Reactions, nuclear

Nuclear reactions differ from ordinary chemical reactions in the following ways  

Although there is no change in the total of the mass numbers, the quantity of matter does chang significantly. Some matter is changed to energy. 

The atom reacts independently of other atoms to which it might be bonded. 

Reactions are those of specific isotopes rather than the naturally occurring mixtures of isotopes 

The quantities usually used in calculations are atoms rather than moles of atoms. 

The final outcome of these reactions, as a function of rj or equivalently Slboh2, is shown in Fig. 4.3. The primordial helium mass fraction TP, shown on a large scale, is not very sensitive to r), since this parameter only affects the time for neutron decay before nucleosynthesis sets in, and it can be fitted by the relation FP = 0.226 + 0.025log 0 + 0.0075(g - 10.75) + 0.014(r1/2( ) - 10.3 min). 

The deuterium abundance, on the other hand, is a steeply decreasing function because it is destroyed by two-body reactions with p, n, D and 3He. 3He declines more gently because this nucleus is more robust. 7Li has a bimodal behaviour because at low baryon densities it is synthesized from 3H by reaction (Eq. 4.46) and both nuclei are destroyed by two-body reactions, whereas at higher densities it 

Our goal in this chapter is to help you learn about nuclear reactions, including nuclear decay as well as fission and fusion. If needed, review the section in Chapter 2 on isotopes and the section in Chapter 13 on integrated rate laws which discusses first-order kinetics. And just like the previous nineteen chapters, be sure to Practice, Practice, Practice. 

Most nuclear reactions involve the breaking apart of the nucleus into two or more different elements or subatomic particles. If we know all but one of the particles, then the unknown particle can be determined by balancing the nuclear equation. When chemical equations are balanced, we add coefficients to ensure that there are the same number of each type of atom on both the left and right of the reaction arrow. However, in order to balance nuclear equations we ensure that there is the same sum of both mass numbers and atomic numbers on the left and right of the reaction arrow. Recall that we can represent a specific isotope of an element by the following symbolization  

A is the mass number (sum of protons and neutrons), Z is the atomic number (number of protons), and X is the element symbol (from the periodic table). In balancing nuclear reactions, ensure that the sum of all A values on the left of the reaction arrow equals the sum of all A values to the right of the arrow. The same will be true of the sums of the atomic numbers, Z. Knowing that these sums have to be equal allows you to predict the mass and atomic number of an unknown particle, if we know all the others. 

If we bombard chlorine-35 with a neutron, we create hydrogen-1 along with an isotope of a different element. Write a balanced nuclear reaction for this process. 

The sum of the mass numbers on the left of the equation is 36 (35 + 1) and on the right is 1 + x. The mass number of the unknown isotope must be 35. The sum of the atomic numbers on the left is 17 (17 + 0) and 1 + y on the right. The atomic number of the unknown must then be 16. This atomic number identifies the element as sulfur, so that we can write a complete nuclear equation  

In a process called radioactive decay, a nucleus spontaneously breaks down by emitting radiation. This process is shown by writing a nuclear equation with the atomic symbols of the original radioactive nucleus on the left, an arrow, and the new nucleus and the type of radiation emitted on the right. 

In a nuclear equation, the sum of the mass numbers and the sum of the atomic numbers on one side of the arrow must equal the sum of the mass numbers and the sum of the 

An unstable nucleus may emit an alpha particle, which consists of 2 protons and 2 neutrons. Thus, the mass number of the radioactive nucleus decreases by 4, and its atomic number decreases by 2. For example, when uranium-238 emits an alpha particle, the new nucleus that forms has a mass number of 234. Compared to uranium with 92 protons, the new nucleus has 90 protons, which is thorium. 

In alpha decay, the mass number of the new nucleus decreases by 4 and its atomic number decreases by 2. 

When francium-221 undergoes decay, an alpha particle is emitted. 

Write a balanced nuclear equation showing mass numbers and atomic numbers for radioactive decay. 

The ordinary chemical reactions discussed to this point involve changes in the outer electronic structures of atoms or molecules. In contrast, nuclear reactions result from changes taking place within atomic nuclei. You will recall (Chapter 2) that atomic nuclei are represented by symbols such as 

The atomic number Z (number of protons in the nucleus) is shown as a left subscript. The mass number A (number of protons + number of neutrons in the nucleus) appears as a left superscript. 

The reactions that we discuss in this chapter will be represented by nuclear equations. An equation of this type uses nuclear symbols such as those above in other respects it resembles an ordinary chemical equation. A nuclear equation must be balanced with respect to nuclear charge (atomic number) and nuclear mass (mass number). To see what that means, consider an equation that we will have a lot more to say about later in this chapter  

The reactants are an N-14 nucleus and a neutron the products are a C-14 nucleus and an H-1 nucleus. The atomic numbers add to 7 on both sides  

When matter is irradiated with charged particles (protons, deuterons, helium-3, helium-4), some of the nuclides are transformed by nuclear reactions into radionuclides. The possibility of a nuclear reaction A(a,b)B is determined by the energy Q liberated per reaction. Q can be deduced from the mass difference between starting and end products by  

If the reaction is energetically possible (Q 0 or, if Q 0, E Ej), it can take place with a high probability if the energy is sufficient to overcome the coulomb barrier between the target nucleus and the incident particle. The Coulomb barrier energy (MeV) is approximately given by  

It increases with the atomic numbers of the target nucleus and of the incident particle. Fig. II-3 gives the Coulomb barrier energy for incident protons, deuterons and helium-4 as a function of the atomic number of the target nucleus. 

More recent data are available in Nuclear Data Tables (20) and Atomic Data and Nuclear Data Tables (21). 

The determination of an absolute cross-section requires the irradiation of a thin target. 

Throughout this book you have been studying traditional chemistry and chemical reactions. This has involved the transfer or sharing of electrons from the electron clouds, especially the valence electrons. Little has been said up to this point regarding the nucleus. Now we are going to shift our attention to nuclear reactions and, for the most part, ignore the electron clouds. 

No specific nuclear equations are provided, but review first-order equations in the Kinetics chapter. 

After discovery of the natural radioactivity of uranium, thorium, and radium, many other elements were found to have radioactive isotopes. All the elements heavier than bismuth (Bi, atomic number 83) and a few lighter than bismuth have natural radioactivity. While studying radium, Rutherford found that besides emitting alpha particles, radiiun was also producing radioactive 

Soon after Becquerel s discovery of uranium s radioactivity, Marie Sklodowska Curie (1867—1934), also working in France, studied the radioactivity of thorium (Th) and began to search systematically for new radioactive elements. She showed that the radioactivity of uranium was an atomic property— that is, its radioactivity was proportional to the amount of the element present and was not related to any particular compound. Her experiments indicated that other radioactive elements were probably also present in certain uranium samples. With painstaking technique, she and her husband Pierre Curie (1859-1906) separated the element radium (Ra) from uranium ore and found that it is more than one million times more radioactive than uranium. In 1903, Marie and Pierre Curie shared the Nobel Prize in physics with Henri Becquerel for their discovery of radioactivity. After Pierre died. 

Pierre and Marie Curie with their daughter, Irene. Irene grew up to continue the study of radioactivity with her husband, Frederic JoUoL Together, Irene and Frederic won a Nobel Prize in 1935 for production of the first artificial radioactive isotope. 

Marie continued her research and discovered polonium (Po), which she named after her native Poland. In 1911, she became the first person to win a second Nobel Prize, this one for the discoveries of radium and polonium. In 1921, Marie Curie came to the United States, where she was given 1 g of pure radium, purchased with donations from American women interested in her work. 

Recall that an a particle is a helium atom without its electrons and has a + 2 charge. The a particle is sometimes also represented as in nuclear equations. 

These cave drawings, found in Chauvet Cave in France, have been authenticated by C-14 dating to 30,000-28,000 B.c. It is the oldest known artwork in the world. 

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If we examine a specific reaction, we can see how this works. Take for instance  

29328U - 23940Th + 4He The masses of each of the particles in the equation are  

The change in mass can be determined by subtracting the mass of the reactant (parent nuclei—in this case, uranium-238), from the combined masses of the products  

To determine the energy change, we can now use Einstein s equation and solve for AE. Before we can do this, we must convert the mass to kilograms (because the energy unit of joules requires the mass in kilograms)  

It turns out that the mass of an individual atom is always less than the sum of its parts. That is, if you add up the masses of all the components of an atom, you will not get the total mass of the atom. As an example, let s look at oxygen-16. 

Oxygen-16 contains 8 protons and 8 neutrons. Therefore, we would expect the mass to equal 

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Porter C E and Thomas R G 1956 Fluctuations of nuclear reaction widths Phys. Rev. 104 483-91... 

Energy redistribution is the key primary process in chemical reaction systems, as well as in reaction systems quite generally (for instance, nuclear reactions). This is because many reactions can be separated into two steps ... 

This overview covers the major teclnhques used in materials analysis with MeV ion beams Rutherford backscattering, chaimelling, resonance scattering, forward recoil scattering, PIXE and microbeams. We have not covered nuclear reaction analysis (NRA), because it applies to special incident-ion-target-atom combinations and is a topic of its own [1, 2]. 

The meaning of the symbolic expression indicating a nuclear reaction ... 

The easiest principle to appreciate is conservation of mass. Except for nuclear reactions, an element s total mass at the end of a reaction must be the same as that present at the beginning of the reaction thus, an element serves as the most fundamental reaction unit. Consider, for example, the combustion of butane to produce CO2 and H2O, for which the unbalanced reaction is... 

Neutron Activation Analysis Few samples of interest are naturally radioactive. For many elements, however, radioactivity may be induced by irradiating the sample with neutrons in a process called neutron activation analysis (NAA). The radioactive element formed by neutron activation decays to a stable isotope by emitting gamma rays and, if necessary, other nuclear particles. The rate of gamma-ray emission is proportional to the analyte s initial concentration in the sample. For example, when a sample containing nonradioactive 13AI is placed in a nuclear reactor and irradiated with neutrons, the following nuclear reaction results. 

Many artificial (likely radioactive) isotopes can be created through nuclear reactions. Radioactive isotopes of iodine are used in medicine, while isotopes of plutonium are used in making atomic bombs. In many analytical applications, the ratio of occurrence of the isotopes is important. For example, it may be important to know the exact ratio of the abundances (relative amounts) of the isotopes 1, 2, and 3 in hydrogen. Such knowledge can be obtained through a mass spectrometric measurement of the isotope abundance ratio. 

Fig. 1. Nuclear reactions for the production of heavy elements by intensive slow neutron irradiation. The main line of buildup is designated by heavy...

Radiocarbon dating (43) has probably gained the widest general recognition (see Radioisotopes). Developed in the late 1940s, it depends on the formation of the radioactive isotope and its decay, with a half-life of 5730 yr. After forms in the upper stratosphere through nuclear reactions of... 

Dioxygea difluoride has fouad some appHcatioa ia the coaversioa of uranium oxides to UF (66), ia fluoriaatioa of actinide fluorides and oxyfluorides to AcF (67), and in the recovery of actinides from nuclear wastes (68) (see Actinides and transactinides Nuclear reaction, waste managel nt). 

Neutron-rich lanthanide isotopes occur in the fission of uranium or plutonium and ate separated during the reprocessing of nuclear fuel wastes (see Nuclearreactors). Lanthanide isotopes can be produced by neutron bombardment, by radioactive decay of neighboring atoms, and by nuclear reactions in accelerators where the rate earths ate bombarded with charged particles. The rare-earth content of solid samples can be determined by neutron... 

Pulsed plasmas containing hydrogen isotopes can produce bursts of alpha particles and neutrons as a consequence of nuclear reactions. The neutrons are useful for radiation-effects testing and for other materials research. A dense plasma focus filled with deuterium at low pressure has produced 10 neutrons in a single pulse (76) (see Deuterium AND TRITIUM). Intense neutron fluxes also are expected from thermonuclear fusion research devices employing either magnetic or inertial confinement. 

Delayed Proton and Neutron Decays. By means of a variety of nuclear reactions, as weh as the spontaneous fission of synthetic nucHdes, large numbers of isotopes of some elements have been produced. For example, whereas the only stable isotope of Cs (Z = 55) is Cs (JV = 78), ah of the Cs isotopes from Cs where 77 = 59 and = 0.57 s, to Cs where N = 93 and = 0.13 s, have been observed. At the low mass end of this series, the last proton is only loosely bound, and at the high mass end, the last neutron is only loosely bound. 

A.ccekrator-Producedlsotopes. Particle accelerators cause nuclear reactions by bombarding target materials, which are often enriched in a particular stable isotope, with rapidly moving protons, deuterons, tritons, or electrons. Proton reactions are most commonly used for production purposes. 

Occurrence and Recovery. Rhenium is one of the least abundant of the naturally occurring elements. Various estimates of its abundance in Earth s cmst have been made. The most widely quoted figure is 0.027 atoms pet 10 atoms of silicon (0.05 ppm by wt) (3). However, this number, based on analyses for the most common rocks, ie, granites and basalts, has a high uncertainty. The abundance of rhenium in stony meteorites has been found to be approximately the same value. An average abundance in siderites is 0.5 ppm. In lunar materials, Re, when compared to Re, appears to be enriched by 1.4% to as much as 29%, relative to the terrestrial abundance. This may result from a nuclear reaction sequence beginning with neutron capture by tungsten-186, followed by p-decay of of a half-hfe of 24 h (4) (see Extraterrestrial materials). 

Oil Contamination of Helium Gas. For more than 20 years, helium gas has been used in a variety of nuclear experiments to collect, carry, and concentrate fission-recoil fragments and other nuclear reaction products. Reaction products, often isotropically distributed, come to rest in helium at atmospheric concentration by coUisional energy exchange. The helium is then allowed to flow through a capillary and then through a pinhole into a much higher vacuum. The helium thus collects, carries, and concentrates products that are much heavier than itself, electrically charged or neutral, onto a detector... 

The principal methods for deterrnination of the deuterium content of hydrogen and water are based upon measurements of density, mass, or infrared spectra. Other methods are based on proton magnetic resonance techniques (77,78), F nuclear magnetic resonance (79), interferometry (80), osmometry (81), nuclear reaction (82), combustion (83), and falling drop methods (84). 

It has been claimed that the D-D fusion reaction occurs when D2O is electroly2ed with a metal cathode, preferably palladium, at ambient temperatures. This claim for a cold nuclear fusion reaction that evolves heat has created great interest, and has engendered a voluminous titerature filled with claims for and against. The proponents of cold fusion report the formation of tritium and neutrons by electrolysis of D2O, the expected stigmata of a nuclear reaction. Some workers have even claimed to observe cold fusion by electrolysis of ordinary water (see, for example. Ref. 91). The claim has also been made for the formation of tritium by electrolysis of water (92). On the other hand, there are many experimental results that cast serious doubts on the reahty of cold fusion (93—96). Theoretical calculations indicate that cold fusions of D may indeed occur, but at the vanishingly small rate of 10 events per second (97). As of this writing the cold fusion controversy has not been entirely resolved. 

Tritium was first prepared in the Cavendish Laboratory by Rutherford, OHphant, and Harteck in 1934 (2,3) by the bombardment of deuterophosphoric acid using fast deuterons. The D—D nuclear reaction produced tritium ( D-H D — -H energy), but also produced some He by a... 

Hot atom reactions have also been used to label organic compounds with T. Irradiation of helium-3 with neutrons according to the nuclear reaction produces very energetic tritium atoms that can displace ordinary hydrogen in organic compounds. This procedure is not very selective, and the labeling pattern must be determined to enable the tritiated product to be used effectively as a tracer (34). 

The principal source of natural tritium is the nuclear reactions induced by cosmic radiation in the upper atmosphere, where fast neutrons, protons, and deuterons coUide with components of the stratosphere to produce tritium ... 

Nuclear Reactions. The primary reaction for the production of tritium is... 

Production-Scale Processing. The tritium produced by neutron irradiation of Li must be recovered and purified after target elements are discharged from nuclear reactors. The targets contain tritium and He as direct products of the nuclear reaction, a small amount of He from decay of the tritium and a small amount of other hydrogen isotopes present as surface or metal contaminants. 

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