Nuclear fission balancing equations, 64

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 ... 

Balance the following equations for the nuclear fission of 235U ... 

The principles of balancing nuclear equations apply to all nuclear reactions. Nuclear fission occurs when a highly unstable isotope splits into smaller particles. Nuclear fission usually has to be induced in a particle accelerator. Here, an atom can absorb a stream of high-energy particles such as neutrons, Jn. This will cause the atom to split into smaller fragments. 

It is characteristic of nuclear reactions of the type occurring in nuclear reactors that the sum of the number of neutrons and protons in the reactants equals the sum in the products. The same is true of the charge of the reactants and products. Consequently, in balancing nuclear reactions, the sum of the s of the reactants must equal the sum of the. 4 s of the products and the sum of the Z s of the reactants must equal the sum of the Z s of the products. As an example of a balanced equation for a nuclear reaction, we may consider one of the fission reactions that occurs when absorbs a neutron ... 

Skill 20.6 Apply strategies for writing and balancing equations for nuclear reactions (e.g., fission, fusion, radioactivity and bombardment). 

Write one balanced equation that illustrates nuclear fission. 

Radioactive nuclei emit a particles, 13 particles, positrons, or y rays. The equation for a nuclear reaction includes the particles emitted, and both the mass numbers and the atomic numbers must balance. Uranium-238 is the parent of a natural radioactive decay series. A number of radioactive isotopes, such as and C, can be used to date objects. Artificially radioactive elements are created by the bombardment of other elements by accelerated neutrons, protons, or a particles. Nuclear fission is the splitting of a large nucleus into smaller nuclei plus neutrons. When these neutrons are captured efficiently by other nuclei, an uncontrollable chain reaction can occur. Nuclear reactors use the heat... 

The most abundant isotope of uranium, 238U, does not undergo fission. In a breeder reactor, however, a 238U atom captures a neutron and emits two /3 particles to make a fissionable isotope of plutonium, which can then be used as fuel in a nuclear reactor. Write a balanced nuclear equation. 

Energy released during fission is calculated by using Einstein s equation. -> For a balanced nuclear reaction,... 

We are now in position to derive equations that will give the degree uf bumup nuclear fuel can experience before it ceases to be critical. First, we must determine how the concentration of each nuclide that affects the neutron balance changes with time. We consider fuel that at time zero contains N s atoms of U per cubic centimeter, atoms of U, and no other uranium isotopes, plutonium, or fission products. This fuel is then exposed to a thermal-neutron flux 0(0, which may be a function of time. The variation in concentration of each nuclide in this fuel with time is obtained as follows. 

The uranium-239 then undergoes two beta decays, first to Np, and then to Pu, which is a fissionable material and the desired product. Write balanced nuclear equations for the bombardment reaction and the two beta-decay reactions. 

Complete and balance the nuclear equations for the following fission or fusion reactions ... 

As laid out in the Equation 21.1 definition of /c-effective, the basic neutron balance relationship is between fission neutron production and neutron loss mechanisms, the two neutron loss mechanisms being neutron absorption and neutron leakage. Nuclear reactors, for which criticality must be created and maintained for extended periods, tend to be large devices—both for neutron balance reasons and because of the large fuel inventory required to deliver substantial amounts of power for long periods of time. The result of this, from the point of view of the A -effective equation, is that neutron leakage is a relatively unimportant neutron... 

In another fission reaction, uranium-235 bombarded with a neutron produces strontium-94, another small nucleus, and three neutrons. Write the balanced nuclear equation for the fission reaction. 

Plutonium-239 is also a fissionable isotope. In one of the possible reactions, it produces three neutrons and strontium-90. Write a balanced nuclear equation for this process. 

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