Critical fission reaction

Every fission reaction releases some neutrons, and these neutrons can be recaptured by other nuclei, causing more fission reactions. When the amount of fissionable material is small, most neutrons escape from the sample, and only a few neutrons are recaptured. Increasing the amount of material increases the likelihood that neutrons will be recaptured and cause additional fission reactions. The critical mass is defined as the amount of material that is just large enough to recapture one neutron, on average, for every fission reaction. 

As long as the amount of fissionable material is less than the critical mass, the rate of fission events does not grow, and the rate of energy release remains low. In contrast, a sample behaves quite differently when the amount of fissionable material is larger than the critical mass. Above the critical mass, more than one neutron, on average, is recaptured for every fission that occurs. Now the number of fission reactions grows rapidly. As an illustration, consider what happens when two neutrons are recaptured from each fission reaction. As shown in figure 22-11 on... 

Notice that the reaction consumes one neutron, but the reaction releases three neutrons. Those three neutrons are then free to initiate additional fission reactions. This type of situation in which there is a multiplier effect is a chain reaction. We can use isotopes that undergo chain reaction in both the production of bombs and in nuclear power plants. U-235 is fissionable, but U-238 is not. There is a certain minimum quantity of fissionable matter needed to support a chain reaction, the critical mass. 

CRITICAL MASS. The amount of concentrated fissionable material that can just support a self-sustaining fission reaction. See also Nuclear Power Technology. 

Of the fast neutrons produced in fission, some of them will be moderated to thermal energies and will induce other fission reactions while others will be lost. The ratio of the number of neutrons in the next generation to that in the previous generation is called the multiplication factor k. If the value of k is less than 1, then the reactor is subcritical and the fission process is not self-sustaining. If the value of k is greater than 1, then the number of fissions will accelerate with time and the reactor is supercritical. The goal of reactor operation is to maintain the system in a critical state with k exactly equal to 1. The extreme upper limit for the multiplication factor would correspond to the mean number of neutrons per fission ( 2.5 for 235U(n,f)) if each neutron produces a secondary fission. 

In the 1941 paper with Yu. B. Khariton [40], the problem of the critical size of a sample of 235 U in the fission of nuclei by fast neutrons was considered. The calculations showed that, in order to sustain a chain fission reaction by fast neutrons in a sample of 235 U surrounded by a heavy neutron reflector, it is sufficient to have only ten kilograms of pure 235U isotope. Here also a theory is given which allows calculation of the critical mass of... 

In the chain reaction shown in Figure 14.5, if there is so little uranium that the released neutrons escape before they have a chance to cause a fission reaction, the reaction stops. The critical mass is the minimum mass of fissionable material needed in order for the reaction to continue. The critical mass concept is the key to the design of a fission-type nuclear weapon. In such a weapon, two smaller-than-critical masses are present but are separated. When these subcritical masses are suddenly combined, the rapidly escalating fission reactions produce an explosion of incredible intensity. 

The neutrons produced by this fission reaction can potentially collide with other U-235 nuclei. The likelihood of the extra neutrons striking other nuclei increases as the mass of the sample increases. At a characteristic mass, the neutrons are assured to collide with U-235 nuclei, and as a result, a chain reaction begins. In this chain reaction, the neutrons from one fission will strike other nuclei and cause additional fission reactions. The mass at which a self-sustaining chain reaction will occur is known as the critical mass. Fission reactions are responsible for the production of nuclear power and for the design of nuclear weapons. 

In addition to the product nuclides, neutrons are produced in the fission reactions of This makes it possible to produce a self-sustaining fission process—a chain reaction (see Fig. 21.12). For the fission process to be self-sustaining, at least one neutron from each fission event must go on to split another nucleus. If, on the average, less than one neutron causes another fission event, the process dies out the reaction is said to be subcritical. If exactly one neutron from each fission event causes another fission event, the process sustains itself at the same level and is said to be critical. If more than one neutron from each fission event causes another fission event, the process rapidly escalates and the heat buildup causes a violent explosion. This situation is described as supercritical. 

A sample of fissionable material must have sufficient mass in order for a fission chain reaction to occur. If it does not, neutrons escape from the sample before they have the opportunity to strike other nuclei and continue the chain reaction— the chain reaction never begins. A sample that is not massive enough to sustain a chain reaction is said to have subcritical mass. A sample that is massive enough to sustain a chain reaction has critical mass. When a critical mass is present, the neutrons released in one fission cause other fissions to occur. If much more mass than the critical mass is present, the chain reaction rapidly escalates. This can lead to a violent nuclear explosion. A sample of fissionable material with a mass greater than the critical mass is said to have supercritical mass. Figure 25-18 shows the effect of mass on the initiation and progression of a fission reaction. 

Typically, two or three neutrons are produced per fission reaction. These neutrons can collide with other fissionable atoms to repeat the process. If sufficient fissionable material, the critical mass, is contained in a small enough volume, a sustained chain reaction can result. If too few fissionable atoms are present, most of the neutrons escape and no chain reaction occurs. Figure 26-11 depicts a fission chain reaction. 

Figure 23.8 shows two types of fission reactions. For a chain reaction to occur, enough uranium-235 must be present in the sample to capture the neutrons. Otherwise, many of the neutrons will escape from the sample and the chain reaction will not occur, as depicted in Figure 23.8(a). hi this situation the mass of the sample is said to be subcritical. Figure 23.8(b) shows what happens when the amount of the fissionable material is equal to or greater than the critical mass, the minimum mass of fissionable material required to generate a self-sustaining nuclear chain reaction, hi this case most of the neutrons will be captured by uranium-235 nuclei, and a chain reaction will occur. 

For obvious reasons, an atomic bomb is never assembled with the critical mass already present. Instead, the critical mass is formed by using a conventional explosive, such as TNT, to force the fissionable sections together, as shown in Figure 23.9. Neutrons from a source at the center of the device trigger the nuclear chain reaction. Uranium-235 was the fissionable material in the bomb dropped on Hiroshima, Japan, on August 6, 1945. Plutonium-239 was used in the bomb exploded over Nagasaki three days later. The fission reactions generated were similar in these two cases, as was the extent of the destruction. 

The fission of U-235 is used exclusively in nuclear power plants located in the United States. There are many different fission reactions of U-235, but all the fission reactions are self-sustaining chain reactions. Explain. Differentiate between the terms critical, subcritical, and supercritical. What is the critical mass How does a nuclear power plant produce electricity What are the purposes of the moderator and the control rods in a fission reactor What are some problems associated with nuclear reactors What are breeder reactors What are some problems associated with breeder reactors ... 

If more than a critical mass of fissionable material is present, very few neutrons escape. The chain reaction thus multiplies the number of fissions, which can lead to a nuclear explosion. A mass in excess of a critical mass is referred to as a supercritical mass. The effect of mass on a fission reaction is illustrated in T FIGURE 21.15. 

In the period of 1998-99, two sets of experiments focused on problems of rapid decrease of concentration of boric acid in reactor coolant at nuclear reactor core inlet were performed at the University of Maryland, US, under the auspices of OECD. The situation, when there is an inadvertent supply of boron-deficient water into the reactor vessel, could lead to a rapid (very probably local) increase of reactor core power in reactor, operated at nominal power, or to a start of fission reaction in shut-down reactor (secondary criticality). In the above mentioned experiments the transport of boron-deficient coolant through reactor downcomer and lower plenum was simulated by flow of cold water into a model of reactor vessel. These experiments were selected as the International Standard Problem ISP-43 and organisations, involved in thermal — hydraulic calculations of nuclear reactors, were invited to participate in their computer simulation. Altogether 10 groups took part in this problem with various CFD codes. The participants obtained only data on geometry of the experimental facility, and initial and boundary conditions. 

Uranium-235, uranium-233, and plutonium-239 undergo fission when they capture a neutron, splitting into lighter nuclei and releasing more neutrons. The neutrons produced in one fission can cause further fission reactions, which can lead to a nuclear chain reaction. A reaction that maintains a constant rate is said to be critical, and the mass necessary to maintain this constant rate is called... 

In nuclear fission, a heavy nuclens sphts into two smaller nnclei when bombarded with a neutron. The process releases large amonnts of energy and additional neutrons, which can lead to a chain reaction if critical mass is present. Nuclear fission reactions are employed in atomic bombs and nuclear reactors. (23.5)... 

As it was shown before, the condition for the establishment of a chain reaction is that at least one of the neutrons originating from fission is inducing a new fission reaction. This condition is expressed by the neutron multiplication factor k (also called criticality factor), k is defined as... 

A nuclear weapon is a fission assembly with a very short neutron cycle time t = 10 s. The criticality factor in a fission weapon is near k=2. From these parameters and Eq. (57.34) it can be easily estimated that the fission reaction in a bomb is over in less than 10 s. 

One metric for criticality is the fc-effective eigenvalue, which can be looked at in several ways. The simplest is as the average number of fission events that result from the neutrons emitted from a single original fission event. If this number is 1, then the rate of fission reactions will be maintained with time. If greater than 1, the reaction rate will increase and if less than 1, it will decrease ... 

In order for a fission chain reaction to occur, the sample of fissionable material must have a certain minimum mass. Otherwise, neutrons escape from the sample before they have the opportunity to strike other nuclei and cause additional fission. The chain stops if enough neutrons are lost. The amount of fissionable material large enough to maintain the chain reaction with a constant rate of fission is called the critical mass. When a critical mass of material is present, one neutron on average from each fission is subsequently effective in producing another fission. The critical mass of uraiiium-235 is about 1 kg. If more than a critical mass of fissionable material is present, very few neutrons escape. The chain reaction thus multiplies the number of fissions, which can lead to a nuclear explosion. Amass in excess of a critical mass is referred to as a supercritical mass. The effect of mass on a fission reaction is illustrated in Figure 21.16 A. 

Explain the following terms that apply to fission reactions (a) chain reaction (b) critical mass. 

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