Nuclear Chemistry

Radioactivity & Nuclear chemistry

Atomic theory in the nineteenth century presumed that nuclei had fixed compositions. But in 1896, the French scientist Henri Becquerel found that a uranium compound placed near a photographic plate made an image on the plate, even if the compound was wrapped in black cloth. He reasoned that the uranium compound was emitting some kind of radiation that passed through the cloth to expose the photographic plate. Further investigations showed that the radiation was a combination of particles and electromagnetic rays, with its ultimate source being the atomic nucleus. These emanations were ultimately called, collectively, radioactivity.

• .1: Radioactivity
  Nuclei can undergo reactions that change their number of protons, number of neutrons, or energy state. Many different particles can be involved and the most common are protons, neutrons, positrons, alpha (α) particles, beta (β) particles (high-energy electrons), and gamma (γ) rays (which compose high-energy electromagnetic radiation). As with chemical reactions, nuclear reactions are always balanced. When a nuclear reaction occurs, the total mass (number) and the total charge remain unchanged.

.2: Patterns of Nuclear Stability

Protons and neutrons are called nucleons and a nuclide is an atom with a specific number nucleons. Unstable nuclei decay spontaneously are radioactive and its emissions are called radioactivity. Nuclei are bound by the strong nuclear force. Stable nuclei generally have even numbers of protons and neutrons with a ratio of at least 1. Nuclei that contain magic numbers of protons and neutrons are often especially stable including superheavy elements, with atomic numbers near 126.

• 3: Nuclear Transmutations
  Hydrogen and helium are the most abundant elements in the universe. Heavier elements are formed in the interior of stars via multiple neutron-capture events. Successive fusion reactions of helium nuclei at higher temperatures create elements with even numbers of protons and neutrons up to Mg and then up to Ca. Eventually, the elements up to Fe-56 and Ni-58 are formed by exchange processes at even higher temperatures. Heavier elements can only be made by the explosion of a supernova.

• .4: Rates of Radioactive Decay
  Unstable nuclei undergo spontaneous radioactive decay. The most common types of radioactivity are α decay, β decay, γ emission, positron emission, and electron capture. Nuclear reactions also often involve γ rays, and some nuclei decay by electron capture. Each of these modes of decay leads to the formation of a new stable nuclei sometimes via multiple decays before ending in a stable isotope. All nuclear decay processes follow first-order kinetics and each radioisotope has its own half-life. The spontaneous change of an unstable nuclide into another is radioactive decay. The unstable nuclide is called the parent nuclide; the nuclide that results from the decay is known as the daughter nuclide. The daughter nuclide may be stable, or it may decay itself. The radiation produced during radioactive decay is such that the daughter nuclide lies closer to the band of stability than the parent nuclide, so the location of a nuclide relative to the band of stability can serve as a guide to the kind of decay it will undergo.

• 5: Energy Changes in Nuclear Reactions
  Unlike a chemical reaction, a nuclear reaction results in a significant change in mass and an associated change of energy, as described by Einstein’s equation. Nuclear reactions are accompanied by large changes in energy, which result in detectable changes in mass. The experimentally determined mass of an atom is always less than the sum of the masses of the component particles (protons, neutrons, and electrons) by an amount called the mass defect that corresponds to the nuclear binding energy.

• 6: Nuclear Fission
  Many heavier elements with smaller binding energies per nucleon can decompose into more stable elements that have intermediate mass numbers and larger binding energies per nucleon. Sometimes neutrons are also produced. This decomposition is called fission, the breaking of a large nucleus into smaller pieces. The breaking is rather random with the formation of a large number of different products. Fission usually does not occur naturally, but is induced by bombardment with neutrons.

• 7: Nuclear Fusion
  The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process called fusion. The principal source of energy in the sun is a net fusion reaction in which four hydrogen nuclei fuse and produce one helium nucleus and two positrons. This is a net reaction of a more complicated series of events.

8: Biological Effects of Radiation
The effects of radiation on matter depend on the energy of the radiation. Nonionizing radiation is relatively low in energy, and the energy is transferred to matter in the form of heat. Ionizing radiation is relatively high in energy, and when it collides with an atom, it can completely remove an electron to form a positively charged ion that can damage biological tissues.

9 Magic number, - The magic numbers for atoms are 2, 10, 18, 36, 54, and 86, corresponding to the total number of electrons in filled electron shells. (Electrons within a shell have very similar energies and are at similar distances from the nucleus.) In the chemical elements of atomic number 17 to 19, for example, the chloride ion (Cl⁻), the argon atom (Ar), and the potassium ion (K⁺) have 18 electrons in closed-shell configurations and are chemically quite stable. The number of electrons present in the neutral atoms constituting the relatively unreactive noble gases exactly correspond to the atomic magic numbers.
The magic numbers for nuclei are 2, 8, 20, 28, 50, 82, and 126. Thus, tin (atomic number 50), with 50 protons in its nucleus, has 10 stable isotopes, whereas indium (atomic number 49) and antimony (atomic number 51) have only 2 stable isotopes apiece. The doubly magic alpha particle, or helium-4 nucleus, composed of two protons and two neutrons, is very stable. In nuclei, this increased stability occurs when there is a large energy gap between a series of filled energy levels and the next level, which is empty. Such large gaps are said to separate shells, although these shells are not as clearly linked to the spatial structure of the nucleus as electron shells are to their orbits.

10 Nuclear Binding Energy and Mass Defect
Binding Energy
Nuclear binding energy is the energy required to split a nucleus of an atom into its component parts: protons and neutrons, or, collectively, the nucleons. The binding energy of nuclei is always a positive number, since all nuclei require net energy to separate them into individual protons and neutrons.
Mass Defect
Nuclear binding energy accounts for a noticeable difference between the actual mass of an atom’s nucleus and its expected mass based on the sum of the masses of its non-bound components.
Recall that energy (E) and mass (m) are related by the equation:

E=mc2

Here, c is the speed of light. In the case of nuclei, the binding energy is so great that it accounts for a significant amount of mass.
The actual mass is always less than the sum of the individual masses of the constituent protons and neutrons because energy is removed when when the nucleus is formed. This energy has mass, which is removed from the total mass of the original particles. This mass, known as the mass defect, is missing in the resulting nucleus and represents the energy released when the nucleus is formed.
Mass defect (M_d) can be calculated as the difference between observed atomic mass (m_o) and that expected from the combined masses of its protons (m_p, each proton having a mass of 1.00728 amu) and neutrons (m_n, 1.00867 amu):

Md=(mn+mp)−mo

Nuclear Binding Energy
Once mass defect is known, nuclear binding energy can be calculated by converting that mass to energy by using E=mc². Mass must be in units of kg.
Once this energy, which is a quantity of joules for one nucleus, is known, it can be scaled into per-nucleon and per-mole quantities. To convert to joules/mole, simply multiply by Avogadro’s number. To convert to joules per nucleon, simply divide by the number of nucleons.
Nuclear binding energy can also apply to situations when the nucleus splits into fragments composed of more than one nucleon; in these cases, the binding energies for the fragments, as compared to the whole, may be either positive or negative, depending on where the parent nucleus and the daughter fragments fall on the nuclear binding energy curve. If new binding energy is available when light nuclei fuse, or when heavy nuclei split, either of these processes result in the release of the binding energy. This energy—available as nuclear energy—can be used to produce nuclear power or build nuclear weapons. When a large nucleus splits into pieces, excess energy is emitted as photons, or gamma rays, and as kinetic energy, as a number of different particles are ejected.Nuclear binding energy is also used to determine whether fission or fusion will be a favorable process. For elements lighter than iron-56, fusion will release energy because the nuclear binding energy increases with increasing mass. Elements heavier than iron-56 will generally release energy upon fission, as the lighter elements produced contain greater nuclear binding energy. As such, there is a peak at iron-56 on the nuclear binding energy curve.

Nuclear binding energy curveThis graph shows the nuclear binding energy (in MeV) per nucleon as a function of the number of nucleons in the nucleus. Notice that iron-56 has the most binding energy per nucleon, making it the most stable nucleus.
The rationale for this peak in binding energy is the interplay between the coulombic repulsion of the protons in the nucleus, because like charges repel each other, and the strong nuclear force, or strong force. The strong force is what holds protons and neutrons together at short distances. As the size of the nucleus increases, the strong nuclear force is only felt between nucleons that are close together, while the coulombic repulsion continues to be felt throughout the nucleus; this leads to instability and hence the radioactivity and fissile nature of the heavier elements.
Example
Calculate the average binding energy per mole of a U-235 isotope. Show your answer in kJ/mole.
First, you must calculate the mass defect. U-235 has 92 protons, 143 neutrons, and has an observed mass of 235.04393 amu.

Calculate the average binding energy per mole of a U-235 isotope. Show your answer in kJ/mole.

First, you must calculate the mass defect. U-235 has 92 protons, 143 neutrons, and has an observed mass of 235.04393 amu

Electron capture occurs when an inner shell electron combines with a proton and is converted into a neutron. The loss of an inner shell electron leaves a vacancy that will be filled by one of the outer electrons. As the outer electron drops into the vacancy, it will emit energy. In most cases, the energy emitted will be in the form of an X-ray. Like positron emission, electron capture occurs for “proton-rich” nuclei that lie below the band of stability. Electron capture has the same effect on the nucleus as does positron emission: The atomic number is decreased by one and the mass number does not change. This increases the n:p ratio, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. Whether electron capture or positron emission occurs is difficult to predict. The choice is primarily due to kinetic factors, with the one requiring the smaller activation energy being the one more likely to occur.

Figure 3.4 summarizes these types of decay, along with their equations and changes in atomic and mass numbers.

Summary of the type, nuclear equation, representation, and any changes in the mass or atomic numbers for various types of decay.

Radioactive Half Lives

Each radioactive nuclide has a characteristic, constant half-life (t1/2), the time required for half of the atoms in a sample to decay. An isotope’s half-life allows us to determine how long a sample of a useful isotope will be available, and how long a sample of an undesirable or dangerous isotope must be stored before it decays to a low-enough radiation level that is no longer a problem.

For example, cobalt-60, an isotope that emits gamma rays used to treat cancer, has a half-life of 5.27 years (Figure 3.5). In a given cobalt-60 source, since half of the nuclei decay every 5.27 years, both the amount of material and the intensity of the radiation emitted is cut in half every 5.27 years. Note that for a given substance, the intensity of radiation that it produces is directly proportional to the rate of decay of the substance and the amount of the substance. Thus, a cobalt-60 source that is used for cancer treatment must be replaced regularly to continue to be effective.

The Decay of Cobalt-60. For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on. Note that every half-life is the same length of time.

Since every half-life for a radionuclide is the same length of time, we can use the following equation to calculate how much radioactive nuclide is remaining after the passage of any number (n) of half-lives: