the main components of a thermal fission reactor
  • Explain how particle accelerators are used in fusion and how they can be used to study matter
  • Analyse nuclear processes in terms of mass defect and binding energy

Discovery of the Neutron

The apparatus used by the Jolliot's whose results Chadwick
interpreted to account for the neutron.

In 1920, Rutherford guessed that there had to be a new kind of particle in the nucleus, about as heavy as a proton but with no electric charge, which he called the neutron. Others thought that whatever it was in the nucleus might be high energy gamma ray photons. In 1932, Frederic & Irene Joliot (Irene was the daughter of Marie Curie) fired alpha particles (helium nuclei) at beryllium and it was seen that the beryllium ejected something from the nucleus that caused paraffin to release protons. Whatever it was could pass through thick sheets of lead, but they were stopped by water or paraffin wax. Since large numbers of very energetic protons were emitted from the paraffin when it absorbed whatever was coming out of the nucleus, they assumed that whatever was being ejected from the beryllium nuclei must be an extremely energetic form of gamma radiation. Chadwick, however, disagreed.

Chadwick showed that whatever was ejected from the beryllium nuclei could not be radiation because it did not have sufficient energy to then eject protons from paraffin wax. Whatever it was that could knock protons out of other atoms had to be a fairly heavy particle, not a massless particle such as gamma radiation. Using the velocity of the ejected protons and the laws of conservation of energy and momentum, Chadwick calculated the mass of the unknown particle. It was just a little heavier than the proton. He had no doubt that this was Rutherford's neutron.

Chadwick explained the process occurring in the experiment as:

Chadwick explained that when the neutrons emitted from the beryllium collided with the light hydrogen nuclei in the paraffin, the neutron came to a sudden stop and the hydrogen nucleus (proton) moved off with the same momentum as the neutron had before the collision.

Neutron Scattering Experiments

Neutrons are produced in nuclear reactors when a large nucleus breaks apart and forms two smaller nuclei. We will learn more about this later but the discovery of the neturon opened up new possibilities for all sorts of research applications. Neutrons are ideal for probing the inner structure of matter because of the following properties:

  • They are neutral and can therefore penetrate deeply into matter.

  • The de Broglie wavelength of neutrons is comparable to the spacing of the atoms in an atomic lattice. Neutron diffraction experiments can determine the interatomic spacing in some materials in much the same way as the Braggs did with X-rays.

  • The energy of thermal neutrons is similar to the energies of the lattice vibrations in solids.

  • They scatter well from protons, making them useful in determining the structure of solids containing hydrogen bonds (eg organic molecules).

Neutrons are directed from a reactor core onto a sample of material. The neutrons collide with atomic nuclei and scatter in directions determined by the neutron's wavelength and the structure of the material under study. From the diffraction patterns obtained, physicists can deduce the internal structure of the material.



Fermi was the first physicist to
produce a controlled nuclear fission

After the discovery of the neutron which was large and uncharged, Enrico Fermi tried to extend the number of known elements through transmutation. In 1934 he bombarded uranium-235 with neutrons expecting that the uranium would take up the neutron and then it would undergo beta decay to produce an isotope of neptunium as shown in the equation below.

Two lighter nuclei were actually produced as fission products in an artificial transmutation as shown in the equation below.

Fermi has actually succeeded in producing the first artificial transmutation using nuclear fission - when heavier nuclei are split into two or more lighter nuclei.

Large nuclei are unstable because protons at the surface of the nucleus are repelled by a force proportional to the total number of protons in the nucleus, but attracted towards the interior by a force proportional to the number of nucleons in its immediate vicinity (which is constant for light or heavy nuclei). Thus the electrical repulsion sets a maximum limit to the number of protons in a nucleus. The maximum limit to the number of neutrons is set by the strong nuclear force that seeks to bind pairs of neutrons to pairs of protons. Thus if the neutron excess becomes too large, a neutron spontaneously changes into a proton.

Since very heavy nuclei have too many of both neutrons and protons, they spontaneously emit tightly bound nuclear sub assemblies. This is naturally occurring fission or transmutation.

In the fission process, the target nucleus is hit by a neutron
that causes the ejection of more neutrons and the fission
of the nucleus into two fission fragments.

Fission or transmutation may be artificially triggered by bombardment with neutrons. Heavy nuclei break up under such bombardment into a pair of lighter nuclei with the release of energy far exceeding the total kinetic energy of the colliding particles. This excess energy is due to the reduction of nuclear mass. Furthermore, as the nucleus breaks the fragments fly apart under electrical repulsion and heat up the environment by collisions with neighbouring particles. The fragments are also in a highly excited state and its nucleons rearrange into configurations appropriate to medium weight nuclei by release of gamma radiation. As these medium weight nuclei would have smaller neutron proton ratios, some neutrons convert to protons by beta emission.

As stated, some nuclei can be made unstable by firing an extra neutron into them. This is called a fission reaction because the nuclei split into two fragments. When the nucleus decays, more neutrons are ejected. If these neutrons cause further fissions to occur a chain reaction occurs.

At each step of this process, mass is converted into energy which is released as the kinetic energy of the particles in the system. Controlled chain reactions produce enormous amounts of energy this way and they take place in nuclear reactors, which use a fissionable material such as uranium-235.

Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts, often producing free neutrons and lighter nuclei. Fission of heavy elements is an exothermic reaction which can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments (heating the material where fission takes place). Fission is a form of nuclear transmutation because the resulting fragments are not the same element as the original atom.


Nuclear Reactors

To maintain a chain reaction a minimum of one neutron per fission must cause a further fission to take place. This requires specific conditions.

  • The fission material must be larger than a certain critical size (otherwise not enough neutrons can cause fissions)

  • Slow neutrons are better at causing fission (too fast and they escape without causing a fission).

  • The fission material must have enough atoms capable of undergoing fission (uranium-235 which is fissionable is less than 1% of naturally occurring uranium, while uranium-238 is found in 99% of natural uranium, but absorbs neutrons)

If the chain reaction set up is allowed to proceed unchecked then a vast amount of energy is released in a small time, that is, it is an atom bomb.

A device that allows the chain reaction to proceed at a controlled rate is a nuclear reactor. Its most common application is the generation of electrical power. Other practical applications are in the production of artificial radioactive isotopes for their variety of uses, of high intensity neutron beams for nuclear research and of transuranic elements (Z>92) such as plutonium. A reactor that produces transuranic elements is called a fast breeder reactor.

Fermi and the First Fission Reactor

A fission reaction occurs when two nuclei approach each other so that a re-arrangement of their nucleons occurs with one or more new nuclei being formed. Nuclear transmutation occurs when very heavy elements such as absorbs a neutron that causes the target nucleus to decay into two smaller fragments.

Fermi achieved the first artificially produced nuclear fission in 1934. He was able to irradiate unranium-235 with slow neutrons and produce a radioactive product that produced alpha particles. He incorrectly assumed that this product was an isotope of neptunium (atomic number 93) but later the products were discovered to be the lighter elements of bromine and lanthanum.

Fermi in 1939, escaped to the United States where he continued his research into fission. Delayed by economic and security constraints, he secretly build Chicago Pile 1, the world’s first nuclear fission reactor in 1942. Having theoretically calculated that fission was possible from naturally occurring uranium, he set about construction of a pile of graphite blocks to slow or moderate the speed at which the neutrons would travel. He used cadmium control rods to absorb neutrons and control the rate of reaction. This demonstration of a controlled nuclear fission reaction started an accelerated program by the US army to develop a nuclear bomb, the Manhattan Project.

Fission Reactors

The essential components of a controlled nuclear fission reactor.

During nuclear fission, a parent nucleus splits into two new daughter nuclei of approximately the same mass, plus several neutrons. This is quite a rare event, more often it happens when a neutron hits and is captured by the nucleus. Its then splits releasing energy, mostly as kinetic energy of the heavier decay product. This results in fission as a source of nuclear energy. The energy released per atom is about 220 MeV and is approximately 50,000,000 times greater per atom than from a chemical reaction such as combustion.

Note that as a general rule, energy is released from a nuclear reaction when the binding energy of the products is less than that of the reactants. Energy is released because some mass is converted to energy. Cleary then, we can also say that energy is released from a nuclear reaction when the mass of the products is less than that of the reactants.

In a thermal reactor there is a steady release of heat as the fissionable material splits into its daughter fragments.

Nuclear Fuel
This is the fissionable material, usually uranium oxide in which the natural uranium has been enriched with extra uranium-235.

An average of 2.5 neutrons are released in each fission event. These neutrons are very energetic and are fast-moving. Fast-moving neutrons are unlikely to be absorbed by a nucleus and initiate further fission. The chance of a slow-moving neutron being captured by the nucleus is much larger. Slow-moving neutrons are called thermal neutrons and placing a moderator around the reactor core slows fast-moving neutrons down. The moderator is made from a material with a similar mass to the neutron. The moderator must not absorb the neutrons but merely slow them down in a single collision. Graphite, water, heavy water (D2O) or liquid sodium are all suitable moderators

Control rods
The regulation of a chain reaction is usually achieved by using control rods. Control rods are made from a material such as boron that readily absorbs neutrons, such as cadmium or boron. Control rods can be raised or lowered into the reactor core to speed up or slow down the chain reaction as needed.

The energy release is a single fission reaction is about 200 MeV. In a small reactor most of this energy is converted into thermal energy. This thermal energy is removed from the core by a coolant that flows through the reactor core. In many reactors, heavy water is used as both the coolant and the moderator.

A video showing how nuclear fission is used to generate electricity.


Fusion and Particle Accelerators

Two types of particle accelerators used to fuse charged particles and
nuclei together and to study new particles which are produced in
these interactions.

Particle accelerators are used to make charged particles attain the speeds necessary to fuse matter. These particles have to overcome the repulsive electrostatic force of protons when entering matter. Uncharged particles such as neutrons can be made to penetrate matter, especially the nucleus more easily but they cannot be accelerated and controlled by electric and magnetic fields. Yet they are excellent nuclear probes since they are not affected by the electrons around the nucleus or by the positive charge on the nucleus. By using accelerators, however, the forces between particles and the forces involved in their structure can be investigated.

An accelerator is essentially a machine that produces and electrically accelerates charged particles, such as protons, electrons, alpha particles and other heavier ions to large kinetic energies. Linear accelerators accelerate charged particles in a vacuum through a series of electrodes of alternating voltage. Kinetic energies up to 20 GeV are possible.

Synchrotrons are essentially a linear accelerator in the shape of a ring, so that the charged particles can gain more energy with each cycle. Electromagnets keep the particles in a curved path. As the speed increases the magnetic field is also increased to compensate for the extra relativistic mass increase. Kinetic energies of more than 1000 GeV are possible. Ordinary matter is made up of protons, neutrons and electrons but collision experiments with accelerators have produced hundreds of other elementary particles as well as transuranic elements - those artifically synthesised elements with atomic numbers greater than uranium.


Mass Defect and Binding Energy

Energy and Mass

The equivalence and interchangability of mass and energy has already been studied in Eintein's theory of relativity in the following way. The gain in energy of a fast moving object can be realised as increased mass. Conversely, if an object is slowed down it will lose mass. The change in energy is linked to the change in mass in Einstein's now famous equation ΔE=Δmc2, where c2 is the speed of light squared. Because c2 is such a large number, the energy gained or lost by everyday large masses such as cars and trains produces no detectable change in their mass. For example, a 1000 kg car which is brought to rest from a speed of 120 km/h has its mass decreased by only 4 x 10-13% of the total. This reduction is so small that it goes unnoticed. On the other hand though, if a fast moving alpha particle is brought to rest its mass changes by 0.2% of the total. For small particles like nucleons, their energy-mass interchange is significant.

Mass (u)

It is not convenient to measure very small masses such as protons, neutrons and electrons in kilograms. For the same reason, changes in mass due to the energy lost in nuclear processes also requires are more convenient unit. For this reason we use units called atomic mass units (u).

  • 1 u is equivalent to a mass of 1.66053866 x 10-27 kg.

  • 1 u is also defined as the mass of 1/12 th of the mass of a single carbon-12 atom.

Atomic mass units are often expressed to more than usually large numbers of significant figures. This is because the mass changes occuring at this nuclear level are small and require several decimal places to be observed.

The mass of individual protons, neutrons and electrons are shown in the table above.

Mass Defect

An alpha particle or helium nucleus has a mass of 4.00150 u. If we were to add the masses of two protons and two neutrons from the table above we would get a mass of 4.03190 u for an alpha particle. The sum of the inidividual masses of the protons and neutrons is 0.03040 u larger than the sum of the alpha particle as a whole. This difference in mass is known as the mass defect and it represents the mass lost when a nucleus is assembled from its constituent parts. As you would expect, the mass lost in assembling the nucleus is converted to energy and this energy is used to bind the nucleus together.

Binding Energy

A graph showing the binding energy per nucleon as a function of the
nucleon number. Those to the left of iron undergo fusion to become
more stable while those on the right undergo fission.

We could convert the mass from atomic mass units to kilograms and then use ΔE=Δmc2 to calculate the energy used to bind the nucleus together in joules. But these numbers are not convenient so instead we calculate the energy in electronvolts using the mass in atomic mass units. Since 1 u is equivalent to 931.5 MeV/c2 we can calculate the binding energy as follows:

ΔE = Δmc2 = 0.03040 x 931.5 = 28.3 MeV

The binding energy of a particular nucleus will depend the total number of nucleons in the nucleus so large nuclei will have higher binding energies. To make standardised comparisons between light and heavy nuclei we use a standard called the binding energy per nucleon. For the helium nucleus above the binding energy per nucelon would be 28.3 / 4 = 7.075 MeV.

The term binding energy is rather misleading. Unbinding energy would be a better term as its represents the energy that needs to go into a nucleus to unbind the nucleons into their individual states. In this regard, energy is released from a nucleus when it is formed from its constituent parts and energy is need to break it apart.

The fusion of hydrogen into

The stability of a nucleus depends on the binding energy per nucleon. The higher the binding energy, the more energy is required to break the nucleus apart. The graph shows that those nuclei near the hump of the graph are the ones that are most stable because they need the most binding energy per nucleon.

In radioactive decay and fission, unstable nuclei decay to form more stable products and in so doing mass is lost and energy is released. The loss of energy from the nucleus increases the binding energy per nucleon and makes the nucleus more stable with each decay.

The fusion of small nuclei into larger ones also involves a loss of mass and an increase in the binding energy per nucleon. Take for example, the fusion of hydrogen-2 (deuterium) and hydrogen-3 (tritium) into a helium nucleus. Mass is lost and converted into about 17.6 MeV of energy, the binding energy per nucleon of the helium product is larger than the reactants and the helium nucleus is more stable than its hydrogen constituents.

Manhattan Project

The Manhattan Project was a research and development program by the United States with the United Kingdom and Canada, that produced the first atomic bomb during World War II. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the US Army Corps of Engineers. The Army component of the project was designated the Manhattan District; "Manhattan" gradually superseded the official codename, "Development of Substitute Materials", for the entire project. Along the way, the Manhattan Project absorbed its earlier British counterpart, Tube Alloys.

The Manhattan Project began modestly in 1939, but grew to employ more than 130,000 people and cost nearly US$2 billion (roughly equivalent to $25.8 billion as of 2012). Over 90% of the cost was for building factories and producing the fissionable materials, with less than 10% for development and production of the weapons. Research and production took place at more than 30 sites, some secret, across the United States, the United Kingdom and Canada.

Two types of atomic bomb were developed during the war. A relatively simple gun-type fission weapon was made using uranium-235, an isotope that makes up only 0.7 percent of natural uranium. Since it is chemically identical to the main isotope, uranium-238, and has almost the same mass, it proved difficult to separate. Three methods were employed for uranium enrichment: electromagnetic, gaseous and thermal. Most of this work was performed at Oak Ridge, Tennessee. In parallel with the work on uranium was an effort to produce plutonium. Reactors were constructed at Hanford, Washington, in which uranium was irradiated and transmuted into plutonium. The plutonium was then chemically separated from the uranium. The gun-type design proved impractical to use with plutonium so a more complex implosion-type weapon was developed in a concerted design and construction effort at the project's weapons research and design laboratory in Los Alamos, New Mexico.

The first nuclear device ever detonated was an implosion-type bomb at the Trinity test, conducted at New Mexico's Alamogordo Bombing and Gunnery Range on 16 July 1945. Little Boy, a gun-type weapon, and the implosion-type Fat Man were used in the atomic bombings of Hiroshima and Nagasaki, respectively. The Manhattan Project operated under a blanket of tight security, but Soviet atomic spies still penetrated the program. It was also charged with gathering intelligence on the German nuclear energy project. Through Operation Alsos, Manhattan Project personnel served in Europe, sometimes behind enemy lines, where they gathered nuclear materials and rounded up German scientists. In the immediate postwar years the Manhattan Project conducted weapons testing at Bikini Atoll as part of Operation Crossroads, developed new weapons, promoted the development of the network of national laboratories, supported medical research into radiology and laid the foundations for the nuclear navy. It maintained control over American atomic weapons research and production until the formation of the United States Atomic Energy Commission in January 1947.

Moment in Time: The Manhattan Project documents the uncertain days of the beginning of World War II when it was feared the Nazis were developing the atomic bomb. The history of the bomb's development is traced through recollections of those who worked on what was known as "the gadget" and its impact on society.