Nuclear Physics

Nuclear physics is the branch of physics that studies the constituents, structure, and behavior of atomic nuclei. It explores the interactions and forces that hold protons and neutrons together, nuclear reactions such as fission and fusion, and the properties of nuclear matter.

Atomic Nucleus

The atomic nucleus is composed of protons and neutrons, collectively called nucleons. Protons carry a positive electric charge, while neutrons are electrically neutral. The number of protons defines the element (atomic number $Z$ ), and the total number of nucleons is the mass number $A$ .

${}^A_ZX = {}^{A}_{Z}\text{Element}$

where $A = Z + N$ and $N$ is the number of neutrons.

Nuclear Forces

The main force binding nucleons is the strong nuclear force, which:

Acts over very short ranges (~1 femtometer = $10^{-15}$ m),
Is much stronger than electromagnetic repulsion between protons,
Is attractive and charge-independent.

This force overcomes the repulsive Coulomb force among protons to keep the nucleus stable.

Nuclear Binding Energy

The binding energy $E_b$ of a nucleus is the energy required to disassemble it into free protons and neutrons. It can be approximated by the semi-empirical mass formula (Weizsäcker formula):

$E_b(Z, A) = a_v A - a_s A^{2/3} - a_c \frac{Z^2}{A^{1/3}} - a_a \frac{(A - 2Z)^2}{A} + \delta(A,Z)$

where

$a_v$ is the volume term coefficient,
$a_s$ is the surface term coefficient,
$a_c$ is the Coulomb term coefficient,
$a_a$ is the asymmetry term coefficient,
$\delta$ is the pairing term.

The binding energy per nucleon peaks near iron ( ${}^{56}Fe$ ), explaining why fusion releases energy for light nuclei and fission for heavy nuclei.

Nuclear Reactions

Nuclear physics studies many types of reactions, including:

Fission: splitting of a heavy nucleus into lighter nuclei, releasing energy.
Fusion: combining light nuclei into heavier nuclei, releasing energy.
Radioactive decay: spontaneous transformation of unstable nuclei, such as alpha, beta, and gamma decay.
Scattering experiments: probing nuclear structure by colliding particles.

The general reaction can be written as:

$A + a \rightarrow B + b$

where $A$ and $a$ are initial particles/nuclei and $B$ and $b$ are reaction products.

Quantum Mechanics in Nuclear Physics

Quantum mechanics plays a central role:

Nucleons occupy discrete energy levels,
Nuclear spin and parity affect stability,
Quantum tunneling explains alpha decay,
Exchange forces and meson theories model nucleon interactions.

Applications of Nuclear Physics

Energy production: nuclear power plants via controlled fission,
Medical uses: radiation therapy, PET scans,
Astrophysics: nucleosynthesis in stars, supernovae,
Particle physics: understanding fundamental particles,
Nuclear weapons: uncontrolled fission and fusion reactions.

Important Constants and Units

Nuclear radius: $R \approx R_0 A^{1/3}$ where $R_0 \approx 1.2\ \text{fm}$
Mass of proton: $m_p \approx 1.00728\ \text{u}$
Mass of neutron: $m_n \approx 1.00866\ \text{u}$
1 atomic mass unit (u) $= 931.5\ \text{MeV}/c^2$

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Nuclear Physics

Contents

Nuclear Physics

Atomic Nucleus

Nuclear Forces

Nuclear Binding Energy

Nuclear Reactions

Quantum Mechanics in Nuclear Physics

Applications of Nuclear Physics

Important Constants and Units

See also