6.10.4 Calculating Binding Energy

• Binding energy can be calculated using the equation:

ΔE = c²Δm

• Where Δm is the mass defect of a nucleus
• This can be calculated using:

  Δm = Zm_p + (A – Z)m_n – m_total

  • Where:
    • Z = proton number
    • A = nucleon number
    • m_p = mass of a proton (kg)
    • m_n = mass of a neutron (kg)
    • m_total = measured mass of the nucleus (kg)

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 = c²Δm

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

Step 3:            Calculate the binding energy per nucleon

Step 4:            Convert to MeV

J → eV: divide by 1.6 × 10^-19

eV → MeV: divide by 10⁶