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A fission chain reaction is shown in stages. A neutron first strikes the nucleus of 235 U. This splits into two fragments, 92 Kr and 141 Ba, along with the release of three neutrons. Each of these three neutrons strikes a separate nucleus of 235 U. The three nuclei all split into two fragments each, of 92 Kr and 141 Ba. Three neutrons are released by each fission, bringing the total of released neutrons up to 9.
In a U-235 fission chain reaction, the fission of the uranium nucleus produces high-energy neutrons that go on to split more nuclei. The energy released in this process can be used to produce electricity.

View a simulation on nuclear fission to start a chain reaction, or introduce nonradioactive isotopes to prevent one. Control energy production in a nuclear reactor.

The atomic bomb

The possibility of a chain reaction in uranium, with its extremely large energy release, led nuclear scientists to conceive of making a bomb—an atomic bomb . (These discoveries were taking place in the years just prior to the Second World War and many of the European physicists involved in these discoveries came from countries that were being overrun.) Natural uranium contains 99.3 % U-238 and only 0.7 % U-235, and does not produce a chain reaction. To produce a controlled, sustainable chain reaction, the percentage of U-235 must be increased to about 50 % . In addition, the uranium sample must be massive enough so a typical neutron is more likely to induce fission than it is to escape. The minimum mass needed for the chain reaction to occur is called the critical mass    . When the critical mass reaches a point at which the chain reaction becomes self-sustaining, this is a condition known as criticality    . The original design required two pieces of U-235 below the critical mass. When one piece in the form of a bullet is fired into the second piece, the critical mass is exceeded and a chain reaction is produced.

An important obstacle to the U-235 bomb is the production of a critical mass of fissionable material. Therefore, scientists developed a plutonium-239 bomb because Pu-239 is more fissionable than U-235 and thus requires a smaller critical mass. The bomb was made in the form of a sphere with pieces of plutonium, each below the critical mass, at the edge of the sphere. A series of chemical explosions fired the plutonium pieces toward the center of the sphere simultaneously. When all these pieces of plutonium came together, the combination exceeded the critical mass and produced a chain reaction. Both the U-235 and Pu-239 bombs were used in World War II. Whether to develop and use atomic weapons remain two of the most important questions faced by human civilization.

Calculating energy released by fission

Calculate the energy released in the following spontaneous fission reaction:

238 U 95 Sr + 140 Xe + 3n ,

The atomic masses are m ( 238 U ) = 238.050784 u , m ( 95 Sr ) = 94.919388 u , m ( 140 Xe ) = 139.921610 u , and m ( n ) = 1.008665 u .

Strategy

As always, the energy released is equal to the mass destroyed times c 2 , so we must find the difference in mass between the parent 238 U and the fission products.

Solution

The products have a total mass of

m products = 94.919388 u + 139.921610 u + 3 ( 1.008665 u ) = 237.866993 u .

The mass lost is the mass of 238 U m products or

Δ m = 238.050784 u 237.8669933 u = 0.183791 u .

Therefore, the energy released is

E = ( Δ m ) c 2 = ( 0.183791 u ) 931.5 MeV/ c 2 u c 2 = 171.2 MeV .

Significance

Several important things arise in this example. The energy release is large but less than it would be if the nucleus split into two equal parts, since energy is carried away by neutrons. However, this fission reaction produces neutrons and does not split the nucleus into two equal parts. Fission of a given nuclide, such as 238 U , does not always produce the same products. Fission is a statistical process in which an entire range of products are produced with various probabilities. Most fission produces neutrons, although the number varies. This is an extremely important aspect of fission, because neutrons can induce more fission , enabling self-sustaining chain reactions.

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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