Spectroscopic Simulation of Atomic Absorption
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[Operating instructions] [Cell definitions and equations] [Student assignment handout]
[Operating instructions] [Cell definitions and equations] [Student assignment handout]
The spectroscopy of a line-source atomic absorption measurement with continuum-source background correction in a steady-state (i.e. flame) atomizer. The purpose of the simulation is to make it clearer how the various spectroscopic aspects relate to each other and to the measured absorbance. Students observe the relationship of the hollow cathode lamp emission profile to the atomic absorption profile, observe the effect of changing line widths, correction of background absorption by continuum-source (D2) method, overcorrection caused by structured background absorption, and the effect of non-absorbing lines, line-overlap interferences, and hyperfine structure.
Download links:
AtomicAbsorption.wkz;
AtomicAbsorption.hqx
Having trouble getting this to work? Download the complete system of modules for
PC or Mac.
Return to the Index.
INPUTS:
shift = collisional shift of absorption line, pm.
abs. width = spectral width of atomic absorption line, pm.
source width = spectral width of hollow-cathode lamp emission line, pm.
atom density = relative concentration of atoms in atomizer, arbitrary units.
stray light = relative intensity of continuum background radiation from hollow-cathode lamp.
background abs. = non-specific background absorption in atomizer.
non-abs. line = intensity of a non-absorbing line from HCL. arbitrarily placed at -60 pm, relative to main resonance line.
interference = peak absorbance of martix absorption line, arbitrarily placed at +60 pm.
hyperfine = relative intensity of hyperfine line, relative to main resonance line.
Array calculations:
A39..A139: wavelength = -100 to +100 (displacement in pm from resonance wavelength)
Total number of wavelength intervals = NumWavelengths
B39..B139: absorbance = PeakAbs/(1+((wavelength-shift)/AbsWidth)^2)+
Interf/(1+((wavelength-80)/AbsWidth)^2)+
Hyper*PeakAbs/(1+((wavelength-6)/AbsWidth)^2)
C39..C139: transmission = 10^(-absorbance-BackAbs)
D39..D139: SourceIntensity = exp(-((wavelength)/SourceWidth)^2)+StrayLight/100+
NonAbs*exp(-((wavelength+60)/SourceWidth)^2)+
Hyper*exp(-((wavelength-6)/SourceWidth)^2)
E39..E139: TransmittedIntensity = transmission*SourceIntensity
Graph shows spectral profile in region ±100 pm around resonance line.
Gray line: SourceIntensity
Blue line: transmission
Red line: TransmittedIntensity
OUTPUTS:
Peak abs. = "true" peak absorbance at center of absorption line.
Width ratio = ratio of absorption width to source width.
Cont. A = absorbance measured with continuum source.
Uncorr. A = absorbance measured with line source.
Corrected A = atomic absorbance corrected for background absorbance (equals Uncorr. A - Cont. A).
measured I = total intensity transmitted through atomizer, measured at the detector over the entire spectral bandpass.
measured I-zero = total incident intensity measured at detector over entire spectral bandpass.
delta I = difference between measured I-zero and measired I.
SNR = signal-to-noise ratio for photon-limited measurement.
Display calculations:
measured I = MeasI = sum(TransmittedIntensity)
measured I-zero = MeasIzero = sum(SourceIntensity)
delta I = MeasIzero-MeasI
SNR = 1000*CorrectedA*sqrt(MeasI)
Peak abs. = Conc/(AbsWidth)
Width ratio = SourceWidth/AbsWidth
Cont. A = Ac =log((NumWavelengths))/(sum(transmission)))
Line A = Al = log(MeasIzero/MeasI)
CorrectedA = Al-Ac
BUTTONS:
Run calib. curve:
Varies concentration from 0 to 10 units in steps of 1 and records corrected absorbance.
Script:
manual recalc
column letters
define standard
for standard=0 to 10
put standard into C3
put C3 into "J"&standard+2
recalc
put H3 into "K"&standard+2
end for
put 1 into C3
automatic recalc
Plot and fit:
Plots analytical calibration curve on separate sheet, fits straight line to low absorbance
(linear) region.
Script:
{ INSTRUCTIONS: Put data to be fit into two adjacent columns, the x-axis data }
{ (i.e. independent variable) in the first column and the y-axis data (i.e. }
{ (the dependent variable) in the second column. The first row of each column }
{ should contain column labels. Select the data range and run this script. }
{ The script creates a new sheet containing a copy of the data values, the best }
{ fit data, an ANOVA table, and an XY plot of the data and best fit lines. }
{ Print page 2 of this new sheet to get report contain ANOVA table and plot. }
repaint off
column numbers
Define datarange,numrows
select range R1C10..R20C11
Copy
select range R1C1
New Worksheet ""
window size (12780, 7540)
paste values
Select last cell
numrows=row()
select range "R1C1..R"&numrows&"C1"
Copy
select range R1C3
Paste
datarange="$R1$C2..$R4$C3"
Select range datarange
select more range R1C5
select more range R1C6
column letters
Regress
column numbers
select range R1C4
Put "Fit at low conc." Into R1C4
select range R2C4
Put "=R2C3*$R2$C5+$R1$C5" Into R2C4
select range "R2C4..R"&numrows&"C4"
Copy Down
select range "R1C1..R"&numrows&"C4"
Unselect Add Chart Range frac(R25C6..R51C11,0,62,149,252) Using "R1C1..R"&numrows&"C4"
select object 1
XY
Legend Bottom
select chart 1 series 1
symbol color 0
symbol width 20
symbol type 3
symbol size 7 points
line fg 0
line bg 16777215
line pattern 0
line width 40
select chart 1 series 2
line fg 0
line bg 16777215
line pattern 1
line width 20
select range R1C2
select more chart 1 axis 3
axis title range
select range R1C1
select more chart 1 axis 1
axis title range
column letters
Select All
precision 4
text size 9
show cells
select range G52..K52
text size 9
precision 4
unselect
zoom window
select range F23..K52
Report Print Range
Hide Headings
Hide Tool Box
Hide Entry Bar
Hide Cell Grid
window size (9520, 8640)
Put "Intercept =" Into R52C7
Put "=$R1$C5" Into R52C8
Put "Slope =" Into R52C10
Put "=$R2$C5" Into R52C11
select range K52
repaint on
Operating Instructions
Computer Simulation of the Spectroscopy of Atomic Absorption
This is a simulation of the spectroscopy of a line-source atomic
absorption measurement with continuum-source background correction
in a steady-state (i.e. flame) atomizer. The graph displays a plot
of intensity on the y axis vs wavelength displacement from the
resonance wavelength, in pm, on the x axis. The x axis extends
over the spectral bandpass of the monochromator (0.2 nm, or 200 pm,
in this case), which is centered on the resonance wavelength.
There are three lines on the plot in different colors: the spectral
profile of the incident line-source emission line (gray), the
analyte transmission profile (blue), and the spectral profile of
the transmitted line-source emission line (red). (In a real AA
instrument you actually wouldn't be able to see these spectral
profiles, so in that respect this simulation is more instructive
that a real instrument). The purpose of the simulation is to make
it clearer how the various spectroscopic aspects relate to each
other and to the measured absorbance. The input parameters that
you have direct control over are displayed at the top of the screen
in the boxed cells with red labels:
shift Collisional ("red") shift of the absorption line, pm.
abs. width Spectral width of the the atomic absorption line, pm.
source width Spectral width of the hollow-cathode lamp emission
line, pm.
atom density Atom density of analyte atoms, arbitrary units.
stray light Relative intensity of continuum background radiation
from the hollow-cathode lamp.
background abs. Absorbance of the non-specific
background absorption in the atomizer.
non-abs. line Intensity of a non-absorbing line from the HCL,
arbitrarily placed at -60 pm, relative to the main
resonance line.
interference Peak absorbance of a matrix absorption line,
arbitrarily placed at +60 pm.
hyperfine Relative intensity of a hyperfine line, relative
to "main" line.
To change any of these parameters, click on the number, type in a
new value, and press the ENTER key. Recalculation is automatic.
The calculated "outputs" are shown in the black boxes with white
numbers and blue labels:
Peak abs. The "true" peak absorbance at the center of the
absorption line.
Width ratio Ratio of the absorption width to the source width.
Cont. A Absorbance measured with the continuum source.
Line A Absorbance measured with the line source.
Corrected A Atomic absorbance corrected for background absorbance
(This is simply equal to Line A - Cont. A).
measured I Total intensity transmitted through the atomizer,
measured over the entire spectral bandpass.
measured I-zero Total incident intensity measured over the entire
spectral bandpass.
delta I Difference between measured I-zero and measured I.
SNR Theoretical signal-to-noise ratio for photon-noise-
limited measurement.
Of course in a real AA instrument you wouldn't get all these
outputs: usually only the uncorrected and corrected absorbances are
displayed. On some instruments you can read the background
absorbance (Cont A) and the intensities (measured I or measured
I-zero). No instrument displays the true peak absorbance (it's
fundamentally unknown), the width ratio, or the theoretical SNR.
There are also two buttons that automatically acquire an analytical
curve:
Run calib. curve
Varies the atom density from 0 to 10 units in steps of 1 and
records the corrected absorbance.
Plot and fit
Plots the resulting analytical calibration curve on a separate
sheet, fits a straight line to the low absorbance (linear) region,
and displays the slope and intercept of the line.
Student Assignment
Open the file "AAMeasurement".
1. Make sure that all the input parameters are set to their
default values: shift =1, abs. width = 3.5, source width = 1, and
atom density = 1, and all other inputs = 0. (These source and
absorption widths are typical values for the Ca 422 nm resonance
line).
2. Note that the line source absorbance (Line A) is slightly lower
that the Peak abs. Why? Does this lead to inaccuracy in
analytical applications?
3. Increase atom density to 10. Note that Peak abs. increases by
exactly 10 as it should. Did the line source absorbance (Line A)
also increase by ten-fold? Why not?
4. Note that the Corrected A is lower that Line A, because the
continuum source absorbance Cont. A is not zero. Why is this so?
To check that it is not an offset or zero-adjust problem, set atom
density to zero and verify that all absorbances are zero. Does
this have an effect on the analytical linearity also? To test
that, compare the corrected and uncorrected absorbances at atom
density of 1 and 10.
5. Return the atom density to 1. To demonstrate that background
correction is necessary, increase the background abs. and notice
the effect on Cont. A, Corrected A and Line A. (In this idealized
simulated instrument, misalignment between the hollow cathode and
continuum lamps is not included, so the correction is perfect; it
is never this perfect in practice). Note that although the
correction is perfect, the SNR degrades (decreases) when the
background absorbance increases. Why?
6. Return the background abs. to 0 and increase the interference,
which controls the peak absorbance of a matrix absorption line that
falls within the spectral bandpass but does not overlap the
analytical absorption line. Note that the Line A is not much
changed, but the Cont. A, and thus the Corrected A, is. Why? If
only this kind of interference occurs in a particular application,
would it be more accurate to use the corrected or uncorrected
(line) absorbance for analytical purposes? How do the Zeeman and
pulsed HCL methods minimize this problem?
7. Return the interference to 0. Set non-abs line to 0.1. This
controls the relative intensity of a nonresonance (non-absorbing)
line emitted by the hollow cathode lamp that falls within the
spectral bandpass. Note the effect on the absorbances. Click on
the Run calib. curve button and, when it is finished running
through all the atom densities, click on the Plot and fit button to
see the resulting analytical curve. Explain the shape of the
analytical curve. (Note: each analytical curve plot is placed in
a separate window, to allow two or more to be compared; to discard
them, click in the close box in the upper left, the click in NO on
the following dialog box).
8. Return the non-abs line to 0. Set hyperfine to 0.5 and notice
the effect of the transmission profile and the source line profile.
Do an experiment to determine if the presence of hyperfine
structure influences the sensitivity or linearity. What happens if
hyperfine = 1?
9. Return hyperfine to 0. All parameters should now be back at
their default values. Determine by experiment the absorbance that
gives the best SNR. Do your results agree with Ingle and Crouch
for a photon (shot) noise limit? See page 284 of James D. Ingle,
Jr. and Stanley R. Crouch, Spectrochemical Analysis, Prentice Hall,
New Jersey, 1988.
(c) 1991, 2000, 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 to2@umail.umd.edu.