Topic 9 of 9
Energy from fission and fusion
A reaction releases energy when its products have less total rest mass than its reactants. The binding-energy-per-nucleon curve helps explain why both the fusion of light nuclei and the fission of heavy nuclei can do this.
Read the binding-energy curve
Binding energy per nucleon rises rapidly across the light nuclei, reaches a broad maximum near nucleon numbers 50-60 in the iron/nickel region, then decreases gradually for heavier nuclei. It measures an average binding energy, not the total binding energy of a nucleus.
Binding energy per nucleon on the actual nucleon-number scale
The steep light-nucleus rise is compressed by the true horizontal scale. Read the separate enlarged panel below for A = 2 and A = 4. Energy release for a reaction still requires the complete, balanced initial and final account.
Light nuclei: a separately enlarged nucleon-number range
Only the horizontal range is enlarged here; the vertical quantity and scale are unchanged. A larger total binding energy is not automatically a larger binding energy per nucleon. The curve is an approximate trend, not an exact isotope mass table.
Products with greater total binding energy have lower total rest energy for the same complete nucleon account. Multiply each nucleus's binding energy per nucleon by its own A before comparing totals. Local isotope differences exist, and this curve alone does not determine a reaction rate or every kind of nuclear stability.
Fusion combines light nuclei
In the supplied deuterium-tritium reaction, a hydrogen-2 nucleus and a hydrogen-3 nucleus form an alpha particle and a neutron:
Both sides have five nucleons and charge +2e. Use all products when comparing rest masses. The supplied nuclear masses, in u, are 2.01355321, 3.01550072, 4.00150618 and 1.00866492 in the displayed order.
Worked fusion energy
Include the outgoing neutron
- (4.00150618 + 1.00866492)
= 0.01888283 u
Q = 0.01888283(931.5)
= 17.5894 MeV ≈ 17.6 MeV
Here Q is the total energy released per complete reaction, using supplied 1 u c2 = 931.5 MeV. Leaving out the neutron would give a huge false mass deficit. Positive released energy does not remove the initial electric repulsion between the positively charged reactants.
Fission splits a heavy nucleus
One possible neutron-induced fission channel is:
The totals are A = 236 and charge +92e on both sides. Other fragment combinations are possible; this is one supplied channel, not a unique outcome of every fission event.
| Nucleus | A | Binding energy / MeV per nucleon |
|---|---|---|
| Uranium-235 | 235 | 7.60 |
| Barium-141 | 141 | 8.30 |
| Krypton-92 | 92 | 8.60 |
Final total binding = 141(8.30) + 92(8.60)
= 1170.3 + 791.2 = 1961.5 MeV
Energy released ≈ 1961.5 - 1786.0
= 175.5 MeV
Free neutrons contribute no nuclear binding energy. This is an estimate from the supplied rounded averages, not a precision energy value for the channel. The products are more tightly bound overall, so the decrease in total rest energy is available as kinetic energy and radiation.
For both fusion and fission, compare the complete initial and final accounts. Subtracting two per-nucleon values without weighting by nucleon number does not give the reaction energy.