Category: Index
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Bessel Functions
Introduction Bessel functions, named after Friedrich Bessel, are canonical solutions to Bessel’s differential equation: This equation arises in many physical problems, including heat conduction, vibrations of circular membranes, and quantum mechanics. Bessel Functions of the First Kind The Bessel function of the first kind is defined by the series: Alternatively, it can be expressed as…
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Quasar
Introduction A quasar, or a quasi-stellar object (QSO), is an extremely luminous active galactic nucleus (AGN). Quasars are among the most distant objects in the universe, and their extreme brightness is generated by supermassive black holes at the center of galaxies. The Power Source of a Quasar The central engine powering quasars is a supermassive…
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Nuclear Overhauser Effect (NOE)
Introduction The Nuclear Overhauser Effect (NOE) is a crucial phenomenon in nuclear magnetic resonance (NMR) spectroscopy, specifically used for the investigation of macromolecular structures and interactions. Basic Principles of NOE The NOE arises due to the magnetic interactions between different nuclear spins within a molecule in solution. When one nucleus is selectively irradiated, it can…
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Carbon Dating
Introduction Carbon dating, also known as radiocarbon dating, is a scientific method used to determine the age of organic material. This technique is founded on the principles of radioactive decay, and specifically on the decay of carbon-14 isotope. Radioactive Decay of Carbon-14 Carbon-14 is a radioactive isotope of carbon with a half-life of about 5,730…
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Gibbs Free Energy
Introduction Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. It is a useful concept in the field of thermodynamics and is especially relevant in processes such as chemical reactions, phase transitions, and solution formation. Definition Gibbs free energy is…
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Atmosphere
Introduction The atmosphere is the layer of gases, commonly known as air, that surrounds the Earth and is retained by Earth’s gravity. It protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention (via the greenhouse effect), and reducing temperature extremes between day and night. Composition of the Atmosphere The…
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Ionizing Radiation
Introduction Ionizing radiation refers to any form of radiation that has enough energy to remove tightly bound electrons from their atoms, thus creating ions. These types of radiation are largely hazardous due to their high energy and potential for biological damage. Types of Ionizing Radiation Ionizing radiation can be categorized into two main types: direct…
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Helmholtz Free Energy
Introduction Helmholtz free energy, named after the physicist Hermann von Helmholtz, is an important concept in the field of thermodynamics. It quantifies the reversible work available in a system at constant temperature and volume. Definition of the Helmholtz Free Energy The Helmholtz free energy of a thermodynamic system is defined as where is the internal…
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Kerr Black Hole
Introduction A Kerr black hole is a type of rotating black hole that is described by the Kerr metric in general relativity. Named after physicist Roy P. Kerr who discovered this solution in 1963, it describes a black hole rotating about an axis of symmetry. Kerr Metric The Kerr metric is given by the line…
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Galactic Rotation Curve
Introduction A galactic rotation curve is a graph of the orbital speeds of visible stars or gas in a galaxy versus their radial distance from that galaxy’s center. It is crucial in the study of galaxy formation and evolution and has significant implications for the understanding of dark matter. Theoretical Framework Keplerian Rotation If the…