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Silicon Gas-Phase Equilibrium Model

Effect of temperature on the atomic emission radiance of silicon atoms Si, Si+, and SiO species, when an Si sample is nebulized from solution into a flame or plasma at thermal equibrium with constant electron and O radical concentrations. Based on Ingle and Crouch, page 195-197. 

   8.1       Ei                eV        ionization energy  
   8.2       Ed                eV        dissociation energy                     
   16        Mx                amu       Molecular weight of X                  
   28.1      Mm                amu       Atomic weight of metal atoms M         
   44.1      Mmx               amu       Molecular weight of MX  
   4000      T                 K         Temperature of flame/plasma             
             ntotal  7.8225E9  cm-3      number density of metal in all forms 
             pm      3.911E-9  atm       partial pressure of metal atoms  
             nm      7.17663E9 cm-3      number density of metal atoms M 
             ni      546273901 cm-3      number density of metal ions M+  
   1E13      ne                cm-3      number density of electrons    
   1E15      nx                cm-3      number density of species X     
             nmx     99597608  cm-3      number density of MX molecules   
             Kd      7.2056E16 cm3       diatomic dissociation constant    
             Ki      7.6118E10 cm3       ionization constant                    
             alphai  .07073427           degree of ionization                   
             betaa   .91743413           free atom fraction                                   
   5         F                 mL/min    solution flow rate   
   .1        epsilon                     nebulization/vaporization efficiency
   1         go                          statistical weight of lower state      
   1         g1                          statistical weight of upper state      
             c       .00001    mole/L    analyte molar concentration
   1         cg                µg/mL     concentration 
   10        Q                 L/min     total gas flow rate                   
   1         ZT                          partition coefficient                  
   6         nT                moles     relative # moles burnt gases           
   7         n298              moles     relative # moles unburnt gases         
   100       MW                          formula weight of analyte 
   400       lambda            nm        wavelength of light          
   1E8       Aji               sec-1     Einstein A coefficient   
   10        l                 cm        path length          
             Be                w/sr/cm2  total line emission radiance


ntotal=6e17*F*epsilon*go*c/(Q*ef*ZT)	Equation 7-9
ef=(nT*T)/(n298*298)	Equation 7-8
n1 = nm*(g1/go)*exp(-E/(T*1.3805e-23))	Boltzmann equation 2-14
Be=Aji*h*nu*n1*l/(4*Pi()*ZT)	Equation 2-15
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T. C. O'Haver, Chem 623, 1997