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why does a chain reaction not occur in uranium mines

Nuclear fission takes place when a large, somewhat unstable isotope(atoms with the same number of protons but different number ofneutrons) is bombarded by high-speed particles, usually neutrons. These neutrons are accelerated and then slammed into the unstableisotope, causing it to fission, or break into smaller particles. During the process, a neutron is accelerated and strikes the targetnucleus, which in the majority of nuclear power reactors today isUranium-235. This splits the target nucleus and breaks it down intotwo smaller isotopes (the fission products), three high-speedneutrons, and a large amount of energy in a process calledacceleration. This produces a chain reaction that must be controlled or it will'run away' causing a major disaster. The reaction is usuallycontrolled by control rods, which are made of a neutron absorbingmaterial, are placed into the core and are literally raised andlowered to tweak the reaction - if you need to generate more heat,you raise the rods out of the core to let more neutrons split moreatoms. To curb the reaction, you lower the rods into the core toabsorb more of the neutrons before they have a chance to come incontact with the uranium.

In emergency cases (like recently inJapan), the rods are automatically shoved into the core usinggravity, hydraulics or a mechanical spring, causing the chainreaction to stop. This is called "SCRAMing" the reactor. ~ Wondered
The prompt neutron lifetime, l, is the average time between the emission of neutrons and either their absorption in the system or their escape from the system. The neutrons that occur directly from fission are called "," and the ones that are a result of radioactive decay of fission fragments are called ". " The term lifetime is used because the emission of a neutron is often considered its "birth," and the subsequent absorption is considered its "death. " For thermal (slow-neutron) fission reactors, the typical prompt neutron lifetime is on the order of 10 seconds, and for fast fission reactors, the prompt neutron lifetime is on the order of 10 seconds. These extremely short lifetimes mean that in 1 second, 10,000 to 10,000,000 neutron lifetimes can pass. The average (also referred to as the adjoint unweighted ) prompt neutron lifetime takes into account all prompt neutrons regardless of their importance in the reactor core; the effective prompt neutron lifetime (referred to as the adjoint weighted over space, energy, and angle) refers to a neutron with average importance.

The mean generation time, K, is the average time from a neutron emission to a capture that results in fission. The mean generation time is different from the prompt neutron lifetime because the mean generation time only includes neutron absorptions that lead to fission reactions (not other absorption reactions). The two times are related by the following formula: In this formula, k is the effective neutron multiplication factor, described below. The, k, is the average number of neutrons from one fission that cause another fission. The remaining neutrons either are absorbed in non-fission reactions or leave the system without being absorbed. The value of k k 1 ( ): The system cannot sustain a chain reaction, and any beginning of a chain reaction dies out over time. For every fission that is induced in the system, an average total of 1/(1PP k ) fissions occur. k = 1 ( ): Every fission causes an average of one more fission, leading to a fission (and power) level that is constant. Nuclear power plants operate with k = 1 unless the power level is being increased or decreased. k 1 ( ): For every fission in the material, it is likely that there will be " k " fissions after the next mean generation time (K).

The result is that the number of fission reactions increases exponentially, according to the equation, where t is the elapsed time. Nuclear weapons are designed to operate under this state. There are two subdivisions of supercriticality: prompt and delayed. When describing kinetics and dynamics of nuclear reactors, and also in the practice of reactor operation, the concept of reactivity is used, which characterizes the deflection of reactor from the critical state. q=(k-1)/k. is a unit of reactivity of a nuclear reactor. In a nuclear reactor, k will actually oscillate from slightly less than 1 to slightly more than 1, due primarily to thermal effects (as more power is produced, the fuel rods warm and thus expand, lowering their capture ratio, and thus driving k lower). This leaves the average value of k at exactly 1. Delayed neutrons play an important role in the timing of these oscillations. In an infinite medium, the multiplication factor may be described by the ; in a non-infinite medium, the multiplication factor may be described by the.

Not all neutrons are emitted as a direct product of fission; some are instead due to the of some of the fission fragments. The neutrons that occur directly from fission are called "," and the ones that are a result of radioactive decay of fission fragments are called "delayed neutrons. " The fraction of neutrons that are delayed is called b, and this fraction is typically less than 1% of all the neutrons in the chain reaction. The delayed neutrons allow a nuclear reactor to respond several orders of magnitude more slowly than just prompt neutrons would alone. Without delayed neutrons, changes in reaction rates in nuclear reactors would occur at speeds that are too fast for humans to control. The region of supercriticality between k = 1 and k = 1/(1-b) is known as delayed supercriticality (or ). It is in this region that all nuclear power reactors operate. The region of supercriticality for k 1/(1-b) is known as prompt supercriticality (or ), which is the region in which nuclear weapons operate. The change in k needed to go from critical to prompt critical is defined as a.

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