Transcript L10

Introduction to Atomic
Spectroscopy
Lecture 10
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In cases where atoms of large numbers of
electrons are studied, atomic spectra
become too complicated and difficult to
interpret. This is mainly due to presence of a
large numbers of closely spaced energy
levels
It should also be indicated that transition from
ground state to excited state is not arbitrary
and unlimited. Transitions follow certain
selection rules that make a specific transition
allowed or forbidden.
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Atomic Emission and Absorption
Spectra
At room temperature, essentially all atoms are
in the ground state. Excitation of electrons in
ground state atoms requires an input of
sufficient energy to transfer the electron to
one of the excited state through an allowed
transition. Excited electrons will only spend
a short time in the excited state (shorter than
a ms) where upon relaxation an excited
electron will emit a photon and return to the
ground state.
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Each type of atoms would have certain
preferred or most probable transitions
(sodium has the 589.0 and the 589.6 nm).
Relaxation would result in very intense lines
for these preferred transitions where these
lines are called resonance lines.
Absorption of energy is most probable for the
resonance lines of each element. Thus
intense absorption lines for sodium will be
observed at 589.0 and 589.6 nm.
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Atomic Fluorescence Spectra
When gaseous atoms at high temperatures are
irradiated with a monochromatic beam of radiation of
enough energy to cause electronic excitation,
emission takes place in all directions. The emitted
radiation from the first excited electronic level,
collected at 90o to the incident beam, is called
resonance fluorescence. Photons of the same
wavelength as the incident beam are emitted in
resonance fluorescence. This topic will not be
further explained in this text as the merits of the
technique are not very clear compared to
instrumental complexity involved
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Atomic Line Width
It is taken for granted that an atomic line
should have infinitesimally small (or
zero) line width since transition
between two quantum states requires
an exact amount of energy. However,
careful examination of atomic lines
reveals that they have finite width. For
example, try to look at the situation
where we expand the x-axis
(wavelength axis) of the following line:
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The effective line width in terms of
wavelength units is equal to Dl1/2 and is
defined as the width of the line, in
wavelength units, measured at one half
maximum signal (P). The question
which needs a definite answer is what
causes the atomic line to become
broad?
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Reasons for Atomic Line
Broadening
There are four reasons for broadening
observed in atomic lines. These include:
1. The Uncertainty Principle
We have seen earlier that Heisenberg
uncertainty principle suggests that nature
places limits on the precision by which two
interrelated physical quantities can be
measured. It is not easy, will have some
uncertainty, to calculate the energy required
for a transition when the lifetime of the
excited state is short.
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The ground state lifetime is long but the
lifetime of the excited state is very
short which suggests that there is an
uncertainty in the calculation of the
transition time. We have seen earlier
that when we are to estimate the energy
of a transition and thus the wavelength
(line width), it is required that the two
states where a transition takes place
should have infinite lifetimes for the
uncertainty in energy (or wavelength)
to be zero:
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DE>h/Dt
DE = hc/Dl
hc/Dl > h/Dt
Therefore, atomic lines should have
some broadening due to uncertainty in
the lifetime of the excited state. The
broadening resulting from the
uncertainty principle is referred to as
natural line width and is unavoidable.
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2. Doppler Broadening
The wavelength of radiation emitted by a
fast moving atom toward a transducer
will be different from that emitted by a
fast atom moving away from a
transducer. More wave crests and
thus higher frequency will be
measured for atoms moving towards
the transducer. The same occurs for
sound waves
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Assume your ear is the transducer, when
a car blows its horn toward your ear
each successive wave crest is emitted
from a closer distance to your ear since
the car is moving towards you. Thus a
high frequency will be detected. On the
other hand, when the car passes you
and blows its horn, each wave crest is
emitted at a distance successively far
away from you and your ear will
definitely sense a lower frequency.
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The line width (Dl) due to Doppler broadening
can be calculated from the relation:
Dl/lo = v/c
Where lo is the wavelength at maximum power
and is equal to (l1 + l2)/2, v is the velocity of
the moving atom and c is the speed of light.
It is noteworthy to indicate that an atom
moving perpendicular to the transducer will
always have a lo, i.e. will keep its original
frequency and will not add to line broadening
by the Doppler effect.
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In the case of absorption lines, you may
visualize the line broadening due to Doppler
effect since fast atoms moving towards the
source will experience more wave crests and
thus will absorb higher frequencies. On the
other hand, an atom moving away from the
source will experience less wave crests and
will thus absorb a lower frequency. The
maximum Doppler shifts are observed for
atoms of highest velocities moving in either
direction toward or away from a transducer
(emission) or a source (absorption).
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3. Pressure Broadening
Line broadening caused by collisions of
emitting or absorbing atoms with other
atoms, ions, or other species in the
gaseous matrix is called pressure or
collisional broadening. These collisions
result in small changes in ground state
energy levels and thus the energy
required for transition to excited states
will be different and dependent on the
ground state energy level distribution.
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This will definitely result in important line
broadening. This phenomenon is most
astonishing for xenon where a xenon arc
lamp at a high pressure produces a
continuum from 200 to 1100 nm instead of a
line spectrum for atomic xenon. A high
pressure mercury lamp also produces a
continuum output. Both Doppler and
pressure contribution to line broadening in
atomic spectroscopy are far more important
than broadening due to uncertainty principle.
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4. Magnetic Effects
Splitting of the degenerate energy levels does take
place for gaseous atoms in presence of a magnetic
field. The complicated magnetic fields exerted by
electrons in the matrix atoms and other species will
affect the energy levels of analyte atoms. The
simplest situation is one where an energy level will
be split into three levels, one of the same quantum
energy and one of higher quantum energy, while the
third assumes a lower quantum energy state. A
continuum of magnetic fields exists due to complex
matrix components, and movement of species, thus
exist. Electronic transitions from the thus split levels
will result in line broadening
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The Effect of Temperature on
Atomic Spectra
Atomic spectroscopic methods require the conversion
of atoms to the gaseous state. This requires the use
of high temperatures (in the range from 2000-6000
oC). Thee high temperature can be provided through
a flame, electrical heating, an arc or a plasma
source. It is essential that the temperature be of
enough value to convert atoms of the different
elements to gaseous atoms and, in some cases,
provide energy required for excitation. The
temperature of a source should remain constant
throughout the analysis especially in atomic
emission spectroscopy.
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Quantitative assessment of the effect of
temperature on the number of atoms in the
excited state can be derived from Boltzmann
equation:
Where Nj is the number of atoms in excited
state, No is the number of atoms in the
ground state, Pj and Po are constants
determined by the number of states having
equal energy at each quantum level, Ej is the
energy difference between excited and
ground states, K is the Boltzmann constant,
and T is the absolute temperature.
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Boltzmann distribution
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Atom
Wavelength
Cs
852.1 nm
Nj /N0 at
3000 K
7.24  10-3
Na
589.0 nm
5.88  10-4
Ca
422.7 nm
3.69  10-5
Zn
213.9 nm
5.58  10-10
To understand the application of this equation
let us consider the situation of sodium atoms
in the 3s state (Po = 2) when excited to the 3p
excited state (Pj = 6) at two different
temperatures 2500 and 2510K. Now let us
apply the equation to calculate the relative
number of atoms in the ground and excited
states:
Usually we use the average of the emission
lines from the 3p to 3s where we have two
lines at 589.0 and 589.6 nm which is:
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Therefore, at higher temperatures, the number of
atoms in the excited state increases. Let us calculate
the percent increase in the number of atoms in the
excited state as a result of this increase in
temperature of only 10 oC:
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