Step 1: {Understanding Binding Energy per Nucleon}
The binding energy per nucleon (\( BE/A \)) quantifies the energy needed to separate a nucleus into its protons and neutrons, serving as a key indicator of nuclear stability. A higher \( BE/A \) signifies a more stable nucleus. Elements in the mid-range of the periodic table, particularly around iron (\( {}^{56}_{26}Fe \)), exhibit the highest \( BE/A \).
Step 2: {Comparing the Nuclei}
- Lighter nuclei, exemplified by \( {}^{4}_{2}He \) (Helium-4), possess a comparatively low \( BE/A \) because their nucleons are less tightly bound.
- Heavy nuclei, such as \( {}^{208}_{84}Pb \) (Lead-208), also show reduced \( BE/A \) relative to mid-range nuclei. This reduction is attributed to the electrostatic repulsion among protons, which counteracts the nuclear force.
- \( {}^{56}_{26}Fe \) (Iron-56), with its peak \( BE/A \) (approximately 8.8 MeV), is recognized as the most stable nucleus. This characteristic explains why nuclear fusion primarily generates energy when lighter elements fuse up to iron, and why fission of heavier elements releases energy. Consequently, \( {}^{56}_{26}Fe \) is identified as the correct answer.