Saturday, January 1, 2011

Radioactive Decay

Radioactive Decay is the decomposition of an unstable atom into multiple parts. Often, this involves the emission of radiation, hence the name radioactive decay. Some elements of the periodic table have no stable atoms, while some have stable and unstable isotopes, meaning that the number of protons remains the same, but stability can vary with the number of neutrons.

There are 118 known elements on the periodic table, and, among these, numbers 43, 61, and all above 82 possess only isotopes that are radioactive. The remaining 80 have at least one neutron number that results in a stable nucleus, but a vast majority of the possibilities are radioactive, and overcome the force, known as the strong nuclear force or the strong interaction, that binds the particles in a nucleus together.

For example, the element oxygen has 8 protons, and the number of neutrons can range from 4 to 16, because it is known that there are physical limits on how many neutrons can exist for a certain number of protons, called the nuclear drip line. It is simply impossible for 3 neutrons and 8 protons to exist in a nucleus, and if these particles are shoved together, a proton will simply drip out. Similarly, it is impossible for 8 protons and 17 neutrons to be together in a nucleus, because a neutron will "drip" out. Therefore, these nuclei do not qualify as parts of atoms, as they are never in a whole state. Unlike these, isotopes of oxygen between 4 and 16 neutrons can exist. However, all but three of these are unstable, and decay to other atoms within seconds. Atoms with 8 protons and 8, 9, and 10 neutrons, corresponding to Oxygen-16, Oxygen-17, and Oxygen-18 are stable, and occur in nature.

Also, there are different ways that atoms can decay into others. The three most common were the first types of radiation isolated, and there were named alpha, beta, and gamma decay.

Alpha decay involves an unstable nucleus of an atom emitting an entire Helium-4 nucleus, that is, two protons and two neutrons, at once. This nucleus is also known as an alpha particle. The resulting nucleus of the parent atom has two less protons and two less neutrons than it did before alpha decay. Some argue that the Helium nucleus takes two electrons with it when an atom experiences alpha decay, because otherwise there would be an unbalanced charge, and some believe that two electrons are simply released into the environment. An example alpha decay reaction is pictured below.

An example reaction involves Uranium-238, which, by alpha decay loses two neutrons and two protons. Because of this the resulting atom's atomic weight will drop from 238 to 234, and the atomic number will drop by two, becoming Thorium. Therefore the reaction is denoted


The notation above shows the two balanced sides of the reaction, with the Uranium-238 (first number before the atomic symbol is the entire weight, the second is the number of protons) atom on the left, and the Thorium-234 atom and the Helium nucleus (alpha particle) on the right. In this reaction the two elections are assumed to leave the atom with the Helium nucleus.

Beta decay involves a slightly more complicated chain of events, and there are two types: Beta negative and beta positive, denoted B- and B+ respectively. The B- reaction uses the weak nuclear force (one of the four fundamental forces of the Universe) to convert a neutron into a proton. However, there are some byproducts of this reaction, namely an electron and an electron antineutrino. Since a neutron is only slightly heavier than the proton, the loss of a tiny electron (and an electron antineutrino) is enough to convert it into a proton. Also, the change is mass is so minute that the atomic weight remains the same, but the atomic number goes up. This type of decay actually "increases" the complexity of the nucleus, instead of lowering it.

This image is an example beta decay reaction. The main picture shows only the B- particle (electron) being emitted, while the inset shows the entire reaction. The neutron splits into three parts, of which the proton stays in the nucleus, the B- particle may leave the atom or stay and compensate for the gaining of a positive charge via the proton, and the tiny electron antineutrino is emitted. To fully understand this process, one must break it down into even smaller stages, by use of a Feynman Diagram.

A Feynman Diagram graphically represents quantum phenomena to make them easier to understand. In this diagram, time progresses with respect to the vertical axis. The neutron, n, is shown as its three composite parts, u,d, and d, representing one up quark and two down quarks. The weak nuclear force has an effect on the final down quark only, instantly changing it to an up quark. As a result, the three new quarks are up, down, up (u,d,u) and these are the composite particles for a proton, hence the proton end product. However, to make this change happen, a W- boson, the carrier of the weak nuclear force, must be emitted from the down quark, to change it to an up quark. Since a down quark is heavier than an up one, the loss in mass again makes sense. The W- boson is very short lived, however, and nearly instantaneously splits into an electron and an electron antineutrino, denoted by the e- and ve+ respectively.

An example reaction of B- decay is the process of changing the Caesium-137 atom into the Barium-137 atom

137,55Cs = 137,56Ba + e- + ve+

Neutron-rich nuclei are more likely to undergo B- decay.

The other type of Beta decay is B+ decay. It is basically the opposite (in terms of particles) of the previous process, because a proton is converted into a neutron. Since the neutron is heavier than the proton, the reaction needs outside energy to add mass to the reaction (since energy can at any time by changed into mass and vice versa). This must be provided by the environment, and therefore this reaction cannot occur by itself in a vacuum. The byproducts of the reaction are the opposite of B- decay in charge; instead of a electron and an electron antineutrino being emitted, the positron (anti-electron) and electron neutrino are emitted. An example B+ decay reaction involving the transformation of Carbon-11 into Boron-11 is written below

11,6C = 11,5B + e+ + ve-

This reaction also involves the weak nuclear force, but with use of a W+ boson, rather than a W- one. The W+ boson is emitted when a up quark changes into a down quark. This particle then splits into the two mentioned above.

B+ decay is more likely to occur in proton-rich nuclei.

There are other rarer types of Beta decay, such as electron capture, where an electron is "captured" from the orbitals of the atom, and is pulled to the nucleus, where it combines with a proton to form a neutron and an electron antineutrino. An example reaction is

59,28Ni + e- = 59,27Co + ve+

Although the electron on the left side of this equation is presented as if it is separate from the atom, the electron actually originated from what was part of the atom, namely orbiting electrons.

There are also forms of Beta decay where the process happens twice simultaneously. These are called Double Beta Decay, and a similar double exists for electron capture.

Other simple types of radioactive decay include proton emission, if a nucleus is very rich in protons, and neutron emission, if a nucleus is very rich in protons. Note that this is different from proton and neutron "dripping" discussed earlier, because the nucleus does exist as one unit before the the proton or neutron is emitted.

Another famous type is the emission of a larger particle than an alpha particle, namely a heavier atomic nucleus. However, this type of decay, called cluster decay, only occurs among atoms that usually decay through the emission of an alpha particle. Some unstable atoms decay in different ways, with one occurring a certain percentage of the time, and another in the remaining percentage. An example is the atom Radium-223.

Usually, Radium-223 decays through alpha decay:

223,88Ra = 219,86Rn + 4,2He

but for one out of every one billion reactions, something else occurs, and the atom emits a Carbon-14 nucleus!

223,88Ra = 209,82Pb + 14,6C

The second reaction was the first of its kind known to occur and was discovered in 1984 at Oxford University. The heaviest known nucleus to be emitted in this fashion is Silicon-34, happening only once out of trillions and trillions of alpha decays from Plutonium-240, Americium-241, and Curium-242.

Finally, some atoms simply split into two atoms, through a process called spontaneous fission. This processes occurs when a neutron impacts the nucleus and splits it in two. Uranium, Plutonium, and Californium are three elements that have a chance for spontaneous fission, although they are more likely to decay through other processes. Californium-252 has a relatively high fission rate, with 3.09% of reactions result in fission. However, Uranium-235 decays through fission only seven reactions out of 100 billion! There are higher elements which predominately decay by fission, some of which are isotopes of Mendelevium and Rutherfordium. Some of these reactions emit neutrons in turn, and these can lead to chain reactions. Uranium-235 is one of these, and since each reaction gives out energy, it is one of the isotopes used in the detonation of atomic bombs.

Reactions of this type occur to all of the possible unstable isotopes. The chart that maps all the isotopes is known as the table of nuclides, linked to here.

This is another version of the table of nuclides, which shows the predominant mode of decay for every known nuclide. The center of the band of nuclides are the most stable (those in black are stable), and they tend to get less stable away from the center. Isotopes that undergo B+ decay or Proton Emission occur on the right (proton-rich) side of the stable isotopes, while ones that undergo B- decay or Neutron Emission occur the left (neutron-rich) side of the stable isotopes. Also, alpha decay, cluster decay and fission tend to occur with heavier atoms, toward the upper right of the chart.

Some isotopes do not decay directly into a stable nucleus, and go through multiple steps of decay before reaching stability.

An example is Uranium-238. Its decay chain is imaged above (click to enlarge), with each octagon containing the atomic number and mass of an isotope, while the arrows denote the decay chain, with letters representing the type of decay. The half-life, or average time to decay on each step, is also included under each octagon. Sometimes, the decay chain branches, when there are probabilities for other types of decay, but all of the branches converge on the stable isotope Lead-206.

Radioactive decay produces energy, and is therefore valuable as a potential power source, with drawbacks including lower feasibility and harmful radiation. Radiation is also used for other purposes, such as medical procedures, specifically for eliminating cancerous cells.


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