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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:

Concentration, cg g/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

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 =
Number in lower state, nlower
Emission radiance, Be =Aji*E*nupper*l/(4*pi())
radiant cathode sensitivity, Rlambda
photoanodic current, Ie =m*Rlambda*W*H*omega*Top*Be
photon flux on detector, PhotFlux
photoelectron emission rate, Rcp =Klambda*PhotFlux
Signal-to-photon-noise ratio, SNR =Rcp/sqrt(Rcp)

(c) 1991, 2015. This page is part of Interactive Computer Models for Analytical Chemistry Instruction, created and maintained by Prof. Tom O'Haver , Professor Emeritus, The University of Maryland at College Park. Comments, suggestions and questions should be directed to Prof. O'Haver at
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