Reading a graph: mass defect

Problem

The table gives the mass defect per nucleon $\Delta m / A$ for some nuclei.

nuclide	$^{4}$He	$^{16}$O	$^{56}$Fe	$^{120}$Sn	$^{238}$U
$\Delta m/A$ (u/nucleon)	0,00761	0,00868	0,00945	0,00913	0,00807

(a) Which nuclide has the maximum binding energy per nucleon? (b) At equal nucleon number, towards which process does nature tend: fission or fusion? Explain.

Solution

(a) Maximum binding energy per nucleon. The binding energy per nucleon $B/A$ is proportional to the mass defect per nucleon $\Delta m/A$ (via $B = \Delta m \cdot 931{,}5\ \text{MeV/u}$). We simply need to find the maximum in the data row: the largest value is $0{,}00945$, corresponding to iron-56.

$\ev{\text{max binding energy per nucleon} = {}^{56}\text{Fe}}$

(b) Direction of the processes. Every nucleus tends to transform so as to approach the iron peak, because there the binding energy per nucleon is maximum and the system is most stable:

• nuclei heavier than iron ($A > 56$, such as $^{120}$Sn and $^{238}$U) approach the peak by splitting, i.e. via fission;
• nuclei lighter than iron ($A < 56$, such as $^{4}$He and $^{16}$O) approach the peak by joining, i.e. via fusion.

In both cases $\Delta m/A$ increases, and so energy is released.

$\ev{\text{max}=^{56}\text{Fe};\ A>56\Rightarrow\text{fission},\ A<56\Rightarrow\text{fusion}}$

Collegamenti

Argomenti: Fisica nucleare Concetti: Energia di legame nucleare Competenze: Lettura dei grafici