Nuclear fission and nuclear fusion both release energy because the total mass of the final products is smaller than the
total mass of the initial reactants. The missing mass is not destroyed. It reappears as released energy according to
Einstein’s relation \(E = mc^2\). In practical nuclear calculations, this released energy is described by the
reaction Q-value.
Mass defect and Q-value
For a general nuclear reaction, the mass defect is the difference between the total reactant mass and the total product
mass:
Reaction mass defect.
\[
\begin{aligned}
\Delta m &= \sum m_{\mathrm{reactants}} - \sum m_{\mathrm{products}}.
\end{aligned}
\]
If \(\Delta m\) is positive, the reaction is exothermic and releases energy. The Q-value is then
\[
\begin{aligned}
Q &= \Delta m\,c^2.
\end{aligned}
\]
In nuclear physics, masses are often entered in atomic mass units, so the standard conversion is
\[
\begin{aligned}
1\ \mathrm{u}\,c^2 &\approx 931.494\ \mathrm{MeV}.
\end{aligned}
\]
That means the released energy is usually computed with
\[
\begin{aligned}
Q &\approx 931.494\,\Delta m\ \mathrm{MeV}.
\end{aligned}
\]
Energy per nucleon
Because nuclear reactions can involve very different total mass numbers, it is often useful to divide the released
energy by the total number of nucleons in the reactants:
Energy per nucleon.
\[
\begin{aligned}
\frac{Q}{A_{\mathrm{tot}}}
&= \frac{Q}{\sum A_{\mathrm{reactants}}}.
\end{aligned}
\]
This quantity helps compare different reactions on a more even basis. A fission reaction may release much more energy
per reaction than a fusion reaction, but a fusion reaction can still be highly efficient when measured per nucleon.
Why both fission and fusion can release energy
The key idea is the binding energy per nucleon curve. Light nuclei become more stable when they fuse
into somewhat heavier nuclei, while very heavy nuclei become more stable when they split into intermediate-mass fragments.
Both processes move the system toward nuclei with stronger average binding per nucleon.
| Region of nuclei |
Typical trend |
Energy consequence |
| Very light nuclei |
Binding energy per nucleon rises as mass number increases |
Fusion can release energy |
| Very heavy nuclei |
Binding energy per nucleon is lower than near iron/nickel |
Fission can release energy |
| Middle-mass nuclei |
Near the maximum stability region |
Hardest region from which to gain extra binding-energy advantage |
Typical fission example
A common benchmark is neutron-induced fission of uranium-235. Real fission can produce many different fragment pairs,
so the exact Q-value depends on the specific channel. In engineering discussions, one often quotes a typical average
release of about
\[
\begin{aligned}
Q_{\mathrm{fission}} &\approx 200\ \mathrm{MeV}
\end{aligned}
\]
per fission event. This includes the energy ultimately carried by fission fragments, prompt and delayed radiation,
and other decay products. In a simplified calculator, one may represent this average using an effective total product
mass corresponding to that conventional energy release.
Typical fusion example: D-T fusion
A standard fusion benchmark is
D + T → He-4 + n
Using atomic masses for deuterium, tritium, helium-4, and the neutron, the mass defect is positive and gives a
released energy of about
\[
\begin{aligned}
Q_{\mathrm{D\text{-}T}} &\approx 17.6\ \mathrm{MeV}.
\end{aligned}
\]
That is much smaller than the typical energy released in one U-235 fission event, but the D-T reaction involves far
fewer nucleons. This is why the energy per nucleon can be quite competitive.
Worked calculation pattern
The same calculation pattern works for either fission or fusion:
Step 1. Sum the reactant masses.
\[
\begin{aligned}
\sum m_r &= m_{r1} + m_{r2} + \cdots
\end{aligned}
\]
Step 2. Sum the product masses.
\[
\begin{aligned}
\sum m_p &= m_{p1} + m_{p2} + \cdots
\end{aligned}
\]
Step 3. Compute the mass defect.
\[
\begin{aligned}
\Delta m &= \sum m_r - \sum m_p
\end{aligned}
\]
Step 4. Convert to the Q-value.
\[
\begin{aligned}
Q &= \Delta m \cdot 931.494\ \mathrm{MeV}
\end{aligned}
\]
Step 5. Divide by total reactant nucleons if needed.
\[
\begin{aligned}
\frac{Q}{A_{\mathrm{tot}}} &= \frac{Q}{\sum A_{\mathrm{reactants}}}
\end{aligned}
\]
Physical meaning
A positive Q-value means the reaction products have less total rest mass than the reactants. The difference appears as
released kinetic energy or radiation. In fission, much of the energy goes into fast heavy fragments and later radiation.
In fusion, the distribution depends on the reaction channel; for example, D-T fusion sends a large share of the energy
into the neutron.
A negative Q-value means the reaction is endothermic. Such a reaction would require external input
energy to proceed as written.
Advanced note
At university level, nuclear energy calculations are often refined with reaction thresholds, branching ratios, neutron
economy, breeding ratios, and detailed product spectra. Reactor and plasma modeling also track how the released energy
is distributed among charged particles, neutrons, photons, and later decay chains. Even with those refinements, the
mass-defect Q-value remains the fundamental starting point because it sets the basic energy budget of the reaction.
| Concept |
Main relation |
Meaning |
| Mass defect |
\(\Delta m = \sum m_r - \sum m_p\) |
Mass converted into released or required energy |
| Q-value |
\(Q = \Delta m c^2\) |
Total reaction energy |
| Atomic mass unit conversion |
\(1\ \mathrm{u}\,c^2 \approx 931.494\ \mathrm{MeV}\) |
Standard practical conversion |
| Energy per nucleon |
\(Q/A_{\mathrm{tot}}\) |
Normalized comparison between different reactions |
| Typical U-235 fission |
\(\approx 200\ \mathrm{MeV}\) |
Common average engineering benchmark |
| Typical D-T fusion |
\(\approx 17.6\ \mathrm{MeV}\) |
Standard fusion benchmark reaction |