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Meghnad Saha

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Meghnad Saha - Wikipedia, the free encyclopedia He produced the famous equation which he called 'equation of the reaction - isobar for ionization' which later became known as Saha's "Thermo-Ionization Equation". Saha was the leading spirit in organizing the scientific societies like the 'National Academy of Science' ( 1930), ' Indian Institute of Science ' (1935) and the 'Indian Association for the Cultivation of Science' (1944). The lasting memorial to him is the 'Saha Institute of Nuclear Physics' founded in 1943 in Kolkata. en.wikipedia.org /wiki/Meghnad_Saha

Saha ionization equation - Wikipedia, the free encyclopedia The Saha ionization equation was developed by the Indian astrophysicist Meghnad Saha in 1920. This equation simply states that the potential for an atom of ionization state r to ionize is the same as the potential for an electron and an atom of ionization state r+1 ; the potentials are equal, therefore the system is in equillibrium and no net change of ionization will occur. This equation is useful for determining the ratio of particle densities for two different ionization levels. www.wikipedia.org /wiki/Saha_equation

saha.htm Saha graduated with his master's degree in applied mathematics in 1915 and by 1919 he had developed an equation having to do with high-temperature ionization which today bears his name. One of Saha's greatest contributions to the field of astrophysics was the publication of his paper on stellar spectra which linked gas thermodynamics and kinetics to plasma. Born in Seoratali, India, Meghnad Saha was an astrophysicist whose interests lied in the areas of astrophysics and the quantum theory. www.upei.ca /~xliu/multi-culture/saha.htm

saha equation Ionization equilibrium is described by the Saha equation. Thermal equilibrium between atomic and ion states is described by the Boltzman equation, where the statistical weight of the ion state is approximately given by the number density of free states with momenta less than thermal, and the statistical weight of the atomic state by the number density of nuclei. Ionization occurs at a temperature which is much smaller than the ionization potential expressed in temperature units; www.aoc.nrao.edu /~jweather/physics425/node12.html

Patent 5426056: Surface ionization detector for detecting trace amounts of organic molecules As well, equation (4) shows that the ionization efficiency, and hence the surface ionization process as a whole, is very specific to particular molecules since it is strongly dependent on the ionization energy (IE) of the particular species. The Saha-Langmuir equation (2) is based on the assumption that thermal and charge equilibria are established between the species on the surface and the surface material itself. From equation (8) it can be seen that the mass of the ion becomes much larger than the mass of the drift gas molecules, thus the mass dependent term of the equation becomes insignificant. www.freepatentsonline.com /5426056.html

Plasma physics - Wikipedia, the free encyclopedia The degree of ionization is determined by the electron temperature relative to the ionization energy (and more weakly by the density) in accordance with the Saha equation. Although ionization can be caused by UV radiation, energetic particles, or strong electric fields, processes that tend to result in a non- Maxwellian electron distribution function, it is most commonly caused by heating the electrons in such a way that they are close to thermal equilibrium so the electron temperature is relatively well-defined. The simplest possibility is to treat the plasma as a single fluid governed by the Navier Stokes Equations. www.wikipedia.org /wiki/Plasma_physics

Theoretical Principles of Plasma Physics and Atomic Physics Saha Equation: The Saha equation describes the ratio of different stages of ionization of an atom under the assumption of LTE and, like the latter, suffers therefore from the limitation that it is strictly only applicable if elastic collisions are responsible for establishing the energetic distribution of particles. Examples for a detailed balance equation are the Boltzmann Equation and the equation for the atomic Level Population (in contrast, for both of these cases LTE -models with their given energy distribution will generally yield invalid results). Auto- Ionization: Contrary to established opinion, atoms or molecules can ionize each other through collisions even if their translational energy is smaller than the ionization energy. www.incywincy.com /default?catid=40622&cached=www.plasmaphysics.org.uk

Astron. Astrophys. 347, 696-710 (1999) He showed that, just as in the quiet chromosphere, the ionization equation is controlled by spontaneous recombination to the second level and by photoionization from this level by photospheric radiation. For hydrogen, given that it is the most abundant element, we employ a non-LTE correction to the Saha equation, as given by Brown (1973). Using a two-level model of a hydrogen atom Brown calculated the non-LTE effects on the ionization equilibrium of hydrogen in optical flares. aa.springer.de /papers/9347002/2300696/sc3.htm

Relic radiolines of hydrogen at decimeter and meter wavelength band In the presence of thermodynamical equilibrium we can describe ionization state of gas by Saha equation ( Zeldovich et al. In the case of recombination, caused by slow ``decay'' of Lyman quanta at the expense of two-photon processes, one cannot use Saha equation. Exactly therefore the disturbances are not appeared in the period of full ionization, because all recombination acts are compensated by appropriate number of ionizations. www.mrao.cam.ac.uk /yerac/stolyarov/stolyarov.html

Stellar Atmospheres Aller (1963) gives a discussion of computations of ionization using Boltzmann statistics and the Saha equation and also presents tabular data and a graph based on computations using the Goldberg et al. Astronomers are interested in the extent of ionization of the elements in stellar atmospheres as a function of bulk composition (e.g., deviation from solar composition), temperature, and pressure. Below we give a comparison of CONDOR results with results from Aller (1963). solarsystem.wustl.edu /stellar.htm

Research Interests S.Fritzsche Theor.Physik Univ.Kassel In a different derivation of matrix DF equation, we applied the method of rotation (Werner and Meier 1980) in which closed- and open-shell matrix equations need not to be distinguished for the orbital wave functions of the same symmetry. In the closed-shell case the derivation of the matrix DF equations results in a coupled system of generalized eigenvalue equations which have to be solved self-consistently. Ionization processes in many-electron atoms often depend strongly on correlations between the electrons. www.physik.uni-kassel.de /theo/fritzsche/forschung_en.html

Saha, Meghnad N. --  Encyclopædia Britannica Saha, Meghnad N. Indian astrophysicist noted for his development in 1920 of the thermal ionization equation, which, in the form perfected by the British astrophysicist Edward A. Milne, has remained fundamental in all... Indian astrophysicist noted for his development in 1920 of the thermal ionization equation, which, in the form perfected by the British astrophysicist Edward A. Milne, has remained fundamental in all work on stellar atmospheres. This equation has been widely applied to the interpretation of stellar spectra, which are characteristic… www.britannica.com /eb/article?tocId=9064747

Lecture 9 - Statistical Mechanics (2/11/99) The ionization energy from He II to He III is four times 13.6 eV because the energy goes as the charge squared, and He II looks like hydrogen with a single electron, but more positive charge in the nucleus. The ionization energy of He 24.6 eV is slightly less than twice hydrogen because of the screening of the other electron. Ionization states of atoms are designated by the chemical symbol for the element (H=hydrogen, He=Helium, C=Carbon, etc) and a Roman numeral (I=neutral, II=singly ionized, III=doubly ionized, etc.) www.aoc.nrao.edu /~smyers/courses/astro12/L9.html

1 Introduction The plasma of the stellar interior is treated as a mixture of perfect gases of all species (atoms, ions, nuclei and electrons), and the Saha equation is solved to yield the degrees of ionization or molecular formation. This simple equation of state essentially contains a mixture of ideal gases, ionization of the chemicals is dealt with by the Saha equation, excited states and molecules are neglected, complete pressure ionization is artificially imposed above certain temperatures and pressures, and no Coulomb-pressure correction is included (see Although the MHD equation of state was originally designed to provide the level populations for opacity calculations of stellar envelopes, the associated thermodynamic quantities of MHD can none the less be reliably used also for stellar cores. www.edpsciences.org /journal/index.cfm?v_url=aas/full/1999/06/ds6265/node1.html

Meghnad Saha - TheBestLinks.com - February 16, October 6, TheBestLinks.com:Find or fix a stub, 1956, ... Meghnad Saha ( October 6 1893 – February 16 1956) was an Indian astrophysicist. He made a major theoretical contribution to understanding the ionization of stellar atmospheres. Meghnad Saha, February 16, October 6, TheBestLinks.com:Find or fix a stub, 1956... www.thebestlinks.com /Meghnad_Saha.html

Patent 4023038: Increased ionization rate in laser enrichment Since plural transitions may typically be employed to reach the ionization continuum, it is apparent that each of N energy states will be populated to an extent which is only 1/N of the population of the illuminated particles. The method of claim 2 wherein the step of applying further energy to ionize the particles is achieved by impact ionization and the plural distinct closely spaced energy levels below the ionization level are within a small fraction of an electron volt of the ionization level for the particles of the one isotope type. The concept is implemented in the preferred embodiment in a system for elemental uranium enrichment but may be more broadly applied to ionization of molecular or atomic particles in a medium generally. www.freepatentsonline.com /4023038.html

EQUATION OF STATE Unlike the deeper interiors of stars, their atmospheres are not fully ionized, and the ionization state must be calculated. ) is the fraction of the ionization state j that is in excitation state i. The energy above the ground state where this begins is the ionization potential c www.physics.uc.edu /~sitko/Astrophysics-II/5-EquationsOfState/5-EquationsOfState.htm

UNLV XAMS research interests The distinction between shallow and deep core levels is significant because the ultimate degree of ionization in the two cases is different, resulting in measurable differences in the decay dynamics of core holes produced by x-ray absorption. Theoretical prediction of the energy dependence of double ionization of helium by a single photon is a fundamental problem in atomic physics which requires solution of the Coulomb three-body problem. Thus, photoionization can be distinguished from Compton ionization in an experiment that uses an electron-energy analyzer with a broad pass energy centered near E as the trigger for an ion-TOF analyzer. www.unlv.edu /Research_Centers/Xray_Atomic_and_Molecular_Spectroscopy/xamsrese.htm

3 The population of excited and ionized Na atoms The Boltzmann and Saha equations can be applied on systems in local thermodynamic equilibrium as it happens, in first approximation, for the plasma cloud. In the case of ionized states, it is necessary to use the Saha equation that gives the ratio between the i +1 and the i ionized atoms ( i =0 is the neutral atom): Other alkaline metals (like potassium), with low ionization energy, are less abundant than sodium and other elements have higher ionization energy, so we can consider the sodium as the major contributor to the free electron population. www.edpsciences.org /articles/aa/abs/2002/41/aah3635/node3.html

The Saha-Boltzmann Equation The book does a reasonable job, describing the equations describing the distribution of particles among bound levels and ionization states and they won't be repeated here. www.ess.sunysb.edu /dpeterso/AST341/notes/Lec12/node1.html

Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations The Saha equation, which relates temperatures to ion densities, is sometimes used under circumstances that do not justify the assumptions of thermodynamic equilibrium upon which it is based. This equation reduces to Saha's equation in the limit of thermal equilibrium. Under certain conditions results are expected that differ enormously from those predicted by the Saha equation. www.osti.gov /energycitations/product.biblio.jsp?osti_id=4047330

AllRefer.com - Meghnad Saha (Physics, Biography) - Encyclopedia His theory of high-temperature ionization of elements and its application to stellar atmospheres, expressed in the Saha equation, is fundamental to modern astrophysics; subsequent development of his ideas has led to increased knowledge of the pressure and temperature distributions of stellar atmospheres. Meghnad Saha [m A gnAd´ sA´hA] Pronunciation Key, 1893–1956, Indian physicist. AllRefer.com - Meghnad Saha (Physics, Biography) - Encyclopedia reference.allrefer.com /encyclopedia/S/Saha-Meg.html

Astron. Astrophys. 326, 187-194 (1997) The free energy is minimized in order to obtain the Saha equation which is required to find the number of particles in each degree of ionization. Most of the physical quantities appearing in the equations for energy and pressure of different kinds of gases can be identified, explicitly or implicitly, in terms of number density of electrons. Because of the low abundance of heavy elements in the solar mixture, probably it is unnecessary for those elements, to calculate the quantities such as partition functions and the number of elements at any degree of ionization, with high accuracy. aa.springer.de /papers/7326001/2300187/sc3.htm

SPECTRAL LINE FORMATION Note that the Boltzmann equation can be used to evaluate some of the above fractions, and that the Saha equation can be used to evaluate the others. Ionization equilibrium means that the number of electrons that are ionized equals the number of electrons that recombine with ions. The ionization fraction goes from 0 to 100% in temperature range of only ~300 K. This explains why Balmer lines are strongest in A-type stars (T = 10000K), despite the fact that a temperature that is 8 times higher is required in order to get substantial excitation into the n=3 and higher energy levels. personal.tcu.edu /~pmarcum/courses/P3113/handouts/spectral_lect.html

MAS211, Introduction to Stellar Structure Degree of ionization, Saha's equation, application to stellar interiors and atmospheres, mean molecular weight. Concept of ideal gas, temperature, Maxwell Boltzmann distribution, ideal gas equation of state, ionization, equation of state for a degenerate gas, application to stellar interiors. Maxwell velocity distribution, ideal gas equation of state, degeneracy and the condition for its onset, equation of state for degenerate plasma. www.maths.qmw.ac.uk /~sharon/courses/MAS211.html

Homework 2 (c) [6 pts] Which parameter of the Saha ionization-equilibrium equation is most important in explaining the spectral differences between (i) giants and dwarfs of spectral type G; (ii) B and A dwarfs. www.astro.indiana.edu /~classweb/a202s0497/homework2.html

Re: Question : as an approximation in the Saha Equation. One would then have : to solve two simultaneous equations, but that would not change : the result significantly and is not required for : this excercise. To be more accurate, one : must include the fact that the neutral density is not constant; : it is reduced as the ionization density increases (since it is : the neutral atoms that are being ionized). www.eecs.umich.edu /~dpu/wwwboard/messages/51.html

Payne-Gaposchkin,_Cecilia_Helena@869182814.html From the spectra of stars, she determined stellar temperatures and chemical abundances using the thermal ionization equation of Saha. Dissertation: Application of the theory of thermal ionization (Saha's equation) to the study of temperatures and chemical abundance in stars. Payne-Gaposchkin's discovery that hydrogen was the most abundant substance in the universe is not officially or generally credited to her, this discovery having been made when she was a 25-year old doctoral candidate at Harvard. www.physics.ucla.edu /~cwp/internal/Astrophysics/Payne-Gaposchkin,_Cecilia_Helena@869182814.html

ASTR 498N Lecture 2 The Saha equation applies to thermodynamic equilibrium.  As in the case of the Boltzmann formula, an ionization temperature T The Saha equation is sometimes multiplied through by kT and written in terms of P describing the relative number densities of two ionization states of the same ion, r -times ionized and ( r +1)-times ionized, in terms of the ionization potential χ www.astro.umd.edu /~drabin/Lecture2.htm

Use of relaxation and correlation methods for NLTE problems To remove some of these drawbacks we propose to replace the equations of statistical equilibrium for the populations of atomic states and corrections to the corresponding equation of radiative transfer by the time-dependent equations and to solve them as the evolutionary equations from some adopted initial values. To reduce the number of equations, the concept of strongly correlated or clustered states which are with each other in the thermal equilibrium is treated shortly. In the result the system of equations turns into the non-linear relative to atomic state populations, but as we show further this circumstance does not complicate or modify the method of solution of these equations. www.aai.ee /~sapar/meetings/tuebingen/relax.html

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