5.11 Binding Energy per Nucleon Graph

• When comparing the stability of different nuclei, it is useful to look at the binding energy per nucleon
• The binding energy per nucleon is defined as:

The binding energy of a nucleus divided by the number of nucleons in the nucleus

• A higher binding energy per nucleon indicates a higher stability since it requires more energy to pull the nucleus apart

• Iron (A = 56) has the highest binding energy per nucleon, which makes it the most stable of all the elements

By plotting a graph of binding energy per nucleon against nucleon number, the stability of elements can be inferred

Key Features of the Graph

• At low values of A:
  • Nuclei tend to have a lower binding energy per nucleon, hence, they are generally less stable
  • This means the lightest elements have weaker electrostatic forces and are the most likely to undergo fusion

• Helium (⁴He), carbon (¹²C) and oxygen (¹⁶O) do not fit the trend
  • Helium-4 is a particularly stable nucleus hence it has a high binding energy per nucleon
  • Carbon-12 and oxygen-16 can be considered to be three and four helium nuclei, respectively, bound together

• At high values of A:
  • The general binding energy per nucleon is high and gradually decreases with A
  • This means the heaviest elements are the most unstable and likely to undergo fission

Step 1: Calculate the mass defect

Number of protons, Z = 26

Number of neutrons, A – Z = 56 – 26 = 30

Mass defect, Δm = Zm_p + (A – Z)m_n – m_total

Δm = (26 × 1.673 × 10^-27) + (30 × 1.675 × 10^-27) – (9.288 × 10^-26)

Δm = 8.680 × 10^-28 kg

Step 2: Calculate the binding energy of the nucleus

Binding energy, ΔE = Δmc²

E = (8.680 × 10^-28) × (3.00 × 10⁸)² = 7.812 × 10^-11 J

Step 3: Calculate the binding energy per nucleon

Binding energy per nucleon = 

Step 4: Convert to MeV

J → eV: divide by 1.6 × 10^-19

eV → MeV: divide by 10⁶

binding energy per nucleon =