6.4NuclearStretch

Mass-Energy Equivalence and Binding Energy

Weigh a nucleus and weigh its separate protons and neutrons, and the nucleus always comes up lighter. That "missing" mass has been converted directly into the energy holding the nucleus together — exactly as Einstein’s equation predicts.

45 min Video by Science Shorts Module 6.4 Nuclear and particle physics

Binding Energy — A-level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Use $E = m c^{2}$
Explain mass defect
Calculate binding energy from mass defect
Explain binding energy per nucleon and the shape of its curve against nucleon number

Mass-energy equivalence

Any energy change corresponds to a mass change, related by $c^{2}$ .

Δ E = Δ m c^{2}

Mass-energy equivalence.

Mass defect and binding energy

A nucleus’s mass is always less than the sum of its separate nucleon masses — the mass defect. Binding energy is the energy needed to completely separate a nucleus into individual nucleons.

Δ m = (Z m_{p} + N m_{n}) - m_{nucleus} E_{B} = Δ m c^{2}

Mass defect and binding energy.

1Sum of separate masses:

1.6726 \times 1 0^{- 27} + 1.6749 \times 1 0^{- 27} = 3.3475 \times 1 0^{- 27}

kg.

2Mass defect:

3.3475 \times 1 0^{- 27} - 3.3436 \times 1 0^{- 27} = 3.9 \times 1 0^{- 30}

kg.

3Binding energy:

E_{B} = Δ m c^{2} = 3.9 \times 1 0^{- 30} \times (3.00 \times 1 0^{8})^{2}

Answer

E_{B} \approx 3.51 \times 1 0^{- 13}

J (about 2.2 MeV)

Binding energy per nucleon

Binding energy per nucleon measures nuclear stability fairly, peaking near iron/nickel ( $A \approx 56$ ) — the most stable nuclei of all.

1Use

\frac{E _{B}}{A} = \frac{6.4 \times 1 0 ^{- 11}}{16}

Answer

4.0 \times 1 0^{- 12}

J per nucleon

Tip — Both fission (heavy → medium) and fusion (light → medium) release energy for the same reason: the products move closer to this stability peak.

Equation recap

Δ E = Δ m c^{2}

Mass-energy equivalence.

E_{B} = Δ m c^{2}

Binding energy.

Common mistakes to avoid

Thinking binding energy is stored energy waiting to be released spontaneously.

Binding energy must be SUPPLIED to separate a nucleus — a higher value means a MORE stable nucleus.

Comparing total binding energy between different-sized nuclei to judge stability.

Always compare binding energy PER NUCLEON, since total binding energy naturally grows with size.

Key takeaways

E=mc² relates energy and mass changes.
Mass defect: nuclear mass is less than the sum of separate nucleon masses; binding energy Eb=Δmc².
Binding energy per nucleon peaks near iron/nickel, the most stable nuclei.

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Mass-Energy Equivalence and Binding Energy

45 min Video by Science Shorts Module 6.4 Nuclear and particle physics