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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 model the temperature dependence); 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.

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

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)

(c) 1994, 2008, 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 toh@umd.edu.

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