Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Nuclear and particle physics ↓


Atomic Structure


Understanding atomic structure is a fundamental aspect of nuclear and particle physics. It provides information about the forces that hold the atomic nucleus together and the arrangement of nucleons (protons and neutrons) within the nucleus. The study of atomic structure also aids in understanding various nuclear reactions and phenomena. This exploration will introduce you to the basic concepts of atomic structure and its components, using simple language to reveal the complex and fascinating world of the atomic nucleus.

Atomic nucleus

The atomic nucleus resides at the center of the atom. While atoms are the building blocks of matter, the nucleus forms the dense central core, accounting for nearly all of the atom's mass. Within the nucleus, two types of particles, protons and neutrons, collectively known as nucleons, are held together by the nuclear force.

Protons have a positive electric charge, while neutrons have no charge. The interactions between these nucleons define the atomic structure and determine the stability and properties of the nucleus.

Forces in the nucleus

At the core of atomic structure is the interaction of various forces. The elementary forces include the strong nuclear force, the electromagnetic force, and the weak nuclear force.

Strong nuclear force

The strong nuclear force is the dominant force within the nucleus. It is responsible for binding nucleons together and acts over short distances. This force is attractive and overcomes the repulsive electromagnetic force between protons, which tends to separate them due to their positive charges.

Proton Neutron

The strength of the nuclear force decreases rapidly beyond a distance comparable to the size of the nucleon, typically around a few femtometers (1 femtometer = 1 x 10^-15 meters). Despite being the strongest force at small distances, its effect becomes negligible at larger distances.

Electromagnetic force

The electromagnetic force is responsible for the repulsion between positively charged protons. Unlike the strong nuclear force, it acts to infinite extent. However, within the confines of the nucleus, its repulsive effect is prevented by the strong nuclear force, maintaining the integrity of the nucleus.

Weak nuclear force

The weak nuclear force plays an important role in nuclear decay processes, such as beta decay, where a neutron turns into a proton or vice versa, emitting a beta particle. Although it is weaker than the strong force, it is essential for the transformation of elements and for energy production in stars.

Atomic Model

To understand nuclear structure in greater depth, scientists have developed several models that describe the arrangement and behaviour of nucleons within the nucleus. Let us look at some of the major models that provide a glimpse into the complexity of nuclear structure.

Liquid droplet model

The liquid drop model compares the nucleus to an incompressible liquid drop. This model captures the bulk properties of the nucleus, such as binding energy, by considering surface tension and volume energy. It successfully explains some aspects of nuclear stability and the distribution of nucleons.

Nucleus

While the fluid droplet model provides a good approximation, it does not take into account nuclear shell effects, which leads us to the next important model.

Shell Model

The shell model of the nucleus takes inspiration from the arrangement of electrons around the atomic nucleus. In this model, nucleons occupy specific energy levels or shells. These shells are filled with nucleons, just as electrons fill atomic orbitals.

Shells

Nucleons display a strong preference for completely filling certain shells, leading to high stability. This model effectively explains magic numbers, specific numbers of nucleons that result in particularly stable nuclei.

Collective models

The collective model bridges the gap between the liquid drop and shell models. It takes into account both the individual motion of the nucleons and the collective excitation. This model is used to describe properties such as the rotational and vibrational states of the nucleus.

By considering both individual particle interactions and collective motions, the collective model provides a more comprehensive understanding of nuclear structure.

Binding energy and stability

An important aspect of nuclear structure is the binding energy, which represents the energy needed to split a nucleus into its constituent protons and neutrons. The binding energy per nucleon is a measure of stability, and it varies among different nuclei.

The binding energy is given by Einstein's famous equation:

        E = mc²

In this context, E represents energy, m represents the mass defect, and c is the speed of light. The mass defect arises because the mass of the nucleus is slightly less than the sum of the individual masses of the protons and neutrons. This mass difference is converted into binding energy, which contributes to nuclear stability.

Radioactivity and Nuclear Decay

Some nuclei are unstable and undergo radioactive decay to achieve a more stable state. It is necessary to understand nuclear structure to understand these decay processes, which include alpha decay, beta decay, and gamma decay.

Alpha Decay

In alpha decay, a nucleus emits an alpha particle, which consists of two protons and two neutrons, resulting in a new nucleus with a lower atomic and mass number. This process is common in heavier nuclei seeking greater stability.

Beta Decay

Beta decay involves the transformation of a neutron into a proton or vice versa, accompanied by the emission of a beta particle (electron or positron). This process helps adjust the proton-to-neutron ratio, increasing nuclear stability.

Gamma Decay

Gamma decay occurs when an excited nucleus releases excess energy in the form of gamma rays, which is a high-energy electromagnetic radiation. Unlike alpha and beta decay, gamma decay does not change the composition of the nucleus.

Nuclear reactions

In addition to decay processes, nuclear reactions involve interactions between nuclei or nucleons that result in the release of energy, nuclear transmutations, or the production of new elements.

Nuclear fission

Nuclear fission is a reaction in which a heavy nucleus splits into two or more smaller nuclei, releasing a huge amount of energy. This process powers nuclear reactors and atomic bombs.

Nuclear Fusion

In contrast, nuclear fusion combines lighter nuclei into heavier ones, releasing energy. Fusion powers stars, including the Sun, and holds promise as a potential source of clean, unlimited energy on Earth.

Nuclear reactions and structure have helped unravel the mysteries of the universe, providing insight into stellar processes, the formation of elements, and the forces that shape matter at the most fundamental level.

Conclusion

The structure of the atomic nucleus is a fascinating and complex topic in nuclear and particle physics. By investigating the interactions between nucleons, the forces that govern atomic nuclei, and the models that represent their structure, we gain a deeper understanding of the natural world.

With ongoing research and advancements in nuclear physics, scientists continue to unravel the intricacies of nuclear structure, and uncover new applications and insights that benefit science, technology and our understanding of the universe.


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Atomic Structure

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