Why does the binding energy per nucleon remain nearly constant for nuclei with mass numbers between 30 and 170?
**Mass defect** Δm = Z m_p + N m_n - M_nucleus, binding energy BE = Δm c², 1 u =931.5 MeV/c², BE per nucleon = BE/A, measures stability, peak ~8.8 MeV at Fe-56, for A=36 BE=288 MeV BE/A=8 MeV, for A=12 BE=96 MeV BE/A=8 MeV, for A=16 BE=127.5 MeV BE/A≈7.97 MeV, higher BE/A more stable. The nuclear force is short-ranged, affecting only neighboring nucleons. In medium-sized nuclei (A = 30 to 170), most nucleons are inside the nucleus, surrounded by a constant number of neighbors, leading to a saturation effect and nearly constant binding energy per nucleon. Using E_n = -13.6/n² eV, r_n = n²
Ref: NCERT > Physics Book > Atoms and Nuclei > Mass Defect, Binding Energy and Binding Energy per Nucleon