Aston's curve and the direction of energy release

Problem

Explain why both the fission of heavy nuclei (such as $^{235}\text{U}$) and the fusion of light nuclei (such as $^{2}\text{H} + {}^{3}\text{H}$) release energy. Use the binding energy per nucleon curve to help, and indicate where the two processes sit relative to the maximum.

Binding energy per nucleon curve: the peak is at iron; the arrows show the direction in which fusion and fission proceed.

Solution

The curve shows the binding energy per nucleon $E_l/A$ as a function of the mass number $A$: it rises rapidly for light nuclei, reaches a maximum around iron ($A \approx 56$, $E_l/A \approx 8{,}8\ \text{MeV}$) and then decreases slowly for heavy nuclei.

The key point is this: a process releases energy when the products are more tightly bound than the reactants, i.e. when they have a higher $E_l/A$. The increase in binding energy corresponds to a decrease in mass, and that missing mass is released as energy according to $E = \Delta m\, c^2$.

• Fusion ($^{2}\text{H} + {}^{3}\text{H}$): the light nuclei sit on the steep branch to the left of the maximum. By fusing they climb towards the peak, increasing $E_l/A$: so they release energy.
• Fission ($^{235}\text{U}$): the heavy nuclei sit to the right of the maximum, at a lower $E_l/A$. By splitting into fragments of intermediate mass they move closer to the peak, increasing $E_l/A$: here too energy is released.

Both processes, starting from opposite extremes, “slide” towards the bottom of the energy valley represented by iron.

$\ev{\text{fission (}A>56\text{) and fusion (}A<56\text{) both tend towards the iron maximum}}$

Links

Topics: Nuclear physics Concepts: Nuclear binding energy · Nuclear fission · Nuclear fusion Skills: Reading graphs