|
Spectral Line Shape
Spectral line shape or spectral line profile describes the form of an electromagnetic spectrum in the vicinity of a spectral line – a region of stronger or weaker intensity in the spectrum. Ideal line shapes include Lorentz distribution, Lorentzian, Normal distribution, Gaussian and Voigt function, Voigt functions, whose parameters are the line position, maximum height and half-width. Actual line shapes are determined principally by Doppler broadening, Doppler, Spectral line#Broadening and shift, collision and proximity broadening. For each system the half-width of the shape function varies with temperature, pressure (or concentration (chemistry), concentration) and phase. A knowledge of shape function is needed for spectroscopic curve fitting and deconvolution. Origins A spectral line can result from an electron transition in an atom, molecule or ion, which is associated with a specific amount of energy, ''E''. When this energy is measured by means of some spectroscopic te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permanganate Spectrum
A permanganate () is a chemical compound with the manganate(VII) ion, , the conjugate base of permanganic acid. Because the manganese atom has a +7 oxidation state, the permanganate(VII) ion is a strong oxidising agent. The ion is a transition metal oxo complex, transition metal ion with a tetrahedral molecular geometry, tetrahedral structure. Permanganate solutions are purple in colour and are stable in pH, neutral or slightly alkaline media. Production Permanganates can be produced by oxidation of manganese compounds such as manganese chloride or manganese sulfate by strong oxidizing agents, for instance, sodium hypochlorite or lead dioxide: :2 MnCl2 + 5 NaClO + 6 NaOH → 2 NaMnO4 + 9 NaCl + 3 H2O :2 MnSO4 + 5 PbO2 + 3 H2SO4 → 2 HMnO4 + 5 PbSO4 + 2 H2O It may also be produced by the disproportionation of manganates, with manganese dioxide as a side-product: :3 Na2MnO4 + 2 H2O → 2 NaMnO4 + MnO2 + 4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Protic
In chemistry, a protic solvent is a solvent that has a hydrogen atom bound to an oxygen (as in a hydroxyl group ), a nitrogen (as in an amine group or ), or fluoride (as in hydrogen fluoride). In general terms, any solvent that contains a labile is called a protic solvent. The molecules of such solvents readily donate protons () to solutes, often via hydrogen bonding. Water is the most common protic solvent. Conversely, polar aprotic solvents cannot donate protons but still have the ability to dissolve many salts. Methods for purification of common solvents are available See also * Autoprotolysis In chemistry, autoprotolysis is a molecular autoionization, a chemical reaction in which a proton is transferred between two identical molecules, one of which acts as a Brønsted acid, releasing a proton that is accepted by the other molecule, wh ... References {{Chemical solutions Solvents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. High-resolution nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crysta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL). The number one is recognized as a dimensionless base quantity. Radians serve as dimensionless units for angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios in limits or derivatives often involve dimensionless quantities. In differential geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Spectrum
The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high frequency these are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The electromagnetic waves in each of these bands have different characteristics, such as how they are produced, how they interact with matter, and their practical applications. Radio waves, at the low-frequency end of the spectrum, have the lowest photon energy and the longest wavelengths—thousands of kilometers, or more. They can be emitted and received by antenna (radio), antennas, and pass through the atmosphere, foliage, and most building materials. Gamma rays, at the high-frequency end of the spectrum, have the highest photon energies and the shortest wavelengths—much smaller than an atomic nucleus. Gamma rays, X-rays, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m−1). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the '' ordinary frequency'', defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the ''angular frequency'', defined as the phase angle divided by time (in radians per second). In multidimensional systems, the wavenumber is the magnitude of the '' wave vector''. The space of wave vectors is called ''reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full Width At Half Maximum
In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the ''y''-axis which are half the maximum amplitude. Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric. The term full duration at half maximum (FDHM) is preferred when the independent variable is time. FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of spectrometers. The convention of "width" meaning "half maximum" is also widely used in signal processing to define bandwidth as "width of frequency range where less than half the signal's power is attenuated", i.e., the power is at least half the maximum. In signal processing terms, this is at most −3 dB of att ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalizing Constant
In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one. For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes' theorem, a normalizing constant is used to ensure that the sum of all possible hypotheses equals 1. Other uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions. A similar concept has been used in areas other than probability, such as for polynomials. Definition In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e.g., to make it a probability density function or a probability mass function. Examples If we start from the simple Gaussian function p(x) = e^, \quad x\in(-\infty,\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Distribution
The Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f(x; x_0,\gamma) is the distribution of the -intercept of a ray issuing from (x_0,\gamma) with a uniformly distributed angle. It is also the distribution of the Ratio distribution, ratio of two independent Normal distribution, normally distributed random variables with mean zero. The Cauchy distribution is often used in statistics as the canonical example of a "pathological (mathematics), pathological" distribution since both its expected value and its variance are undefined (but see below). The Cauchy distribution does not have finite moment (mathematics), moments of order greater than or equal to one; only fractional absolute moments exist., Chapter 16. The Cauchy dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voigt DistributionPDF
Voigt (mainly written Vogt, also Voight) is a German surname, and may refer to: * Alexander Voigt, German football player * Alwin Voigt (1852–1922), German school teacher, writer, and ornithologist * Angela Voigt, East German long jumper * Christian August Voigt (1808–1890), Austrian anatomist * Cynthia Voigt, author of books for young adults * Deborah Voigt, American opera singer * Edward Voigt, born in Bremen, Germany, former U.S. Representative from Wisconsin * Edwin Edgar Voigt, bishop * Ellen Bryant Voigt, German American poet * Erika Voigt, actress *Frank Voigt, musician; flute player in the 1970s progressive rock band Think *Frederick Augustus Voigt (1892–1957), British journalist and author of German descent * Friedrich Siegmund (Sigismund) Voigt (Voight) ( 1781–1850), German botanist and zoologist * Georg Voigt, German historian * Harry Voigt, German Olympic athlete * Irma Voigt (1882–1953), Dean of Women at Ohio University * Jaap Voigt (born 1941), Dutch fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
