Fission Energy
The discovery of nuclear fission by bombarding
uranium with neutrons did not reveal all the story.
Further study revealed that only the isotope ^{235}U undergoes
fission reaction when bombarded by slow neutrons.
^{235}U (n, 3 n) fission products with mass number ranges 80160
This fission reaction releases a lot of energy. The following examples
illustrate the amount of energy released in the fission process.
Example 1
If a ^{235}U atom splits up into two nuclides with mass number
117 and 118, estimate the energy released in the process.
Solution
A search of stable nuclides with mass numbers 117 and 118 are
^{117}Sn^{50}, and ^{118}Sn^{50},
their masses being 116.902956 and 117.901609 amu respectively.
The mass of ^{235}U is 235.043924 amu. The difference in mass
235.043924  (116.902956 + 117.901609)
= 0.2394 amu (931.5 MeV) / (1 amu)
= 223 MeV.
Discussion
Actually, the fission is induced by neutrons, and usually the split is
uneven. In reality, two neutrons are also released, but they were ignored
in this example to make the estimate simple. Furthermore, the fission
products are beta emitters as illustrated by example 2.
Example 2
Assume the neutron induced fission reaction to be,
^{235}U + n ® ^{142}Cs^{55}
+ ^{90}Rb^{35} + 4 n.
explain the results and estimate the energy released.
Solution
The neutronrich fission products are beta emitters:
^{142}Cs^{55} ( , b) ^{142}Ba^{56}
( , b) ^{142}La^{57}
( , b) ^{142}Ce^{58}
( , b) ^{142}Pr^{59}
( , b) ^{142}Nd^{60} (stable)
^{90}Rb^{37} ( , b) ^{90}Sr^{38}
( , b) ^{90}Y^{39}
( , b) ^{90}Zr^{40} (stable)
The masses of n, ^{142}Nd^{60} and ^{90}Zr^{40}
are 1.008665, 141.907719 and 89.904703 amu respectively.
The energy per fission and the decay energy are estimated as follows.
Energy = 235.04924  (89.904703 + 141.907719 + 3 x 1.008665)
= 0.210823 amu (931.5 MeV / amu)
= 196 MeV (1.6022e13 J / MeV)
= 3.15e11 J
Example 3
Estimate the energy released by the fission of 1.0 kg of ^{235}U.
Solution
From the results of the previous two examples, energy released by
1.0 kg uranium235 is estimated below:
(3.15e11 J) 1000 g (1 mol / 235 g) (6.023e23 / mol)
= 8.06e13 J (per kg).
Discussion
This is a large amount of energy, and it is equivalent to the energy produced
by burning tones of coal or oil.
Fission Energy Distribution
Energy (MeV) distribution in fission reactions


Kinetic energy of fission fragments  167 MeV

Prompt (< 106 s) gamma ray energy  8

Kinetic energy of fission neutrons  8

Gamma ray energy from fission products  7

Beta decay energy of fission products  7

Energy as antineutrinos (ve)  7

In the fission process, the fragments and neutrons move away at high
speed carrying with them large amounts of kinetic energy. The neutrons
released during the fission process are called fast neutrons because
of their high speed. Neutrons and fission fragments fly apart
instantaneously in a fission process. No delayed liberation of
neutrons was ever observed. Gamma rays (photons) equivalent to
8 MeV of energy are released within a microsecond of fission.
As mentioned earlier, the two fragments are beta emitters.
Recall that beta decays are accompanied by antineutrino emissions,
and the two types of particles carry away approximately equal
amounts of energy. Beta decays often leave the nuclei at excited states,
and gamma emission follows. Estimated average values of various
energies are given in a table here.