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Spontaneous fission can occur, but this is usually not the most common decay mode for a given nuclide. For example, 238 U size 12{ {} rSup { size 8{"238"} } U} {} can spontaneously fission, but it decays mostly by α size 12{α} {} emission. Neutron-induced fission is crucial as seen in [link] . Being chargeless, even low-energy neutrons can strike a nucleus and be absorbed once they feel the attractive nuclear force. Large nuclei are described by a liquid drop model    with surface tension and oscillation modes, because the large number of nucleons act like atoms in a drop. The neutron is attracted and thus, deposits energy, causing the nucleus to deform as a liquid drop. If stretched enough, the nucleus narrows in the middle. The number of nucleons in contact and the strength of the nuclear force binding the nucleus together are reduced. Coulomb repulsion between the two ends then succeeds in fissioning the nucleus, which pops like a water drop into two large pieces and a few neutrons. Neutron-induced fission can be written as

n + A X FF 1 + FF 2 + xn , size 12{n+"" lSup { size 8{A} } X rightarrow "FF" rSub { size 8{1} } +"FF" rSub { size 8{2} } + ital "xn"} {}

where FF 1 size 12{"FF" rSub { size 8{1} } } {} and FF 2 size 12{"FF" rSub { size 8{2} } } {} are the two daughter nuclei, called fission fragments    , and x size 12{x} {} is the number of neutrons produced. Most often, the masses of the fission fragments are not the same. Most of the released energy goes into the kinetic energy of the fission fragments, with the remainder going into the neutrons and excited states of the fragments. Since neutrons can induce fission, a self-sustaining chain reaction is possible, provided more than one neutron is produced on average — that is, if x > 1 size 12{x>1} {} in n + A X FF 1 + FF 2 + xn . This can also be seen in [link] .

An example of a typical neutron-induced fission reaction is

n + 92 235 U 56 142 Ba + 36 91 Kr + 3 n.

Note that in this equation, the total charge remains the same (is conserved): 92 + 0 = 56 + 36 size 12{"92"+0="56"+"36"} {} . Also, as far as whole numbers are concerned, the mass is constant: 1 + 235 = 142 + 91 + 3 size 12{1+"235"="142"+"91"+3} {} . This is not true when we consider the masses out to 6 or 7 significant places, as in the previous example.

A neutron gets absorbed in a nucleus, making it narrower in the middle, then finally breaking into two parts and ejecting some neutrons.
Neutron-induced fission is shown. First, energy is put into this large nucleus when it absorbs a neutron. Acting like a struck liquid drop, the nucleus deforms and begins to narrow in the middle. Since fewer nucleons are in contact, the repulsive Coulomb force is able to break the nucleus into two parts with some neutrons also flying away.

A uranium nucleus struck by a neutron produces two fragments and three neutrons, two of which continue to strike two other uranium nuclei and hence, initiate a chain reaction.
A chain reaction can produce self-sustained fission if each fission produces enough neutrons to induce at least one more fission. This depends on several factors, including how many neutrons are produced in an average fission and how easy it is to make a particular type of nuclide fission.

Not every neutron produced by fission induces fission. Some neutrons escape the fissionable material, while others interact with a nucleus without making it fission. We can enhance the number of fissions produced by neutrons by having a large amount of fissionable material. The minimum amount necessary for self-sustained fission of a given nuclide is called its critical mass    . Some nuclides, such as 239 Pu size 12{ {} rSup { size 8{"239"} } ital "Pu"} {} , produce more neutrons per fission than others, such as 235 U size 12{ {} rSup { size 8{"235"} } U} {} . Additionally, some nuclides are easier to make fission than others. In particular, 235 U size 12{ {} rSup { size 8{"235"} } U} {} and 239 Pu size 12{ {} rSup { size 8{"239"} } ital "Pu"} {} are easier to fission than the much more abundant 238 U size 12{ {} rSup { size 8{"238"} } U} {} . Both factors affect critical mass, which is smallest for 239 Pu size 12{ {} rSup { size 8{"239"} } ital "Pu"} {} .

Practice Key Terms 9

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Source:  OpenStax, Physics for the modern world. OpenStax CNX. Sep 16, 2015 Download for free at http://legacy.cnx.org/content/col11865/1.3
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