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Encyclopedia > Nuclear reaction

In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide to produce products different from the initial particles. In principle a reaction can involve more than two particles colliding, but because the probability of three or more nuclei to meet at the same time at the same place is much less than for two nuclei, such an event is exceptionally rare. While the transformation is spontaneous in the case of radioactive decay, it is initiated by a particle in the case of a nuclear reaction. If the particles collide and separate without changing, the process is called an elastic collision rather than a reaction. Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ... A subatomic particle is a particle smaller than an atom: it may be elementary or composite. ... In physics, a particle is an object, or body, with only a few degrees-of-freedom, including position, and perhaps orientation in space. ... Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. ... For other uses, see Collision (disambiguation). ...

In the symbolic figure shown to the right, 6Li and deuterium react to form the highly excited intermediate nucleus 8Be which then decays immediately into two alpha particles. Protons are symbolically represented by red spheres, and neutrons by blue spheres. Image File history File links This is a lossless scalable vector image. ... General Name, Symbol, Number lithium, Li, 3 Chemical series alkali metals Group, Period, Block 1, 2, s Appearance silvery white/grey Standard atomic weight 6. ... Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in 6500 of hydrogen (~154 PPM). ... General Name, Symbol, Number beryllium, Be, 4 Chemical series alkaline earth metals Group, Period, Block 2, 2, s Appearance white-gray metallic Standard atomic weight 9. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... This article or section does not adequately cite its references or sources. ...

Contents

The reaction equation

A nuclear reaction can be written in terms of a formula just like a chemical reaction. Nuclear decays can be written in a similar way, but with only one nucleus on the left side.


Every particle partaking in the reaction is written with its chemical symbol, with the mass number at the upper left and the atomic number at the lower left. The neutron is written "n"; the proton can be written "1H" or "p". The mass number (A), also called atomic mass number or nucleon number, is the number of nucleons (protons and neutrons) in an atomic nucleus. ... It has been suggested that List of elements by atomic number be merged into this article or section. ...


The equation is correct only if the sums of the mass numbers on both sides are identical (as required by the conservation law for baryon number), and if the sums of the atomic numbers on both sides are identical (as required by the conservation law for electric charge). In the example shown above, this leads to (assuming we would know only one particle to the right): In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... In particle physics, the baryon number is an approximate conserved quantum number. ...

{}^{6}_{3}mathrm{Li}+{}^{2}_{1}mathrm{H}rightarrow{}^{4}_{2}mathrm{He} + ?.

To make the sums correct, the second nucleus to the right must have atomic number 2 and mass number 4; it is therefore also Helium-4. The complete equation therefore reads:

{}^{6}_{3}mathrm{Li}+{}^{2}_{1}mathrm{H}rightarrow{}^{4}_{2}mathrm{He}+{}^{4}_{2}mathrm{He},

oder more simply:

{}^{6}_{3}mathrm{Li}+{}^{2}_{1}mathrm{H}rightarrow2 {}^{4}_{2}mathrm{He}.

Shorter notation

Many common particles are often abbreviated, the nucleus 4He, e.g., the alpha particle, is written with the Greek letter "α". Deuterons (heavy hydrogen nuclei 2H) are called "d". Also, the atomic numbers can be omitted after verifying the equation, since they are uniquely given by the chemical symbols. In many practical cases, a light particle (the "projectile") hits a comparatively heavy nucleus (the "target"), a light particle (the "ejectile") is emitted, and another nucleus remains. In these cases, the reaction can be written in a simplified way:

Target nucleus (Projectile, Ejectile) Final nucleus

In this way, we can rewrite the preceding equation as follows:

{}^{6}_{3}mathrm{Li}+drightarrowalpha+alpha,

then omitting atomic numbers:

{}^{6}mathrm{Li}+drightarrowalpha+alpha,

and so we arrive at the shortened version:

  •         6Li(d,α)α.

Energy conservation

Kinetic energy may be released during the course of a reaction (exothermic reaction) or kinetic energy may have to be supplied for the reaction to take place (endothermic reaction). This can be calculated by reference to a table of very accurate particle rest masses (see http://physics.nist.gov/PhysRefData/Compositions/index.html), as follows. According to the reference tables, the 63Li nucleus has a relative atomic mass of 6.015 atomic mass units (abbreviated u), the deuteron has 2.014 u, and the helium-4 nucleus has 4.0026 u Thus: Vapours of hydrogen chloride in a beaker and ammonia in a test tube meet to form a cloud of a new substance, ammonium chloride A chemical reaction is a process that results in the interconversion of chemical substances. ... Vapours of hydrogen chloride in a beaker and ammonia in a test tube meet to form a cloud of a new substance, ammonium chloride A chemical reaction is a process that results in the interconversion of chemical substances. ... In reference to a certain isotope of a chemical element, atomic mass (though also called relative atomic mass and atomic weight) is the mass of one atom of the isotope expressed in units (atomic mass unit, amu) such that the carbon-12 isotope has an atomic mass of exactly 12. ... The unified atomic mass unit (u), or Dalton (Da), is a small unit of mass used to express atomic and molecular masses. ... Look up U, u in Wiktionary, the free dictionary. ...

  • Total rest mass on left side = 6.015 + 2.014 = 8.029 u
  • Total rest mass on right side = 2 × 4.0026 = 8.0052 u
  • Missing rest mass = 8.029 - 8.0052 = 0.0238 atomic mass units.

In a nuclear reaction, the total (relativistic) energy is conserved. The "missing" rest mass must therefore reappear as kinetic energy released in the reaction; its source is the nuclear binding energy. Using Einstein's mass-energy equivalence formula E = mc², the amount of energy released can be determined. We first need the energy equivalent of one atomic mass unit: Conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms (for instance, friction turns kinetic energy into thermal energy). ... Binding energy is the energy required to disassemble a whole into separate parts. ... 15ft sculpture of Einsteins 1905 E = mc² formula at the 2006 Walk of Ideas, Germany In physics, mass-energy equivalence is the concept that all mass has an energy equivalence, and all energy has a mass equivalence. ...

1 u c2 = (1.66054 × 10-27 kg) × (2.99792 × 108 m/s)2 
= 1.49242 × 10-10 kg (m/s)2 = 1.49242 × 10-10 J (Joule)
× (1 MeV / 1.60218 × 10-13 J)
= 931.49 MeV,
so 1 u c2 = 931.49 MeV.

Hence, the energy released is 0.0238 × 931 MeV = 22.4 MeV. The joule (IPA pronunciation: or ) (symbol: J) is the SI unit of energy. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...


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 that the pair of electrons in the helium atom occupy a filled 1s electron orbital). Consequently, alpha particles appear frequently on the right hand side of nuclear reactions. In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... In nuclear physics, a magic number is a number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. ...


The energy released in a nuclear reaction can appear mainly in one of three ways:

When the product nucleus is metastable, this is indicated by placing an asterisk ("*") next to its atomic number. This energy is eventually released through nuclear decay. The kinetic energy of an object is the extra energy which it possesses due to its motion. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... This article is about electromagnetic radiation. ... Metastability is the ability of a non-equilibrium state to persist for a long period of time. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... This article refers to the typographical symbol. ...


A small amount of energy may also emerge in the form of X-rays. Generally, the product nucleus has a different atomic number, and thus the configuration of its electron shells is wrong. As the electrons rearrange themselves and drop to lower energy levels, internal transition X-rays (X-rays with precisely defined emission lines) may be emitted. In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... [[Image:Valence shell 011 Sodiumup of one or more electron subshells, or sublevels, which have two or more orbitals with the same angular momentum quantum number l. ... A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies. ...


Q-value and energy balance

In writing down the reaction equation, in a way analogous to a chemical equation, one may in addition give the reaction energy on the right side:

Target nucleus + projectile -> Final nucleus + ejectile + Q.

For the particular case discussed above, the reaction energy has already been calculated as Q = 22.4 MeV. Hence:

63Li + 21H → 42He + 42He + 22.4 MeV

The reaction energy (the "Q-value") is positive for exothermal reactions and negative for endothermal reactions. On the one hand, it is the difference between the sums of kinetic energies on the final side and on the initial side. But on the other hand, it is also the difference between the nuclear rest masses on the initial side and on the final side (in this way, we have calculated the Q-value above).


Reaction rates

If the reaction equation is balanced, that does not mean that the reaction really occurs. The rate at which reactions occur depends on the particle energy, the particle flux and the reaction cross section. flux in science and mathematics. ... In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ...


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: The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... Electrostatics (also known as Static Electricity) is the branch of physics that deals with the forces exerted by a static (i. ... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ...

  • particle accelerators
  • nuclear decay (alpha particles are the main type of interest here, since beta and gamma rays are rarely involved in nuclear reactions)
  • very high temperatures, on the order of millions of degrees, producing thermonuclear reactions
  • cosmic rays

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. For the DC Comics Superhero also called Atom Smasher, see Albert Rothstein. ... At the end of the 20th century, Thermonuclear has came to imply anything which has to do with fusion nuclear reactions which are triggered by particles of thermal energy. ... Cosmic rays can loosely be defined as energetic particles originating outside of the Earth. ...


Neutrons, 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. This article or section does not adequately cite its references or sources. ... This article does not cite its references or sources. ... In physics, the de Broglie hypothesis is the statement that all matter (any object) has a wave-like nature (wave-particle duality). ... The wavelength is the distance between repeating units of a wave pattern. ...


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:

  • Fusion reactions - two light nuclei join to form a heavier one, with additional particles (usually protons or neutrons) thrown off to conserve momentum.
  • Fission reactions - a very heavy nucleus, spontaneously or after absorbing additional light particles (usually neutrons), splits into two or sometimes three pieces. (α decay is not usually called fission.)
  • Spallation - a nucleus is hit by a particle with sufficient energy and momentum to knock out several small fragments or, smash it into many fragments.
  • Induced gamma emission belongs to a class in which only photons were involved in creating and destroying states of nuclear excitation.

The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing fusion power. ... For the generation of electrical power by fission, see Nuclear power plant An induced nuclear fission event. ... In general, spallation is a process in which fragments of material are ejected from a body due to impact or stress. ... In physics, induced gamma emission (IGE) refers to the process of fluorescent emission of gamma rays from excited nuclei, or from nuclear isomers. ...

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.

  • (p,p') tests differenced between nuclear states
  • (α,α') measures nuclear surface shapes and sized. Since α particles that hit the nucleus react more violently, elastic and shallow inelastic α scattering are sensitive to the shapes and sizes of the targets, like light scattered from a small black object.
  • (e,e') is useful for probing the interior structure. Since electrons interact less strongly than do protons and neutrons, they reach to the centers of the targets and their wave functions are less distorted by passing through the nucleus.

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. In nuclear physics, the nuclear shell model is a model of the atomic nucleus. ...

  • (α,n) and (α,p) reactions. Some of the earliest nuclear reactions studied involved an alpha particle produced by alpha decay, knocking a nucleon from a target nucleus.
  • (d,n) and (d,p) reactions. A deuteron beam impinges on a target; the target nuclei absorb either the neutron or proton from the deuteron. The deuteron is so loosely bound that this is almost the same as proton or neutron capture. A compound nucleus may be formed, leading to additional neutrons being emitted more slowly. (d,n) reactions are used to generate energetic neutrons.
  • The strangeness exchange reaction (K,π) has been used to study hypernuclei.

In particle physics, strangeness, denoted as , is a property of particles, expressed as a quantum number for describing decay of particles in strong and electro-magnetic reactions, which occur in a short period of time. ... In particle physics, Kaons (also called K-mesons and denoted K) are a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. ... In particle physics, pion (short for pi meson) is the collective name for three subatomic particles: π0, π+ and π−. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force. ... A Hypernucleus is a nucleus which contains at least one hyperon in addition to nucleons. ...

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. The Coulomb barrier, named after physicist Charles-Augustin de Coulomb (1736—1806), is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo nuclear fusion. ...

  • Low energy (e, e' xn), (γ, xn) (the xn indicating one or more neutrons), where the gamma or virtual gamma energy is near the Giant dipole resonance These increase the need for radiation shielding around electron accelerators

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. This article may be too technical for most readers to understand. ...


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. This article may be too technical for most readers to understand. ... The nuclear force (or nucleon-nucleon interaction or residual strong force) is the force between two or more nucleons. ... This article may be too technical for most readers to understand. ...


See also


  Results from FactBites:
 
Nuclear Reactions (1138 words)
Nuclear reactions and nuclear scattering are used to measure the properties of nuclei.
Reactions that exchange energy or nucleons can be used to measure the energies of binding and excitation, quantum numbers of energy levels, and transition rates between levels.
Nuclear reactions can also be produced in nature by high-velocity particles from cosmic rays, for instance in the upper atmosphere or in space.
Nuclear reaction - Wikipedia, the free encyclopedia (1737 words)
A nuclear reaction can be represented by an equation similar to a chemical equation, and balanced in an analogous manner.
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.
Direct nuclear reactions are most often calculated by some form of distorted wave Born approximation.
  More results at FactBites »

 
 

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