Signal and Photon SNR of Atomic Emission Spectrometry

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[Cell definitions and equations]

Simplified model of trace metal analysis in solution by a flame or plasma emission spectrometry. Includes the effects of solution transport, nebulization, excitation, collection of a fraction of the resulting light, detection with a monochromator and photomultiplier tube, and computation of the photon signal-to-noise ratio. The main purpose of this simulation is to demonstrate that atomic emission spectroscopy is capable of trace analysis of solutions under the right conditions and to illustrate how the signal-to-noise ratio varies with temperature and with the excitation energy of the element.

This model can not be expected to predict signals and signal-to-noise ratios perfectly because of its many simplifying assumptions: thermal equilibrium is assumed; overall atomization efficiency lumps together the nebulization efficiency and the free-atom fraction due to ionization and compound formation in the vapor phase (and does not include the temperature dependence of those factors); self-absorption is ignored; only photon noise considered, no background emission is assumed. However, even with these drastically simplifying assumptions, order-of-magnitude predictions are obtained in many cases.

Note: You may adjust the temperature and the wavelength with either the sliders or by typing into the inputs column.

Download links:

WingZ version: AES.wkz
Wingz player application and basic set of simulation modules, for windows PCs or Macintosh

OpenOffice version: AES.ods;
Excel version: AES.xls

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Cell definitions and equations:

Inputs:		
Concentration, cg	µg/mL
Solution flow rate, F	mL/sec
Overall atomization efficiency, epsilon	
Total gas flow rate, Q	L/sec
Flame/plasma temperature, T	K
Relative # moles burnt gases, nT	
Relative # moles unburnt gases, nRT		
Formula weight of analyte, MW	g/mole
Wavelength of line, lambda	nm
Einstein A coefficient, Aji	sec-1
Statistical weight of lower state,glower	
Statistical weight of upper state, gupper		
Path length, l		cm
Quantum efficiency of photocathode, Klambda	
Photomultiplier gain, m	
Slit width, W	cm
Slit height, H	cm
Solid angle of monochromator, omega	sr
Monochromator transmission factor, Top	

Outputs:		
analyte molarity, c =0.001*cg/MW	
frequency of transition, fo =(2.998E+17)/lambda	
energy of transition, E	=(6.6261E-34)*freq	
Boltzman factor	=exp(-E/(T*1.3805E-23))	
gas expansion factor, ef =(nT*T)/(nRT*298)	
Number in upper state , nupper	=
nlower*(gupper/glower)*exp(-E/(T*1.3805E-23)) 	
Number in lower state, nlower	
   =6.00E+17*F*epsilon*c/(Q*ef)	
Emission radiance, Be	=Aji*E*nupper*l/(4*pi())	
radiant cathode sensitivity, Rlambda	
   =(Klambda*1.602E-19)/E	
photoanodic current, Ie	=m*Rlambda*W*H*omega*Top*Be	
photon flux on detector, PhotFlux	
   =Aji*nupper*W*H*omega*Top/(4*pi())	
photoelectron emission rate, Rcp =Klambda*PhotFlux	
Signal-to-photon-noise ratio, SNR =Rcp/sqrt(Rcp)