This article is about nuclear technology. For the car-free environment event, see Critical Mass. For the English Anarcho Environmentalist pressure group founded in 1984, see Critical Mass (pressure group). This term is also used figuratively, meaning something like "be sufficient to work properly", especially when a sufficiently large amount is needed to cause growth, such as the Chandrasekhar limit.

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 (eg the nuclear fission cross-section) and physical properties of the material, its geometry (shape), and its purity, as well as whether it is surrounded by a neutron reflector or interrupted by an absorber.

An assembly in which a chain reaction is possible is called critical, and is said to have obtained criticality. In a larger assembly, the reaction will increase at an exponential rate, and this is termed supercritical. An assembly that is capable of sustaining a chain reaction without needing the contribution of neutrons whose release is delayed is called prompt critical (and is therefore also supercritical).

If an assembly is smaller than critical, then the fission reaction will decrease with time, 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.

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.

Bare-sphere critical masses of some other isotopes whose half-lives exceed 100 years are compiled in the following table.

• uranium-233: 15 kg [1] (http://www.nti.org/e_research/cnwm/overview/technical2.asp)
• uranium-235: 50 kg [2] (http://www.nti.org/e_research/cnwm/overview/technical2.asp)
• neptunium-237: 60kg [3] (http://www.isis-online.org/publications/fmct/book/New%20chapter%205.pdf)
• plutonium-239: 10 kg [4] (http://www.nti.org/e_research/cnwm/overview/technical2.asp)
• plutonium-240: 40 kg [5] (http://www.nti.org/e_research/cnwm/overview/technical2.asp)
• plutonium-242: 100kg [6] (http://www.nti.org/e_research/cnwm/overview/technical2.asp)
• americium-241: 60-100kg [7] (http://www.isis-online.org/publications/fmct/book/New%20chapter%205.pdf)
• americium-242m: 9-18kg [8] (http://www.isis-online.org/publications/fmct/book/New%20chapter%205.pdf)
• americium-243: 50-150kg [9] (http://www.isis-online.org/publications/fmct/book/New%20chapter%205.pdf)
• curium-245: 12kg [10] (http://wwwsoc.nii.ac.jp/aesj/publication/JNST2002/No.10/39_1072-1085.pdf)
• curium-246: 70kg [11] (http://wwwsoc.nii.ac.jp/aesj/publication/JNST2002/No.10/39_1072-1085.pdf)
• curium-247: 7kg [12] (http://wwwsoc.nii.ac.jp/aesj/publication/JNST2002/No.10/39_1072-1085.pdf)
• californium-251: 9kg [13] (http://www.nti.org/db/nistraff/1999/19990670.htm)

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.

The critical mass is inversely proportional to the square of the density: if the density is 1% more and the mass 2% less then 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 weapon.

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 hollow sphere. Detonation is produced by exploding a shaped charge surrounding the hollow sphere, increasing the density and reducing the size of the cavity to produce a prompt critical configuration. This is known as an implosion type weapon.

See also

• Nuclear chain reaction
• Nuclear weapon design
• Criticality accident