imported>EatchaBot: बॉट: पुनर्प्रेषण ठीक कर रहा है

2020-03-02T05:17:53Z

बॉट: पुनर्प्रेषण ठीक कर रहा है

नया पृष्ठ

'''साहा समीकरण''' का विकाश सुप्रसिद्ध [[भारत|भारतीय]] खगोलविज्ञानी (एस्ट्रोफिजिसिस्ट्) [[मेघनाद साहा]] ने [[१९२०|1920]] में किया था। इसके द्वारा [[वर्णपट्ट]] के आधार पर [[तारा|तारों]] के वर्गीकरण की व्याख्या की गई है। For a gas composed of a single atomic species, the Saha equation is written:

:<math>\frac{n_{i+1}n_e}{n_i} = \frac{2}{\Lambda^3}\frac{g_{i+1}}{g_i}\exp\left[-\frac{(\epsilon_{i+1}-\epsilon_i)}{k_BT}\right]</math>

where:

* <math>n_i\,</math> is the density of atoms in the ''i''-th state of ionization, that is with ''i'' electrons removed.
* <math>g_i\,</math> is the [[Degenerate energy level|degeneracy]] of states for the ''i''-ions
* <math>\epsilon_i\,</math> is the energy required to remove ''i'' electrons from a neutral atom, creating an ''i''-level ion.
* <math>n_e\,</math> is the [[electron density]]
* <math>\Lambda\,</math> is the [[thermal de Broglie wavelength]] of an electron
::<math>\Lambda \ \stackrel{\mathrm{def}}{=}\ \sqrt{\frac{h^2}{2\pi m_ek_BT}}</math>
* <math>m_e\,</math> is the [[Mass of electron#Properties and behavior|mass of an electron]]
* <math>T\,</math> is the [[temperature]] of the gas
* <math>k_B\,</math> is the [[Boltzmann constant]]
* <math>h\,</math> is [[Planck's constant]]

In the case where only one level of ionization is important, we have <math>n_1=n_e</math> and defining the total density ''n''  as <math>n=n_0+n_1</math>, the Saha equation simplifies to:

:<math>\frac{n_e^2}{n-n_e} = \frac{2}{\Lambda^3}\frac{g_1}{g_0}\exp\left[\frac{-\epsilon}{k_BT}\right]</math>

where <math>\epsilon</math> is the energy of ionization.

The Saha equation is useful for determining the ratio of particle densities for two different ionization levels. The most useful form of the Saha equation for this purpose is

:<math>\frac{Z_i}{N_i} = \frac{Z_{i+1}Z_e}{N_{i+1}N_e}</math>,

where ''Z'' denotes the [[partition function (statistical mechanics)|partition function]]. The Saha equation can be seen as a restatement of the equilibrium condition for the [[chemical potential]]s:

:<math>\mu_i = \mu_{i+1} + \mu_e\,</math>

[[श्रेणी:भौतिकी]]

साहा समीकरण - अवतरण इतिहास

imported>EatchaBot: बॉट: पुनर्प्रेषण ठीक कर रहा है