Chemistry Reference
In-Depth Information
For a quantitative analysis, the determination of the net intensity of peaks is
relevant, ranging from about 10
2
to some 10
6
counts. For that reason, the
determination of the content of
one
element is restricted to four orders of
magnitude. This dynamic range can be spanned for one definite instrumental
setting of parameters. However, up to six orders of magnitude can be reached
simply if the tube current and acquisition time are changed.
Precision and accuracy are the decisive figures of merit for quantitative
analyses. The
precision
can be characterized by the relative standard devia-
tion of repeated quantitative determinations. The
accuracy
is defined
by the mean relative deviation of the actual determination from the nominal
or true value.
According to Equation 4.8, the concentration of an analyte is determined by
the ratio of net intensities. Consequently,
multiplicative
errors are compensated
and instrumental fluctuations, for example, of current or voltage, do not
influence the results. Only the photon counting is decisive, which is controlled
by Poisson statistics. The net intensities of both the analyte peak and the
internal standard peak are obtained by subtracting the spectral background
from the respective gross intensities. Because of this subtraction, nonspecific
additive
errors are eliminated that are caused, for example, by different
carriers. Such fluctuations do not affect the result, which again is only influ-
enced by the photon noise.
The
relative
standard
deviation
of
the
concentration
c
x
follows
from
Equation 4.12 and is given by
s
rel
N
x
N
is
s
rel
c
x
(6.4)
where
N
is the net intensity of either the analyte or the internal standard with
index
x
or
is
, respectively. Due to the counting statistical fluctuations, it follows
that
s
s
2
N
x
N
2
x
s
2
N
is
s
rel
c
x
(6.5)
N
is
where
s
(
N
x
) and
s
(
N
is
) are the absolute standard deviations of the respective
net intensities. These quantities are determined by the square root law:
p
N
x
b
sN
x
N
b
;
x
(6.6)
p
N
is
b
sN
is
N
b
;
is
(6.7)
where
N
x
+
b
and
N
is
+
b
are gross intensities, and
N
b
,
x
and
N
b
,is
are the back-
ground corrections of the analyte and the internal standard, respectively. If we
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