Nuclear equation balancing

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

To summarize, the equation for a nuclear reaction is balanced when the total charge and total mass number of the products equals the total charge and total mass number of the reactants. This conservation requirement is one reason why the symbol for any nuclide includes its charge number (Z) as a subscript and its mass number as a superscript. These features provide a convenient way to keep track of charge and mass balances. Notice that in the equation for neutron decay, the sum of the subscripts for reactants equals the sum of the subscripts for products. Likewise, the sum of the superscripts for reactants equals the sum of the superscripts for products. We demonstrate how to balance equations for other reactions as they are introduced. 

A chemical equation describes a chemical reaction in many ways as an empirical formula describes a chemical compound. The equation describes not only which substances react, but the relative number of moles of each undergoing reaction and the relative number of moles of each product formed. Note especially that it is the mole ratios in which the substances react, not how much is present, that the equation describes. In order to show the quantitative relationships, the equation must be balanced. That is, it must have the same number of atoms of each element used up and produced (except for special equations that describe nuclear reactions). The law of conservation of mass is thus obeyed, and also the "law of conservation of atoms. Coefficients are used before the formulas for elements and compounds to tell how many formula units of that substance are involved in the reaction. A coefficient does not imply any chemical bonding between units of the substance it is placed before. The number of atoms involved in each formula unit is multiplied by the coefficient to get the total number of atoms of each element involved. Later, when equations with individual ions are written (Chap. 9), the net charge on each side of the equation, as well as the numbers of atoms of each element, must be the same to have a balanced equation. The absence of a coefficient in a balanced equation implies a coefficient of 1. 

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 ... 

Just as an ordinary chemical equation is a shortened version of the complete thermochemical equation which expresses both energy and mass balance, each nuclear equation has a term (written or implied) expressing energy balance. The symbol Q is usually used to designate the net energy released when all reactant and product particles of matter are at zero velocity. Q is the energy equivalent of the mass decrease (discussed above) accompanying the reaction. Q is usually expressed in MeV. 

Nuclear transmutations are represented by nuclear equations. Nuclear equations show the change in the nucleus as well as the particle emitted during the decay process. Just like chemical equations, these equations must follow the Law of Conservation of Mass and the Law of Conservation of Charge. That is, they are balanced by equating the sum of mass numbers on both sides of a reaction equation and the sum of atomic numbers on both sides of a reaction equation. 

Given this information, what is bXl You can use your knowledge of how to balance a nuclear equation to determine the identity of a radioisotope undergoing alpha particle decay. 

Complete and balance each nuclear equation. Then classify the reaction. 

The superscripts represent the mass numbers, and the (optional) subscripts represent the atomic numbers or charges. Knowing that the superscripts and subscripts must balance allows us to deduce one species involved in a reaction if all the others are given. The process is often called balancing a nuclear equation. ... 

Boron halides, 146-148 Boron hydride, ammoniates of, 154 balance equations and, 138 nuclear resonance studies,... 

The following rules are helpful for balancing a nuclear equation and... 

Write balanced equations for the following nuclear equations. 

Balancing a Nuclear Equation Determining the Age of an Artifact Determining the Original Mass of ... 

Write a balanced equation for the nuclear reaction that produces... 

Write balanced equations that represent the following nuclear reactions. 

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