In this lecture, we explore how tiny the nucleus is, understand how nucleons are bound together, calculate mass defect and binding energy, analyze the binding energy curve, and study why some nuclei are unstable (radioactive).

🔬 Microscopic Dimensions in Atom

The atom and nucleus exist at extremely small scales:

• Atomic radius ≈ 10−10 m10^{-10} \, m10−10m

• Nuclear radius ≈ 10−15 m10^{-15} \, m10−15m

Nuclear radius formula:

R=R0A1/3R = R_0 A^{1/3}R=R0​A1/3

where:

• R0≈1.2×10−15 mR_0 \approx 1.2 \times 10^{-15} \, mR0​≈1.2×10−15m

• $A$ = mass number

This shows nucleus is extremely small compared to the atom.

⚛️ How is the Nucleus Bound Together?

Inside the nucleus:

• Protons repel each other due to electrostatic force

• Yet nucleus remains stable

This is due to a very strong force called the strong nuclear force:

• Attractive

• Very short range

• Stronger than electrostatic repulsion

⚖️ Mass Defect

When nucleons combine to form a nucleus:

• The mass of nucleus is slightly less than the sum of individual nucleon masses

This difference is called mass defect (Δm).

Δm=(Zmp+Nmn)−mnucleus\Delta m = (Z m_p + N m_n) – m_{nucleus}Δm=(Zmp​+Nmn​)−mnucleus​

💥 Binding Energy

Mass defect converts into energy according to:

E=Δmc2E = \Delta m c^2E=Δmc2

This energy is called Binding Energy.

Binding energy is the energy required to completely separate a nucleus into its nucleons.

🔹 Binding Energy per Nucleon

BE per nucleon=BEA\text{BE per nucleon} = \frac{BE}{A}BE per nucleon=ABE​

Higher binding energy per nucleon → More stable nucleus.

📈 Binding Energy Curve

The graph of binding energy per nucleon vs mass number shows:

• Increases sharply for light nuclei

• Peaks near Iron (Fe-56)

• Decreases slowly for heavy nuclei

📌 Significance

• Light nuclei release energy by fusion

• Heavy nuclei release energy by fission

• Iron is most stable element

☢️ Nuclear Instability (Radioactivity)

Some nuclei are unstable because:

• Too many neutrons or protons

• Weak binding energy

• Imbalance in nuclear forces

Unstable nuclei undergo radioactive decay to become stable.

Examples:

• Uranium

• Radium

• Tritium

🎯 By the End of This Lecture

You will:

• Understand nuclear dimensions

• Explain strong nuclear force

• Calculate mass defect

• Calculate binding energy

• Interpret binding energy curve

• Understand nuclear instability

This lecture prepares you for studying radioactivity and nuclear reactions in upcoming lessons.