Question: Explain the terms mass defect and binding energy. How are they related?

Step 1 (Definitions): [1 Mark]

• Mass Defect ($\Delta m$): The difference between the sum of the masses of individual nucleons (protons and neutrons) and the actual observed mass of the nucleus is called the mass defect. $$ \Delta m = [Z m_p + (A - Z) m_n] - M_{nucleus} $$ Where $Z$ is the atomic number, $A$ is the mass number, $m_p$ is the mass of a proton, $m_n$ is the mass of a neutron, and $M_{nucleus}$ is the actual mass of the nucleus.
• Binding Energy ($BE$): The energy required to separate the nucleons of a nucleus to an infinite distance apart, or the energy released when nucleons combine to form a nucleus, is called the binding energy.

Step 2 (Mathematical Relationship): [0.5 Mark]

According to Einstein’s mass-energy equivalence principle ($E = mc^2$), the mass defect is converted into binding energy. The relationship is given by:

$$ BE = \Delta m \times c^2 $$

Where $c$ is the speed of light in vacuum ($c \approx 3 \times 10^8 \, \text{m/s}$).

Step 3 (Final Conclusion): [0.5 Mark]

If $\Delta m$ is expressed in atomic mass units (amu or u), the binding energy can be calculated using the conversion factor $1 \, \text{u} = 931.5 \, \text{MeV}/c^2$. Thus:

$$ BE (\text{in MeV}) = \Delta m (\text{in u}) \times 931.5 \, \text{MeV} $$

This energy acts as the "glue" that holds the nucleons together against the electrostatic repulsion of the protons.

💡 EL10 Concept Insight: Think of a nucleus like a team of people; when they come together, they lose a tiny bit of "weight" (mass defect), and that missing weight turns into the "team spirit" (binding energy) that keeps them stuck together tightly!