Nuclear Structure

Nucleus physics aur chemistry ka core concept hai, kyunki atom ka mass aur majority energy nucleus me concentrated hoti hai. Nuclear structure ka study fundamental particles, nuclear forces, energy levels aur stability ko explain karta hai. Is post me hum nuclear components, nuclear models, binding energy, nuclear reactions, stability criteria, isotopes, and applications detail me discuss karenge.

1. Introduction

Nucleus atom ka central part hai jahan protons aur neutrons (nucleons) reside karte hain. Ye positively charged aur densely packed hota hai.

Key Points:

Atom ka mass majority nucleus me concentrated hai.
Nucleus ka size ~10⁻¹⁵ m (1 femtometer).
Nuclear structure samajhne se nuclear energy, radioactivity aur particle physics me advancements hoti hain.

2. Discovery of the Nucleus

2.1 Rutherford’s Gold Foil Experiment (1911)

Alpha particles incident on thin gold foil.
Observation: Most particles pass, kuch deflect at large angles.
Conclusion: Atom mostly empty space, small dense positively charged nucleus exists.

2.2 Proton and Neutron Discovery

Proton discovered by Rutherford (1917) → hydrogen nucleus.
Neutron discovered by James Chadwick (1932) → neutral particle in nucleus.

3. Components of the Nucleus

3.1 Protons

Symbol: p+p^+p+
Positive charge = +1.6 × 10⁻¹⁹ C
Mass = 1.6726 × 10⁻²⁷ kg

3.2 Neutrons

Symbol: n0n^0n0
Neutral particle
Mass = 1.675 × 10⁻²⁷ kg

3.3 Nuclear Forces

Strong nuclear force → binds protons and neutrons
Attractive, short-range (~1-3 fm)
Overcomes Coulomb repulsion between protons

4. Nuclear Size and Density

Nuclear radius: R=R0A1/3R = R_0 A^{1/3}R=R0A1/3, R0≈1.2×10−15mR_0 \approx 1.2 \times 10^{-15} mR0≈1.2×10−15m
Nuclear density: ρ=massvolume≈2.3×1017kg/m3\rho = \frac{mass}{volume} \approx 2.3 \times 10^{17} kg/m^3ρ=volumemass≈2.3×1017kg/m3
Nearly constant for all nuclei

5. Nuclear Models

5.1 Liquid Drop Model (Weizsäcker)

Nucleus behaves like incompressible liquid drop
Explains: Nuclear binding energy, fission
Semi-empirical mass formula (SEMF)

B=avA−asA2/3−acZ(Z−1)A1/3−aa(A−2Z)2A+δB = a_v A – a_s A^{2/3} – a_c \frac{Z(Z-1)}{A^{1/3}} – a_a \frac{(A-2Z)^2}{A} + \deltaB=avA−asA2/3−acA1/3Z(Z−1)−aaA(A−2Z)2+δ

Terms: volume, surface, Coulomb, asymmetry, pairing

5.2 Shell Model (Mayer & Jensen)

Nucleons occupy energy levels (shells)
Explains magic numbers (2,8,20,28,50,82,126) → extra stability
Analogous to electron configuration in atoms

5.3 Collective Model

Combines liquid drop & shell models
Explains rotational & vibrational states of nucleus

6. Nuclear Binding Energy

Binding energy = Energy required to separate nucleus into individual nucleons
Mass defect: Δm=[Zmp+Nmn−mnucleus]\Delta m = [Zm_p + N m_n – m_{nucleus}]Δm=[Zmp+Nmn−mnucleus]
Einstein relation: E=Δmc2E = \Delta m c^2E=Δmc2

Significance:

Determines nuclear stability
Basis of nuclear fission & fusion energy

Example:

For Helium-4:

B=[(2⋅1.0078+2⋅1.0087)−4.0026]×931.5 MeV≈28.3 MeVB = [(2 \cdot 1.0078 + 2 \cdot 1.0087) – 4.0026] \times 931.5 \text{ MeV} \approx 28.3 \text{ MeV}B=[(2⋅1.0078+2⋅1.0087)−4.0026]×931.5 MeV≈28.3 MeV

7. Nuclear Stability

7.1 Neutron-to-Proton Ratio (N/Z)

Light nuclei: N ≈ Z → stable
Heavy nuclei: N > Z → stable
Determines beta decay tendencies

7.2 Magic Numbers

Extra stability for nuclei with magic numbers of protons/neutrons
Explains existence of stable isotopes

7.3 Binding Energy per Nucleon Curve

Peaks around Iron-56
Explains why fusion releases energy for light nuclei, fission releases energy for heavy nuclei

8. Types of Nuclei

Stable Nuclei: N/Z ratio optimal
Radioactive Nuclei: Unstable → decay via alpha, beta, gamma
Exotic Nuclei: Neutron-rich or proton-rich

9. Nuclear Reactions

9.1 Fission

Heavy nucleus splits → energy release
Example: 235U+n→141Ba+92Kr+3n+energy^{235}U + n \rightarrow ^{141}Ba + ^{92}Kr + 3n + energy235U+n→141Ba+92Kr+3n+energy
Basis of nuclear reactors & weapons

9.2 Fusion

Light nuclei combine → energy release
Example: 2H+3H→4He+n+17.6MeV^2H + ^3H \rightarrow ^4He + n + 17.6 MeV2H+3H→4He+n+17.6MeV
Source of stellar energy

9.3 Radioactive Decay

Alpha (α\alphaα), Beta (β\betaβ), Gamma (γ\gammaγ) decay
Follows half-life law

N=N0e−λtN = N_0 e^{-\lambda t}N=N0e−λt

10. Experimental Techniques to Study Nuclear Structure

Scattering Experiments: Rutherford, electron scattering
Spectroscopy: Gamma-ray spectroscopy → energy levels
Particle Accelerators: Probe nucleus via high-energy collisions
Neutron Activation Analysis: Composition & structure study

11. Applications of Nuclear Structure

11.1 Energy Production

Nuclear reactors (fission)
Fusion research (ITER, tokamak)

11.2 Medicine

Radiotherapy (cancer treatment)
Diagnostic isotopes (PET, SPECT)

11.3 Industry

Radiography (material inspection)
Tracers for chemical processes

11.4 Scientific Research

Particle physics (CERN, LHC)
Nuclear astrophysics (stellar nucleosynthesis)

12. Modern Perspectives

Quantum Chromodynamics (QCD) → quarks & gluons explain nucleon structure
Exotic nuclei & halo nuclei research
Nuclear structure critical for energy security, medical applications, and advanced material research

13. Diagrams to Include

Schematic of nucleus (protons & neutrons)
Binding energy curve
Shell model diagram
Liquid drop model illustration
Fission & fusion process diagram