Saha’s equation

In combination with expression (2.44) for /x, this leads to Saha s equation (aka the Law of Mass Action) in the form... 

At high temperatures, the rates have to be summed over relevant nuclear states and the (2/ + 1)-factors in Saha s equation replaced by partition functions. 

Correcting gj Mi/H to the total abundance (mostly the first ion) using Saha s equation (Eq. 3.7), one can obtain an estimate of a metallic abundance M/H good to about 0.2 dex, provided that the linear part of the curve of growth is well defined and the value of j0n judiciously chosen. 

A particularly simple case is that of neutral metals in F- to early K-type stars where these metals are predominantly singly ionized. Applying Saha s equation (Eq. 3.7) to such metals and also to H, which is itself predominantly ionized to neutral H, one finds... 

From the analogue of Saha s equation for the dissociation of a diatomic molecule AB, one can define a dissociation constant depending only on temperature... 

Verify using Saha s equation (2.48) that the most populated form of the oxygen in the centre of the Sun is fully stripped of electrons (08+) and estimate the proportion of oxygen having one bound electron (07+), using the following information ... 

Theory of a-radioactivity by quantum tunnelling (Gamow et al). Cecilia Payne (later Payne-Gaposchkin) applies Saha s equation to the stellar spectral sequence, finding vast predominance of hydrogen and helium, but does not believe her results. 

From Saha s equation, 07+/08+ = 0.63. Lower states of ionization have lower populations, but are by no means negligible. Neglecting them nonetheless (as they will contribute some opacity), we have 07+/0 < 0.39. The opacity is then... 

THE.l. I. Prigogine, Extension de I equation de Saha au plasma non-isotherme (Extension of Saha s equation to a non-isothermal plasma). Bull. Cl. Set Acad. Roy. Belg. 26, 1-11 (1940). 

Due to the high combustion temperature, the gas is ionized in parts, the grade of ionization is determined by temperature T and ionization energy E (Saha s equation) ... 

The ionization degree can be obtained at any temperature from Saha s equation ... 

Given no other dominant source of electrons, the degree of ionization will increase as the number density (or partial pressure) of the analyte in the source decreases. The extent of ionization also increases as the ionization potential of the element decreases. The degree of ionization can be calculated using Saha s equation. 

Langmuir and Kingdon used Saha s original work [21], which was developed for plasmas, as a starting point to derive an expression for a in terms of experimental parameters. In the absence of an external electric field the equation is written... 

On the basis of the Saha-Eggert equation, the degrees of ionization for the chemical elements can be calculated for a plasma temperature of 6000 K, an electron number density of 1015 and partition functions according to Ref. [5] (Table 15) [501]. They range from over 99% for sodium to 10 s for chlorine. The argon ICP thus has good prospects for the determination of metals but for non-metals has a number of limitations as a result of these considerations. 

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