NationMaster - Encyclopedia: Critical mass (nuclear)

The critical mass of fissile material is the amount needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon the nuclear (e.g. the nuclear fission cross-section) and physical properties of the material (in particularly the density), its geometry (shape), and its purity, as well as whether it is surrounded by a neutron reflector or interrupted by an absorber. See also neutron radiation. Image File history File links A sphere of partially surrounded by neutron-reflecting tungsten-carbide blocks. ... Image File history File links A sphere of partially surrounded by neutron-reflecting tungsten-carbide blocks. ... General Name, Symbol, Number plutonium, Pu, 94 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery white Atomic mass (244) g/mol Electron configuration [Rn] 5f6 7s2 Electrons per shell 2, 8, 18, 32, 24, 8, 2 Physical properties Phase solid Density (near r. ... Tungsten carbide, WC or W2C, is a chemical compound containing tungsten and carbon similar to titanium 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. ... This article or section should include material from Fissile material In nuclear engineering, a fissile material is one that is capable of sustaining a chain reaction of nuclear fission. ... Albert Einsteins letter to President Roosevelt in 1939 about his concern, about (Nuclear chain reactions) Click for closeup of letter 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... A stylized representation of a lithium atom. ... Sketch of induced nuclear fission, a neutron (n) strikes a uranium nucleus which splits into similar products (F. P.), and releases more neutrons to continue the process, and energy in the form of gamma and other radiation. ... Cross section may refer to the following In geometry, Cross section is the intersection of a 3-dimensional body with a plane. ... Nuclear weapon designs are often divided into two classes, based on the dominant source of the nuclear weapons energy. ... Neutron radiation consists of free neutrons. ...

An assembly in which a chain reaction is just possible is called critical, and is said to have obtained criticality. In such an assembly, without new input of free neutrons, e.g. from spontaneous fissions, the reaction will on average be just sustained, and in the case of a steady input of new free neutrons, the reaction will increase linearly. A more than critical assembly is termed supercritical. An assembly that is capable of sustaining a chain reaction without needing the contribution of delayed neutrons is called prompt critical (and is therefore also supercritical). Even larger masses are called superprompt critical. Assembly may refer to the following things: In politics, any body meeting together to discuss matters, a parliament or a legislative assembly such as the French revolutionary Legislative Assembly, or a body more designed to mediate between otherwise independent bodies, such as the United Nations General Assembly. ... A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions. ... 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). ... 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 anything from a few milliseconds to a few minutes later. ... 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. ...

If an assembly is less than critical, then with a steady input of new free neutrons the fission reaction will reach a steady state, and the assembly is said to be subcritical.

The realisation that a supercritical assembly is not necessarily prompt critical is attributed to Enrico Fermi, and made the construction of a nuclear reactor using a fission chain reaction possible. Any prompt critical assembly will explode if not rapidly brought below prompt criticality. Enrico Fermi in the 1940s. ... Core of a nuclear reactor A nuclear reactor is a device in which nuclear chain reactions are initiated, controlled, and sustained at a steady rate (as opposed to a nuclear explosion, where the chain reaction occurs in a split second). ...

Critical mass of a sphere

The shape with minimum critical mass is a sphere. This can be further reduced by surrounding the sphere with a neutron reflector.

In the case of a sphere surrounded by a neutron reflector the critical mass is about 15 kg for uranium-235 (20 to 25 kg for a gun-type assembly) and 10 kg for plutonium-239. 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. ... General Name, Symbol, Number plutonium, Pu, 94 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery white Atomic mass (244) g/mol Electron configuration [Rn] 5f6 7s2 Electrons per shell 2, 8, 18, 32, 24, 8, 2 Physical properties Phase solid Density (near r. ...

Bare-sphere critical masses of some other isotopes whose half-lives exceed 100 years are compiled in the following table. Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ...

The critical mass for lower-grade uranium depends strongly on the grade: with 20 % U-235, and surrounded by a 4 cm thick beryllium neutron reflector, it is over 400 kg; with 15 % U-235, it is well over 1000 kg. General Name, Symbol, Number protactinium, Pa, 91 Chemical series actinides Group, Period, Block ?, 7, f Appearance bright, silvery metallic luster Atomic mass 231. ... General Name, Symbol, Number uranium, U, 92 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery gray metallic Atomic mass 238. ... 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. ... General Name, Symbol, Number neptunium, Np, 93 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery metallic Atomic mass (237) g/mol Electron configuration [Rn] 5f4 6d1 7s2 Electrons per shell 2, 8, 18, 32, 22, 9, 2 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number plutonium, Pu, 94 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery white Atomic mass (244) g/mol Electron configuration [Rn] 5f6 7s2 Electrons per shell 2, 8, 18, 32, 24, 8, 2 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number americium, Am, 95 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery white Atomic mass (243) g/mol Electron configuration [Rn] 5f7 7s2 Electrons per shell 2, 8, 18, 32, 25, 8, 2 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number curium, Cm, 96 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery Atomic mass (247) g/mol Electron configuration [Rn] 5f7 6d1 7s2 Electrons per shell 2, 8, 18, 32, 25, 9, 2 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number californium, Cf, 98 Chemical series actinides Group, Period, Block ?, 7, f Appearance unknown, probably silvery white or metallic gray Atomic mass (251) g/mol Electron configuration [Rn] 5f10 7s2 Electrons per shell 2, 8, 18, 32, 28, 8, 2 Physical properties Phase solid Density (near r. ...

The critical mass is inversely proportional to the square of the density: if the density is 1% more and the mass 2% less than the volume is 3% less and the diameter 1% less. The probability for a neutron per cm travelled to hit a nucleus is proportional to the density, so 1% more, which compensates that the distance travelled before leaving the system is 1% less.

Weapon design

Until detonation is desired, a nuclear weapon must be kept subcritical. In the case of a uranium bomb, this can be achieved by keeping the fuel in a number of separate pieces, each below the critical size either because they are too small or unfavorably shaped. To produce detonation, the uranium is brought together rapidly. In Little Boy, this was achieved by firing a smaller piece of uranium down a gun barrel into a corresponding hole in a larger piece, a design referred to as a gun-type fission weapon. The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 km (11 mi) above the hypocenter. ... The critical size is the minimum size of a nuclear reactor core or nuclear weapon that can be made critical for a specific geometrical arrangement and material composition. ... Little Boy bomb casing Little Boy was the codename given to the nuclear weapon dropped on Hiroshima, Japan on Monday, August 6, 1945. ... The barrel of a gun or other firearm is the tube, usually metal, through which a controlled explosion is released in order to propel a projectile out of the end at great speed. ... Gun-type fission weapons are fission-based nuclear weapons whose design assembles their fissile material into a supercritical mass by the use of the gun method: shooting one piece of sub-critical material into another. ...

No means of physical assembly from separate pieces has been devised to produce a successful plutonium bomb. Instead, the plutonium is present as a subcritical sphere, which may or may not be hollow). Detonation is produced by exploding a shaped charge surrounding the sphere, increasing the density (and collapsing the cavity, if that was present) to produce a prompt critical configuration. This is known as an implosion type weapon. A shaped charge is an explosive charge shaped to focus the effect of the released energy. ... The first nuclear weapons, though large, cumbersome and inefficient, provided the basic design building blocks of all future weapons. ...

Criticality pathways tutorial

There are two typical presentations of how to vary a single parameter and reach criticality. Ultimately, both are fundamentally a function of geometry alone. An attempt to develop intuition on the concept is presented. In neither case would it actually work because the assembly would melt and, perhaps, fly apart, but this is for illustrative purposes only.

Imagine you have many marbles made of U-235 and an empty beaker. You start dropping marbles in the breaker, one by one. At some point the assembly will warm slightly. Add another one. It warms much more. Add another one and it warms a lot more. You are beginning to approach criticality. If you add more, it will melt through the beaker; if you could do it fast enough, it would detonate. From a geometric point of view, you are merely gathering the marbles together, but you can think of it as adding more mass to the assembly.

Start with a fixed but sufficient amount U-235 marbles with holes drilled though in the x, y and z directions, slightly off-center so that they do not intersect at the center of the marble. Thread slender strong rods through beads and build up a 3-D simple cubic lattice, like those models of salt (NaCl) in your chemistry class. The difference is that you can slide the beads along the rods. Grab opposite corners of the cubic lattice and play with them a little, growing and shrinking the cubic lattice. Suddenly, push as hard and fast as you can, to bring all the marbles together, all at once. No human can push hard and fast enough for a detonation, but in principal that could be the result. The high explosives in an implosion-type nuclear weapon provide trivial thermal and no chemical factors to the nuclear detonation; their important contribution is sudden compression and, therefore, geometry alone, just like bringing two sub-critical objects of U-235 together to form a critical mass in a gun type weapon, as mentioned above.

The practical engineering calculations involve two parameters: mass and radius of sphere. Start with sufficient mass, compress it into a smaller sphere via high explosives. Boom. One other useful relationship: The more mass you start with, provided it is not already critical, the less you have to compress it to get critical mass. Most other calculations are related to maximizing the conversion of mass to energy before the pieces fly apart.

If we do not use a trigger, but assemble a sphere of supercritical mass of U-235, a chain reaction may or may not be caused by a single spontaneous decay, with one of the neutrons produced causing a new decay. See nuclear chain reaction. Since there are typically at least tens of such free neutrons per second, it takes only a fraction of a second until the chain reaction starts. Albert Einsteins letter to President Roosevelt in 1939 about his concern, about (Nuclear chain reactions) Click for closeup of letter 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...

Contents

Weapon design

Criticality pathways tutorial

See also