Example 1
A fission reaction has mass difference 3.5×10−28kg. Use c=3.00×108m/s. Find released energy.
ΔE=Δmc2=3.5×10−28×9.00×1016=3.15×10−11J per reaction.
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Year 11 · SACE Stage 1
Fission, chain reactions and mass–energy
Identify reactor component functions and calculate fission energy from mass difference.
Method and worked examples
In induced fission, a suitable heavy nucleus absorbs a neutron and splits into lighter nuclei with additional neutrons and released energy. If enough neutrons induce further fissions, a chain reaction continues. In steady operation, on average one neutron per fission sustains another fission. A moderator slows neutrons; control materials absorb them; coolant carries energy away. Enrichment increases the fraction of a chosen fissile isotope.
For an energy-releasing reaction, the total rest mass of products is lower than that of reactants. Use ΔE=Δmc2 with Δm= mreactants − mproducts and c=3.00×108m/s. Include all relevant products in the mass accounting. Released kinetic energy and radiation can ultimately provide heat for electricity generation; total mass–energy is conserved rather than energy appearing from nothing.
Example 1
Example 2
A model starts with 100 fissions. Each produces on average 2.4 neutrons, but only 100 of those neutrons cause next-generation fission. Is the fission count steady?
Yes. One next-generation fission occurs per original fission on average, so the generation count stays at 100. The emitted 240 neutrons are not all retained to induce fission.
Watch out: A moderator primarily slows neutrons through collisions; control rods primarily absorb neutrons to adjust the reaction rate.