# 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 235U undergoes fission reaction when bombarded by slow neutrons.

235U (n, 3 n) fission products with mass number ranges 80-160
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 235U 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 117Sn50, and 118Sn50, their masses being 116.902956 and 117.901609 amu respectively. The mass of 235U 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,

235U + n ® 142Cs55 + 90Rb35 + 4 n.

explain the results and estimate the energy released.

Solution

The neutron-rich fission products are beta emitters:

142Cs55 ( , b) 142Ba56 ( , b) 142La57 ( , b) 142Ce58 ( , b) 142Pr59 ( , b) 142Nd60 (stable)

90Rb37 ( , b) 90Sr38 ( , b) 90Y39 ( , b) 90Zr40 (stable)

The masses of n, 142Nd60 and 90Zr40 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 (1.6022e-13 J / MeV)
= 3.15e-11 J

Example 3

Estimate the energy released by the fission of 1.0 kg of 235U.

Solution

From the results of the previous two examples, energy released by 1.0 kg uranium-235 is estimated below:

(3.15e-11 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 (< 10-6 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.

E-mail: cchieh@uwaterloo.ca