What is the relationship between nuclear binding energy and the mass defect of the nucleus?

The nuclear binding energy is directly related to the mass defect of a nucleus through Einstein’s mass-energy equivalence principle.

Relationship:

Binding Energy (E) = Mass Defect (Δm) × c²

Where:

• Δm = mass defect
• c = speed of light (= 3 × 10⁸ m/s)

What this means:

• The mass defect represents the mass that is converted into energy when the nucleus is formed
• This energy is the binding energy, which holds the nucleus together

Key implications:

• Higher mass defect → Higher binding energy → More stable nucleus
• Lower mass defect → Lower binding energy → Less stable nucleus

Example:

If a nucleus has a larger mass defect, it means more energy was released during its formation, making it tightly bound and stable

Key Takeaway:

Mass defect and binding energy are directly proportional—mass lost during nucleus formation is converted into binding energy using E = mc².