 A schematic nuclear fission chain reaction. 1. A uranium-235 atom absorbs a neutron, and fissions in two new atoms (fission fragments), releasing three new neutrons and some binding energy. 2. One of those neutrons is absorbed by an atom of uranium-238, and does not continue the reaction. Another neutron is simply lost and does not collide with anything, also not continuing the reaction. However one neutron does collide with an atom of uranium-235, which then fissions and releases two neutrons and some binding energy. 3. Both of those neutrons collide with uranium-235 atoms, each of which fission and release between one and three neutrons, which can then continue the reaction. A nuclear chain reaction occurs when on average more than one nuclear reaction is caused by another nuclear reaction, thus leading to an exponential increase in the number of nuclear reactions. Image File history File links No higher resolution available. ...
Image File history File links No higher resolution available. ...
For the generation of electrical power by fission, see Nuclear power plant An induced nuclear fission event. ...
Uranium-235 is an isotope of uranium that differs from the elements other common isotope, uranium-238, by its ability to cause a rapidly expanding fission chain reaction. ...
≈≈ This article or section does not cite its references or sources. ...
There are two objects with this name: Unterseeboot 238 Uranium-238, the most common isotope of uranium This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...
In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce different products than the initial products. ...
In mathematics, a quantity that grows exponentially is one whose growth rate is always proportional to its current size. ...
An uncontrolled chain reaction within a sufficiently large amount of fission fuel (critical mass) can lead to an explosive energy release and is the concept behind nuclear weapons. The chain reaction could also be adequately controlled and used as an energy source (nuclear reactor). A sphere of plutonium surrounded by neutron-reflecting blocks of tungsten carbide. ...
The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 km (11 mi) above the epicenter. ...
Core of a small nuclear reactor used for research. ...
Some fission equations, showing averages:
- U-235 + neutron -> fission fragments + 2.52 neutrons + 180 MeV.
- Pu-239 + neutron -> fission fragments + 2.95 neutrons + 200 MeV.
This excludes 10 MeV for unusable and hardly detectable neutrinos. An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...
Neutrinos are elementary particles. ...
When a heavy atom undergoes nuclear fission it breaks into two or more fission fragments. The fission fragments consist of atoms more lightweight than the original heavy atom. The sum of their masses do not precisely equal that of the heavy atom, even while accounting for the incident neutron. The difference (mass difference) consists of ejected neutrons and the release of binding energy. The neutrons leave the reaction at high speed, and may collide with other heavy atoms in a phenomenon known as "fission capture". This could result in nuclear fission, forming the basis of a chain reaction. For the generation of electrical power by fission, see Nuclear power plant An induced nuclear fission event. ...
Average generation time
The average generation time is the average time from neutron emission to fission capture. The neutrons travel only short distances, on the order of 10cm (the diameter of a critical mass);. An average neutron's speed varies around ca. 10 000 km/s, resulting in a timescale on the order of 10 ns. This quantity is often referred to as a shake. San Francisco Critical Mass, April 29, 2005 Critical Mass is a bike ride typically held on the last Friday of every month in cities around the world where bicyclists and, less frequently, skateboarders, roller bladers, roller skaters and other self-propelled commuters take to the streets en masse. ...
A shake is an informal unit of time equal to 10 nanoseconds, or 10-8 seconds. ...
Effective neutron multiplication factor The effective neutron multiplication factor or κ, is the average number of neutrons that go on to cause another fission reaction. The remaining neutrons either fail to induce fission, or are never absorbed and exit the system. The value of κ for a combination of two masses is always greater that of its components. In some cases its value is equal to the sum of the component κ values. The magnitude of the difference depends on velocity and distance, as well as physical orientation. Passing a small sphere through a small hole produces a particularly large κ: like firing a fissile 'bullet' into a shaped fissle target.
We can distinguish the following cases:
- k < 1 (sub-critical mass): starting with one fission, we have on average a total of 1/(1 − k) fissions. Any beginning of a chain reaction dies out quickly.
- k = 1 (critical mass): Starting with one free neutron, the expected value of the number of free neutrons resulting from it is 1 at any time; in the course of time there is a decreasing additional probability that the beginning chain reaction has died out, which is compensated by the possibility of multiple neutrons still being present.
- k > 1 (super-critical mass): starting with one free neutron, there is a non-trivial probability that is does not cause a fission or that a beginning chain reaction dies out. However, once the number of free neutrons is more than a few, it is very likely that it will increase exponentially. Both the number of neutrons present in the assembly (and thus the instantaneous rate of the fission reaction), and the number of fissions that have occurred since the reaction began, is proportional to e(k − 1)t / g, where g is the average generation time and t is the elapsed time. This cannot continue, of course: k decreases when the amount of fission material that is left decreases; also the geometry and density can change: the geometry radically changes when the remaining fission material is torn apart, but in other circumstances it can just melt and flow away, etc.
When k is close to 1, this calculation somewhat over-estimates the 'doubling rate'. When a uranium nucleus absorbs a neutron it enters a very-short-lived excited state which then decays by several possible routes. Typically it decays into two fragments, fission products, typically isotopes of Iodine and Cesium, with expulsion of a number of neutrons. The fission products are themselves unstable, with a wide range of lifetimes, but typically several seconds, and decay producing further neutrons. To meet Wikipedias quality standards, this article or section may require cleanup. ...
It is usual to split the population of neutrons which are emitted into two sorts - 'prompt neutrons' and 'delayed neutrons' Typically, the 'delayed neutron fraction' is less than 1 % of the whole. In a nuclear reactor the variable k is typically around 1 to have a steady process. When a value of k = 1 is achieved when all neutrons produced are considered the reaction is said to be 'critical'. This is the situation achieved in a nuclear reactor. The power changes are then slow, and controllable e.g. with control rods. When k = 1 is achieved counting only the 'prompt' neutrons, the reaction is said to be 'prompt critical' - much shorter doubling rates can then occur, depending on the excess criticality (k-1). The change in reactivity needed to go from critical to prompt critical (ie the delayed neutron fraction) is defined as a dollar. In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anytime from a few milliseconds to a few minutes later. ...
A control rod is a rod made of a chemical element capable of absorbing many neutrons without decaying themselves. ...
In nuclear engineering, an assembly is prompt critical if for each nuclear fission event, one or more of the immediate or prompt neutrons released causes an additional fission event. ...
Dollar has these meanings: Dollar, a unit of currency Australian dollar Bahamian dollar Belize dollar Brunei dollar Canadian dollar East Caribbean dollar Hong Kong dollar International dollar Namibian dollar New Zealand dollar Singapore dollar Suriname dollar New Taiwan dollar United States dollar Zimbabwe dollar Petro-dollars is money from petroleum. ...
The value of k is increased by a neutron reflector surrounding the fissile material, and also by increasing the density of the fissile material: the probability for a neutron per cm travelled to hit a nucleus is proportional to the density, while the distance travelled before leaving the system is only reduced by the cube root of the density. In the implosion method for nuclear weapons, detonation takes place by increasing the density with a conventional explosive. Nuclear weapon designs are often divided into two classes, based on the dominant source of the nuclear weapons energy. ...
The first nuclear weapons, though large, cumbersome and inefficient, provided the basic design building blocks of all future weapons. ...
The probability of a chain reaction Suppose a fission caused by a neutron hitting a nucleus produces 3 neutrons (i.e. 2 extra). Also suppose k > 1. The probability that a neutron causes a fission is k / 3. The probability that a free neutron does not cause a chain reaction is (1 - k / 3) (no fission at all) plus the probability of at least one fission, while none of the 3 neutrons produced causes a chain reaction. The latter has a probability of k / 3 times the cube of the first-mentioned probability that a free neutron does not cause a chain reaction. This equation can be solved easily, giving a probability of a chain reaction of  which ranges from 0 for k = 1 to 1 for k = 3.
For values of k which are little above 1 we get approximately k - 1.
Predetonation Detonation of a nuclear weapon involves bringing fissile material into its optimal supercritical state very rapidly. During part of this process the assembly is supercritical, but not yet in optimal state for a chain reaction. Free neutrons, in particular from spontaneous fissions, can cause predetonation. To keep the probability low, the duration of this period is minimized and fissile and other materials are used for which there are not too many spontaneous fissions. In fact, the combination has to be such that it is unlikely that there is even a single spontaneous fission during the period of assembly. In particular the gun method cannot be used with plutonium, see nuclear weapon design. Spontaneous fission (SF) is a form of radioactive decay characteristic of very heavy isotopes, and is theoretically possible for any atomic nucleus whose mass is greater than or equal to 100 amu (elements near ruthenium). ...
The first nuclear weapons, though large, cumbersome and inefficient, provided the basic design building blocks of all future weapons. ...
History The concept was first developed by Leó Szilárd in 1933. He supposedly thought of the idea while waiting for a red light. He then patented the concept the following year. Leó Szilárd (February 11, 1898 – May 30, 1964 Originally Szilárd Leó) was a Jewish Hungarian-American physicist who conceived the nuclear chain reaction and worked on the Manhattan Project. ...
Year 1933 (MCMXXXIII) was a common year starting on Sunday. ...
Leo Szilárd attempted to create a chain reaction using beryllium and indium in 1936 but was unsuccessful. In 1939, Leo Szilárd and Enrico Fermi discovered neutron multiplication in Uranium, proving that the chain reaction was possible. General Name, Symbol, Number beryllium, Be, 4 Chemical series alkaline earth metals Group, Period, Block 2, 2, s Appearance white-gray metallic Atomic mass 9. ...
General Name, Symbol, Number indium, In, 49 Chemical series poor metals Group, Period, Block 13, 5, p Appearance silvery lustrous gray Atomic mass 114. ...
The first artificial self-sustaining nuclear chain reaction was initiated by the Metallurgical Laboratory, led by Enrico Fermi and Leó Szilárd, in a racquets court below the bleachers of Stagg Field at the University of Chicago on December 2, 1942 during the Manhattan Project. The Metallurgical Laboratory or Met Lab at the University of Chicago was part of the World War II–era Manhattan Project, created by the United States to develop an atomic bomb. ...
Enrico Fermi (September 29, 1901 – November 28, 1954) was an Italian physicist most noted for his work on the development of the first nuclear reactor, and for his contributions to the development of quantum theory, particle physics and statistical mechanics. ...
R. P. Keigwin (right) with AEJ Collins the Colleges racquets team at Clifton College circa 1902 Rackets (British English) or Racquets (American English), is an indoor racquet sport played in the United Kingdom, United States, and Canada. ...
Stagg Field was a stadium in Chicago, Illinois. ...
The University of Chicago is a private university located principally in the Hyde Park neighborhood of Chicago. ...
December 2 is the 336th day (337th in leap years) of the year in the Gregorian calendar. ...
Year 1942 (MCMXLII) was a common year starting on Thursday (the link is to a full 1942 calendar). ...
The Manhattan Project resulted in the development of the first nuclear weapons, and the first-ever nuclear detonation, at the Trinity test of July 16, 1945. ...
The only known natural self-sustaining nuclear chain reactions were discovered at Oklo in September 1972. Natural Reactors refer to a handful of Uranium deposits that have been discovered, mostly in Oklo, Gabon. ...
Oklo is a place in the West African state of Gabon. ...
See also A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions. ...
A sphere of plutonium surrounded by neutron-reflecting blocks of tungsten carbide. ...
A criticality accident (also sometimes referred to as an excursion or power excursion) occurs when a nuclear chain reaction is accidentally allowed to occur in fissile material, such as enriched uranium or plutonium. ...
Nuclear physics is the branch of physics concerned with the nucleus of the atom. ...
In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce different products than the initial products. ...
The first nuclear weapons, though large, cumbersome and inefficient, provided the basic design building blocks of all future weapons. ...
Nuclear criticality safety is a field of nuclear engineering dedicated to the prevention of an inadvertent, self-sustaining nuclear chain reaction. ...
Most nuclear reactors use a chain reaction to induce a controlled rate of nuclear fission in fissile material, releasing both energy and free neutrons. ...
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