Field of Science

Simple, atypical but neat estimation of energy released in fission

Simple but neat atypical calculation of energy released in fission (from Glasstone and Sesonske, “Nuclear Reactor Engineering”). It’s a nice illustration of guesstimating based on empirical data.

"The amount of energy released when a nucleus undergoes fission can be calculated by determining the net decrease in mass, from the known isotopic masses, and utilizing the Einstein mass-energy relationship. A simple, but instructive although less accurate, alternative procedure is the following. Disregarding the neutrons involved, since they have a negligible effect on the present calculation, the fission reaction may be represented (approximately) by

Uranium-235 -› Fission product A + Fission product B + Energy.

In uranium-235, the mean binding energy per nucleon is about 7.6 Mev, so that it is possible to write
92 p + 143 n -> Uranium-235 + (235 X 7.6) Mev

where p and n represent protons and neutrons, respectively.

The mass numbers of the two fission product nuclei are mostly in the range of roughly 95 to 140, where the binding energy per nucleon is, as in tin-120, for example, about 8.5 Mev; hence,
92 p + 143 n -› Fission products A and B + (235 X 8.5) Mev

Upon subtracting the two binding energy expressions, the result is

Uranium-235 -> Fission products + 210 Mev."

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