Fission of heavy nuclides
converts a small amount of mass into an enormous amount of energy. The amount
of energy released by fission can be determined based on either the change in
mass that occurs during the reaction or by the difference in binding energy per
nucleon between the fissile nuclide and the fission products.
EO 4.8CHARACTERIZE
the fission products in terms of mass groupings and radioactivity.
EO 4.9Given the
nuclides involved and their masses, CALCULATE the energy released from fission.
EO 4.10 Given
the curve of Binding Energy per nucleon versus mass number, CALCULATE the
energy released from fission.
Calculation of Fission Energy
Nuclear fission results in the release of enormous
quantities of energy. It is necessary to be able to calculate the amount of
energy that will be produced. The logical manner in which to pursue this is to
first investigate a typical fission reaction such as the one listed below.
It can be seen that when the compound nucleus splits, it
breaks into two fission fragments, rubidium93, cesium140, and some neutrons.
Both fission products then decay by multiple ^{}emissions as a result of the high
neutrontoproton ratio possessed by these nuclides.
In most cases, the resultant fission fragments have masses
that vary widely. Figure 21 gives the percent yield for atomic mass numbers.
The most probable pair of fission fragments for the thermal fission of the fuel
uranium235 have masses of about 95 and 140. Note that the vertical axis of the
fission yield curve is on a logarithmic scale. Therefore, the formation of
fission fragments of mass numbers of about 95 and 140 is highly likely.
Figure
21 Uranium235 Fission Yield vs.
Mass Number
Referring now to the binding energy per nucleon curve
(Figure 20), we can estimate the amount of energy released by our
"typical" fission by plotting this reaction on the curve and
calculating the change in binding energy (BE)
between the reactants on the lefthand side of the fission equation and the
products on the righthand side. Plotting the reactant and product nuclides on
the curve shows that the total binding energy of the system after fission is
greater than the total binding energy of the system before fission. When there
is an increase in the total binding energy of a system, the system has become
more stable by releasing an amount of energy equal to the increase in total
binding energy of the system. Therefore, in the fission process, the energy
liberated is equal to the increase in the total binding energy of the system.
Figure 22 Change
in Binding Energy for Typical Fission
Figure 22 graphically depicts that the binding energy per
nucleon for the products (C, rubidium93 and B, cesium140) is greater than
that for the reactant (A, uranium235). The total binding energy for a nucleus
can be found by multiplying the binding energy per nucleon by the number of
nucleons.
The energy released will be equivalent to the difference
in binding energy (BE)
between the reactants and the products.
The energy liberation during the fission process can also
be explained from the standpoint of the conservation of massenergy. During the
fission process, there is a decrease in the mass of the system. There must,
therefore, be energy liberated equal to the energy equivalent of the mass lost
in the process. This method is more accurate than the previously illustrated
method and is used when actually calculating the energy liberated during the
fission process.
Again, referring to the "typical" fission
reaction.
,the instantaneous energy, is
the energy released immediately after the fission process. It is equal to the
energy equivalent of the mass lost in the fission process. It can be calculated
as shown below.
This mass difference can be converted to an energy
equivalent
The
total energy released per fission will vary from the fission to the next
depending on what fission products are formed, but the average total energy
released per fission of uranium235 with a thermal neutron is 200 MeV.
As
illustrated in the preceding example, the majority of the energy liberated in
the fission process is released immediately after the fission occurs and
appears as the kinetic energy of the fission fragments, kinetic energy of the
fission neutrons, and instantaneous gamma rays. The remaining energy is
released over a period of time after the fission occurs and appears as kinetic
energy of the beta, neutrino, and decay gamma rays.
