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Flame Atomic Emission Signal

TK Solver model for the atomic emission signal generated by a solution sprayed into a flame at chemical equilibrium, viewed by a monochromator with a photomultiplier detector.

Variable sheet:

St Input     Name    Output    Unit      Comment                                
   5         cg                g/mL     concentration (g/L,g/mL,mg/mL,g/mL,pp 
   5         F                 mL/min    solution flow rate (mL/sec, mL/min)    
   .03       epsilon                     overall atomization efficiency         
   10        Q                 L/min     total gas flow rate (L/sec, L/min)    
   2000      T                 K         Temperature in K                       
   1         nT                moles     relative # moles burnt gases           
   1         n298              moles     relative # moles unburnt gases         
   63.5      MW                          formula weight of analyte (g/mole)     
   324.7     lambda            nm        wavelength of light (nm, A, m, cm)    
   1E8       Aji               sec-1     Einstein A coefficient (sec-1)         
   2         go                          statistical weight of lower state      
   4         g1                          statistical weight of upper state      
   1         l                 cm        path length (cm, mm, m)               
             Rlambda 26.185157 mA/watt   radiant cathode sensitivity (amps/watt 
   .1        Klambda                     Quantum efficiency of photocathode     
   500000    m                           photomultiplier gain                   
   50        W                 m        slit width (cm, mm, m)                
   5         H                 mm        slit height (cm, mm, m)               
   .02       omega             sr        solid angle of monochromator (steradia 
   .6        Top                         transmission factor of monochromator   
             c       .00007874 mole/L    analyte molar concentration (mole/L)   
             freq    9.2331E14 Hz        frequency (Hz)                         
             E       6.118E-19 J         energy (Joule, erg, eV, kcal/mole)     
             v       30797.659 cm-1      wavenumber (cm-1)                      
             ef      6.7114094           gas expansion factor                   
             n1      50.272252 cm-3      Number in upper state (cm-3)           
             no      1.0559E11 cm-3      Number in lower state (cm-3)           
             Be      2.448E-10 w/sr/cm2  total line emission radiance (watts/st 
             Ie      9.613E-11 amps      photoanodic current (amps)             
             PhotFlu 12001.616 sec-1     photon flux on detector, photons/sec   
             Rcp     1200.1616 sec-1     photoelectron emission rate, sec-1     
             PhotSNR 34.643349           Signal-to-photon-noise ratio    

Rule sheet.
  E = (6.6261E-34)*freq                                                         
  freq = (2.998E10)/lambda   
  lambda = 1/v  
  no=6e17*F*epsilon*c/(Q*ef)              " Equation 7-9                                         
  ef=(nT*T)/(n298*298)                    " Equation 7-8                                         
  n1 = no*(g1/go)*exp(-E/(T*1.3805e-23))  " Boltzman equation 2-14                                                     
  Be=Aji*E*n1*l/(4*Pi())                  " Equation 2-15                                 
  Rlambda=(Klambda*1.602e-19)/E           " Paragraph after equation 4-28  
Download the Flame Emission model.

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T. C. O'Haver, Chem 623, 1994