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Chapter 6 Introduction to Spectrophotometric Methods
Problems 1, 2, 5, 8, 11,14,15,18,19
Note this somewhat of a review of things covered in Chem 232, but there are several
added details that you need to be recognize
Historically Spectroscopy refers to the interaction between electromagnetic radiation
and matter
Now def is broadened to include interaction between matter and energy
Most widely used spectrometric methods still based on Electromagnetic radiation
interacting with matter, this chapter deals with the basics of these interaction
6A General Properties of Electromagnetic Radiation
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Many properties conveniently describes with sinusoidal wave model, dealing with
wavelength, frequency, velocity and amplitude of waveform
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When deal with absorption and emission need to add quantum theory and
remember that light is also quantitized into packets of E called photons
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These representations are not mutually exclusive, but are dual description of the
same phenomena
6B Wave properties of Electromagnetic radiation
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For many purposes figure 6-1a is great ...magnetic and electric fields are at right
angles to each other sinusoidal wave forms in these planes are in phase with
each other (peaks occur and same time)
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Technically this is a plane polarized waveform since all magnetic or all electric
oscillations are in the same plane
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Since the electric component of the waveform is responsible for most of the
phenomena we swill study in this class (the exception is that NMR will use the
magnetic vector), can usually study just the electric vector, as shown in figure 61b
6B-1 Wave parameters
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The amplitude of the waveform refers to its maximum displacement
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The wavelength is the distance between one maximum and the next
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The period, p of a waveform is the time it takes for the waveform to move
from one maximum to the next at some fixed point in space
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The frequency < of the waveform is the number of periods that occur in 1
second, or 1/p
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When you multiply the frequency (in cycles/sec) times the wavelength (in
M/sec) you get the velocity of propagation, vi
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Note that the frequency of the light is fixed by its energy and does not
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change from medium to medium. The velocity of the light and hence the
wavelength of the light does change depending upon how it interacts with
the matter it is traveling through. This is why we include the subscript
In a vacuum light is no longer interacting with matter and achieves its
maximal velocity
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Speed is now a physical constant c=2.99792x108 m/s
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In air interaction is minimal and speed is only .03% slower
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In other media, like glass or crystals effect can be large, and lead
to refraction. This is how lens and prisms work
Another useful parameter is the wavenumber = 1/8 (8 in cm!). It is
equal to the number of waves that can be contained in 1 cm of the
material. Used a lot in IR spectroscopy. Since is proportional to
frequency is also proportional to energy
The power, P and intensity, I, of a beam relate to how much energy the
beam carries and can be related to the amplitude. Strictly speaking
Power is how much energy hits a flat area of surface/unit time and
intensity is how much power passes through a solid angle(spherical
surface)/unit time. There is no significant difference as far as we are
concerned in this class.
6B-2 The Electromagnetic Spectrum
Figure 6-3 regions of the electromagnetic spectrum
Table 6-1 Spectroscopic methods and their wavelengths
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Electromagnetic spectrum is empirically divided into different
regions
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Your eye is sensitive to only a small region,
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Optical methods include IR and UV, hence are more than your eye
can see!
6B-3 Mathematical Description of a wave
A sinusoidal wave is represented with the equation
Where y is the amplitude of the electric field
t is time
N is the phase angle ( how far from Zero we are starting)
And T is the angular velocity
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Determined from frequency
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T=2B< (expressing frequency in radians/sec instead of hertz)
Putting two equations together:
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6B-4 Superposition of waves
When two waves traverse the same space, the amplitudes add
The resultant sum is also a periodic waveform, but it is not necessarily sinusoidal
any more. The creation of a new waveform from the sum of one or more
component waveforms is called interference
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Figure 6-4 a frequencies the same, phases are almost the same(|N1N2|<90) so get constructive interference. New waveform has same
frequency but larger amplitude and different phase than either
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Figure 6-4 b frequencies that same, but waveforms almost out of phase
(|N1- N2|>90 but<270)so waveform undergoes destructive interference.
Resulting waveform has same frequency and lower amplitude and
different phase that either
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Figure 6-5 waveforms with same amplitudes but different frequencies, get
a waveform with a beat pattern
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Figure 6-6 waveforms with special multiples of amplitude and frequencies
sum to create a square wave
This last result is especially important and actually more general. Any periodic
waveform can be decomposed into a sum of sin and cosine functions. Jean
Fourier discovered a mathematical way to do this in early 1800's Involves some
integration of the function e, and is tedious to do by hand. Fortunately is easy for
a computer to do. This mathematical transformation in integral to several
techniques including FT-IR and FT-NMR. Will work with more next week and in
lab, and as it occurs in individual techniques.
6B-5 Diffraction of Radiation
When a wavefront consisting of parallel wave traveling in one direction passes
through an opening, the wavefront tend to get bent near the edges of the
opening. Bending of waveforms near discontinuities is called diffraction.
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when opening is large compared to wavelength, diffraction consists of
minor bending around the edges Figure 6-7a
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When opening is small compared to wavelength, the opening tends to
look like a new point source, with the new waveform radiating out in a
spherical manner Figure 6-7b
Diffraction is a consequence of interference. As we have just seen, interference
is the summing of waveforms
Interference is the basis of X-ray diffraction methods (used to find distance
between atoms in crystals), of how diffraction grating (used in UV, Vis, and IR
monochrometers) as well as several other instruments
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I don’t think we need to worry about the geometry and calculations in the text at
this point
6B-6 Coherent Radiation
To produce an interference pattern you must have sources of radiation that are
Coherent i.e. the sources must have identical frequencies, and the phase
relationship between the frequencies must be constant.
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Light produced by most common sources (filaments and arc lamps) is
incoherent, because light is being produced independently by millions of
different atoms and millions of slightly different times, and there is no way
to get all the different wave sources in sync.
Light produced by a few specialized sources (lasers, radiofrequency and
microwave oscillators) are coherent
Light from incoherent sources like bulbs can be made coherent by using
the single slit device as shown in figure 6-8, since the new light coming
from a single slit is coherent.
6B-7 Transmission of Radiation (Might want to skip if not doing refractive index)
I have already mentioned how light has a maximum speed in a vacuum, but
moves more slowly in a medium containing matter, apparently because the light
is interacting with the matter in some way.
The refractive index of a medium is one way to measure the difference in light
velocities
The refractive index of a substance varies with the frequency (energy) of the
light. For most liquids it is between 1.3 and 1.8, for solids it is 1.3 to2.5 or higher.
Since the energy of the light fixed by its frequency, and we know that the
frequency of the light does not change as the light slows down, we assume that
this interaction does not involve a permanent change or transfer of energy.
What is happening is that the electrons in the medium are getting polarized.
That mean they slosh around in their orbital for an instant, but then, within 10-14
or 10-15 seconds the electrons return to their original position and the energy for
the light is released unchanged, only slightly slowed down.
When the light is reemitted from the polarized particles, it is emitted in all
directions. For small particles destructive interference occurs prevents any light
from being emitted in any direction but the original, so the light continues on its
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original path. For large particles (large in comparison to the wavelength of the
light) this destructive interference is incomplete, and the light is scattered in all
directions. X-ray and light scattering techniques can be used to determine the
size an shape of molecules in solution, but is not a technique we will cover in this
class.
The refractive index of a substance changes with the wavelength. A plot of the
refractive index vs wavelength or frequency is called a dispersion plot (Figure 69) As you can see the plot is quite complex. In ‘Normal’ dispersion the refractive
index increases as the frequency of the light increases (wavelength decreases)
In ‘anomalus’ dispersion the refractive index takes a sharp jog up and down.
Anomalus dispersion always occurs at a frequency where the molecules in the
medium are actually absorbing the EM energy
6B-8 Refraction of Radiation
When radiation passes at an angle through an interface between two media with
different refractive indices, the light undergoes a change in direction known as
Refraction. You can observe refraction whenever you look at an object
underwater. Unless you are staring directly sown at an object underwater, it
always looks to be much closer or shallower than it really is due to refraction.
The book covers the equations that deal with refraction, but since we aren’t
going to be designing instruments where we have to worry about this, I think we
will pass.
6B-9 Reflection of Radiation
When radiation passes at an angle through an interface between two media
there is also a portion of the light that is reflected off the interface. The amount
that is reflected depends on the angle and on the difference in refractive indices
of the media. Again this can be important in instrument design, but we will not
cover this here so skip these equations as well
6B-10 Scattering of Radiation
When light is retained and then reemitted from a polarized atom, ion, or
molecule, the amount of light that is scattered in a new direction depends on the
size of the particle the light was interacting with
Rayleigh Scattering- occurs when the molecules or molecular aggregates are
much smaller that the wavelength of the radiation. Inversely proportional to 84,
direction proportional to size and polarizablity2. The blue color of the sky is a
result of Rayleigh Scattering.
Tyndall Scattering- is the scattering that occurs when the scattering object is
large compared to the wavelength of the radiation. This is the kind of scattering
that lets you see dust or particle suspended in a solution
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Raman Scattering- I said earlier that in scattering no energy is absorbed by the
molecule. This is actually only a first approximation. Sometimes a small bit of
energy is either added or subtracted from the light beam resulting in very tiny
shifts in the frequency of the scattered light. This is called Raman Scattering
and can be a useful instrumental method similar to IR. Hopefully we will be able
to cover this effect when we get to the IR section.
6B-11 Polarization of Radiation
The picture we started with for light, with the electric vector of the light oscillating
In the Y dimension is actually a model for ‘Plane-Polarized’ light. Plan polarized
means that all the electric vector of the light are aligned in 1 plane, in this case
the Y plane. Plane polarized light only occurs naturally from a few sources.
Radio waves emitted by a radio antenna are polarized along the plane of the
antenna, and microwaves created by a klystron tube are polarized by the
construction of the tube. Radiation emitted by a single excited molecule are
polarized by the dipole moment of the excited state of the electron, but in a
solution or a gas, since all the molecules are randomly oriented with respect to
each other, the net emission is also not oriented or polarized.
Light can be polarized by either passing through or being reflected off a medium
that either absorbs reflects, or refracts radiation in one plane. Light reflected off
the surface of the water is polarized in one direction, and your Polaroid
sunglasses are designed to specifically absorb light polarized in this direction, so
the ‘glare’ you see of the water’s surface is cut dramatically, but light from other
sources is not dimmed very much.
6C Quantum-Mechanical Properties of Radiation
That is as far as we can go with light as a wave. To understand emission of absorption,
we need to look at light as a quantum or discrete unit of energy (photons).
6C-1 The Photoelectric Effect
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First observed by Hertz in 1887
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A spark jumped more readily from one sphere to another when the
spheres were illuminated than in the dark
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Explained by Einstein in 1905
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Explanation actually not believed until 1916
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Basis of vacuum phototube (Light sensor in many cheap
spectrophotometers)
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Experimental design Figure 6-13
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Cathode can be coated with various metals
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When Anode is + with respect to cathode current flows
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(light knocks electrons off metal, electrons attracted to + anode so
current flows)
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Some current even when cathode and anode have the same
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potential (light gives enough E that some electrons have enough E
to get to anode and make current even with no potential difference
Takes a certain amount of Negative voltage on Anode to actually
stop the current flow (called stopping voltage)
As you increase the frequency of the light you get more current and
you increase the stopping voltage Figure 6-14
Explanation. Light had energy quantitized. Needed a minimum
amount of E to knock electron off cathode with enough E to push
against unfavorable potential to make current. Wave model of light
with E uniformly distributed in light could make this explanation.
First demonstration that light E is quantitized
Note slope of line in 6-14 is Planck’s constant
6C-2 Energy State of Chemical Species
Quantum Theory first proposed in 1900 by Max Planck
Two important Postulates
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Atoms, Ions and molecules can exist only in certain discrete energy
states. When a molecules changes states it either emits or absorbs
exactly the right amount of energy to change from one state to the other
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The frequency or wavelength is related to the energy difference in state
by the equation )E=h< or hc/8
For atoms or ions (only 1 center of mass) Energy change involves changes in
electronic state of atom or ion
For molecules (more than one center of mass) There are also vibrational and
rotational quantitized energy states as well
Lowest energy state is the ground state
All other states called excited states
6C-3 Emission of Radiation
EM radiation produced when atoms ions or molecules are excited, and then give
off their excess energy as they relax back to ground state
How do particles get excited?
Bombard with electrons or other elementary particles (very high Energy)
Expose to AC electrical current or heat up
Expose to EM radiation
Some exothermic chemical reactions (Chemiluminescence)
Can look at emission as an Emission Spectrum (figure 6-15) Plot of emission
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intensity vs wavelength or frequency
Emission Spectrum frequently has lines bands and a continuum
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Lines - sharp, well defined peaks caused by individual atomic
transitions
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Bands- groups of lines that are so closely spaced that they can’t be
resolved. Usually to transitions in molecules or free radical
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Continuum - overall roll in baseline. Will talk about more in a bit
Line Spectra
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In UV and Vis line spectra come from atoms that are physically separate
from each other, usually this is achieved only in the gas phase
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Typically sharp lines with widths on order of .0001A
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Can see some for Na, K, Sr and Ca in fig 6-15
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Typical E diagram shown in figure 6-17
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For an Na atom the ground state would be a 3s orbital and the E1
state would be a 3p orbital
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Atoms stays in excited state only about 10-8 sec before drops back
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emission shown as a wavy line in this plot
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E2 state would be a 4s orbital
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Xray spectra can also make line spectra (figure 6-16)
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In this case much higher E, and corresponds to transitions from
innermost (core) orbitals instead of valence shell orbital
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In these high energy transitions the physical sate of the element
does not matter, can be solid, liquid, or gas and you will still get the
same sharp emission line
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These are what the scanning electron microscope uses to identify
elements.
Band Spectra
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In gas phase associated with radicals or small molecules
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In figure 6-15 the region between 350 and 400
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Band for OH, MgOH, and MgO closely spaced lines that cannot be
resolved
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Arise because molecules have numerous vibrational and rotational
state for both ground and E1 electronic states
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lifetime of vibrational state in excited molecules is extremely short
(10-15 to 10-8 sec) so not shown in diagram. Also mean that in any
emission process the decay to the vibrational ground state is for all
purposes instantaneous so an emission is almost always from the
ground vibration of an excited state
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Also note that there are generally lots more vibrations states for E0
than are shown in this diagram. And for each vibrational state there
are 10's of rotational state that are on the order of 10 times smaller
as well. This is just an illustration
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Continuum Spectra
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Figure 16-8 When heated all solids emit ‘Blackbody’ radiation
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Emitted by surface
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Does not depend on composition
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Comes from innumerable atomic and molecular oscillations of a
solid
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Shifts to shorter wavelengths as material get hotter
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Need extremely high temp to get into visible or UV range
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In figure 6-15 this is seen in the baseline Note how baseline
increases at longer wavelengths
6C-4 Absorption of Radiation
As radiation passes through a medium, some frequencies may be specifically
removed via absorption
In absorption molecules of the medium are accepting the energy from the EM
radiation but are not returning it because instead of being temporarily polarized,
they have been changed into their excited state.
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Again the energy of the light must exactly match the energy of the
transition in the molecule
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Absorption of light is another phenomena that can be used to characterize
atoms and molecules
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4 different absorption spectra shown in figure 6-19.
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again a wide variety of lines, and curves
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variety depends in complex way on the physical state and
environment of absorbing molecules
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But biggest differences are between atoms and molecules
Atomic Absorption
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usually very simple with a few clear lines
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can usually interpret simply
Na 2 sharp close lines in yellow at 589.0 and 589.6
3s16 2 slightly different 3p orbitals
Also one at 285 (UV) transition to 5p
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In UV and Vis most transitions are with valence electron
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Need X-rays to manipulate inner core electrons
Molecular Absorption
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Generally much more complex
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Even more complex if in liquid or solid
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E of a band is composed of electronic, vibrational and rotational
components
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For each electronic state there are probably a dozen or so
vibrational state, and for each vibrational state, hundreds of
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rotational states, so lots of E to choose from.
Figure 6-20 a standard energy diagram of absorption transitions
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Up arrows an absorption event Note these can be in IR, Visible or
UV regions
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down dashed arrows non-radiative energy lose due to vibration and
rotation
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Lots of different starting and stopping states so much broader
spectra than atomic spectra. Tend to talk about an absorption
BAND instead of an absorption line
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Interactions between the solvent and the molecule broaden out
even more! Tend to make continuous spectra (figure 6-19, b, c, d)
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Pure vibrational spectra can be observed in IR region
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Pure rotational spectra observed in Microwave region, but only in
the gas phase where molecules are free to rotate in an unhindered
manner.
Absorption Induced by Magnetic Fields
Electrons and nuclei of certain atoms undergo special quantitized transitions
when the nuclei are within a magnetic field. Nuclear transitions are observed in
the radiowave region (30-599 MHz) and this leads to NMR spectroscopy.
Electrons undergo transitions in the 9500 MHz region (microwave) and this lead
to Electron Spin Resonance (ESR)
6C-5 Relaxation Processes
Once a molecule absorbs energy, it lifetime in the excited state is limited due to
relaxation. Let’s look at these relaxation processes
Nonradiative Relaxation - Loss of E due to lots of short, fast E exchanges as
molecules collide with each other. E ends up heating the solution ever so slightly
Fluorescence and Phosphorescence - Energy radiated directly out of the
molecule
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Fluorescence fast, <10-5 sec
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Phosphorescence slower
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Lets not worry about resonance and nonresonance fluorescence
6C-6 The Uncertainty principleHeisenberg proposed that there were certain pairs of physical parameters where
you could not know the exact value of both parameters at any one time, like
mass and momentum. In spectroscopy the pair that you deal with is time and
frequency. This can raise its ugly head in certain kinds of spectroscopy, but lets
not worry about it until the time comes
6D Quantitative Aspects of Spectrochemical Measurements
Basics you have had before
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T=P/Po
%T = P/Po×100%
A= -logT
A=,lc (abc, etc)