Edexcel A Level (IAL) Physics-5.9 Nuclear Binding Energy & Mass Deficit- Study Notes- New Syllabus

Nuclear Binding Energy and Using \( \Delta E = c^2 \Delta m \)

Nuclear binding energy is the energy required to completely separate a nucleus into its individual protons and neutrons. It is a measure of how strongly the nucleons are bound together.

 Mass Defect

The mass of a nucleus is less than the total mass of its separate nucleons. This difference is called the mass defect.

\( \Delta m = (\text{total mass of separate nucleons}) – (\text{mass of nucleus}) \)

• \( \Delta m \) = mass defect (kg or u)
• Occurs because energy is released when the nucleus forms

Key idea: Mass is converted into energy during nuclear formation.

Nuclear Binding Energy

The nuclear binding energy is the energy equivalent of the mass defect:

\( \Delta E = c^2 \Delta m \)

• \( \Delta E \) = binding energy (J)
• \( c \) = speed of light \( (3.00\times10^8\ \mathrm{m\,s^{-1}}) \)
• \( \Delta m \) = mass defect (kg)

This equation shows that a small mass defect corresponds to a very large energy.

Meaning of Binding Energy

• Large binding energy → very stable nucleus
• Small binding energy → less stable nucleus
• Energy must be supplied to break the nucleus apart

Binding energy per nucleon is often used to compare stability:

\( \text{binding energy per nucleon} = \dfrac{\text{total binding energy}}{\text{number of nucleons}} \)

Using \( \Delta E = c^2 \Delta m \) in Calculations

Typical steps:

1. Calculate total mass of separate protons and neutrons.
2. Subtract the nuclear mass to find \( \Delta m \).
3. Convert mass units to kg if necessary.
4. Use \( \Delta E = c^2 \Delta m \) to find energy.

Useful conversion:

\( 1\ \mathrm{u} = 1.66\times10^{-27}\ \mathrm{kg} \)

Importance in Nuclear Reactions

• Fusion: light nuclei combine → mass defect → energy released
• Fission: heavy nucleus splits → mass defect → energy released
• Energy output of nuclear power stations
• Energy produced in stars