Information AboutNuclear Reaction |
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In Nuclear Physics , a nuclear reaction is a process in which two Nuclei or Nuclear Particle s collide, to produce different products than the initial products. In principle a reaction can involve more than two particles colliding, but such an event is exceptionally rare. If the particles collide and separate without changing (except possibly in Energy Level s), the process is called a Collision rather than a reaction. REPRESENTATION A nuclear reaction can be represented by an equation similar to a Chemical Equation , and balanced in an analogous manner. Nuclear Decay s can be represented in the same way. Each particle taking part in the reaction is written with its Chemical Symbol , then Atomic Number Subscript ed, and Atomic Mass Superscript ed. The Neutron and Electron , not being chemical elements, are given the symbols n and '''e''' respectively. The Proton may be denoted by "H" (as a Hydrogen nucleus) or as "p". To balance the equation, we must ensure that the sum of the atomic numbers on each side of the equations are equal (required by the Conservation Law of Electric Charge ), and that the sum of the atomic masses on each side are also equal (required by the law of conservation of Baryon Number ). For example: : + → + ? Balancing:
The complete reaction is thus: : + → + which could also be written: : + → 2 Simplified representation Many particles appear in reactions so often that they are usually abbreviated. Thus, a helium nucleus (also known as an Alpha Particle ) is written with the Greek Letter "α". Deuteron s (heavy hydrogen, ) are written simply as "d". Also, because the atomic numbers are implied by the chemical symbols, they are redundant after balancing, and often omitted. Finally, many common reactions take the form of a relatively heavy nucleus being struck by one of a small group of common, reactive particles, and emitting another common particle, to produce another nucleus. For these reactions, the notation can be greatly condensed into the form: : So we could rewrite the preceding example by first abbreviating symbols: : + d → α + α then dropping atomic numbers: :6Li + d → α + α and finally using the condensed form: :6Li(d,α)α ENERGY Energy is usually released during the course of a reaction. This can be calculated by reference to a table of very accurate particle masses, as follows. According to the reference tables, the nucleus as an Atomic Weight of 6.015 Atomic Mass Unit s, the deuteron is 2.014 a.m.u. and the helium nucleus is 4.0026 a.m.u. Thus:
This "missing" mass comes from energy released from the reaction; its source is the nuclear Binding Energy . Using Einstein's famous " E=mc2 " formula, we can work out how much energy has been released. In fact, one atomic mass unit is equivalent to 931 MeV , so the energy released is 0.0238 × 931 MeV = 22.4 MeV. Expressed differently: the mass is reduced by 0.3 %, corresponding to 0.3 % of 90 PJ/kg is 300 TJ/kg. This is a large amount of energy for a nuclear reaction; the amount is so high because the binding energy per Nucleon of the helium-4 nucleus is unusually high, because the He-4 nucleus is Doubly Magic . (The He-4 nucleus is unusually stable and tightly-bound for the same reason that the helium atom is inert: each pair of protons and neutrons in He-4 occupies a filled 1s nuclear orbital in the same way the pair of helium electrons occupy a filled 1s electron orbital). Consequently, alpha particles appear frequently on the right hand side of nuclear reactions. The energy released in a nuclear reaction can appear mainly in one of three ways:
A small amount of energy may also emerge in the form of X-ray s. Generally, the product nucleus has a different atomic number, and thus the configuration of its Electron Shell s is wrong. As the electrons rearrange themselves and drop to lower energy levels, internal transition X-rays (X-rays with precisely defined Emission Line s) may be emitted. REACTION RATES The rate at which reactions occur depends on the particle Flux and the reaction Cross Section . NEUTRONS VERSUS IONS In the initial collision which begins the reaction, the particles must approach closely enough so that the short range Strong Force can affect them. As most common nuclear particles are positively charged, this means they must overcome considerable Electrostatic Repulsion before the reaction can begin. Even if the target nucleus is part of a neutral Atom , the other particle must penetrate well beyond the electron cloud and closely approach the nucleus, which is positively charged. Thus, such particles must be first accelerated to high energy, for example by:
Also, since the force of repulsion is proportional to the product of the two charges, reactions between heavy nuclei are rarer, and require higher initiating energy, than those between a heavy and light nucleus; while reactions between two light nuclei are commoner still. Neutron s, on the other hand, have no electric charge to cause repulsion, and are able to effect a nuclear reaction at very low energies. In fact at extremely low particle energies (corresponding, say, to Thermal Equilibrium At Room Temperature ), the neutron's De Broglie Wavelength is greatly increased, possibly greatly increasing its capture cross section, at energies close to resonances of the nuclei involved. Thus low energy neutrons ''may'' be even more reactive than high energy neutrons. NOTABLE TYPES While the number of possible nuclear reactions is immense, there are several types which are more common, or otherwise notable. Some examples include:
Direct reactions An intermediate energy projectile transfers energy or picks up or loses nucleons to the nucleus in a single quick (10−21 second) event. Energy and momentum transfer are relatively small. These are particularly useful in experimental nuclear physics, because the reaction mechanisms are often simple enough to calculate with sufficient accuracy to probe the structure of the target nucleus. Inelastic scattering Only energy and momentum are transferred.
Transfer reactions Usually at moderately low energy, one or more nucleons are transferred between the projectile and target. These are useful in studying outer Shell structure of nuclei.
Quasi- Elastic knock out reactions The projectile interacts closely with only one nucleon of the target.
Compound nuclear reactions Either a low energy projectile is absorbed or a higher energy particle transfers energy to the nucleus, leaving it with too much energy to be fully bound together. On a time scale of about 10−19 seconds, particles, usually neutrons, are "boiled" off. That is, it remains together until enough energy happens to be concentrated in one neutron to escape the mutual attraction. Charged particles rarely boil off because of the Coulomb Barrier . The excited quasi-bound nucleus is called a compound nucleus.
CALCULATION Applying the methods of Scattering By Two Potentials , the plane wave of each free charged particle is replaced by the exact solution for a charged particle moving in the presence of another point charge. Direct nuclear reactions are most often calculated by some form of distorted wave Born Approximation . Applying again scattering by two potentials, the coulomb solutions and neutron plane waves are replaced by the Optical Model wave functions for the incident and outgoing particles moving in and near the nucleus. These are obtained mostly from elastic scattering experiments, and from inelastic scattering to vibrational and rotational collective excitations. The reaction itself is then modeled by the Born Approximation . That is, the excitation or transfer process is treated as a first order perturbation on elastic scattering. An early improvement on this was to exactly treat the coupling between a small number of excited states, known as coupled channels Born approximation. SEE ALSO
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