# 6.10.4 Calculating Binding Energy

## 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 = Zmp + (A – Z)mn – mtotal

• Where:
• Z = proton number
• A = nucleon number
• mp = mass of a proton (kg)
• mn = mass of a neutron (kg)
• mtotal = measured mass of the nucleus (kg)

#### Worked example Step 1:            Calculate the mass defect

Number of protons, Z = 26

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

Mass defect, Δm = Zmp + (A – Z)mn – mtotal

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  ### Get unlimited access

to absolutely everything:

• Unlimited Revision Notes
• Topic Questions
• Past Papers 