Signal and Photon SNR of Atomic Emission Spectrometry
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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, nebbulization, 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 accurately because of its many simplifying assumptions: thermal equilibrium is assumed; overall atomization efficiency includes nebulization efficiency and free-atom fraction (both assumed independent of temperature); no ionization or compound formation; self-absorption is ignored; only photon noise considered, no background emission is assumed. However, order-of-magnitude predictions may be 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:
AES.wkz;
AES.hqx
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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)