Spectrophotometry

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Spectrophotometry

• Key Concepts
• Lamberts Law of Absorption
• Beers Law
• Beer-Lambert Law
• Absorption Cross-Sections
• Photometric quantities
• Spectrophotometer
• The Cary 50 Spectrophotometer

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Lamberts Law of Absorption
Lambert described how intensity changes with
distance in an absorbing medium.

• The intensity I0 if a beam of light decreases
  exponentially as it passes though a uniform
  absorbing medium with the linear decay constant
  a.
• Restatement In a uniform absorbing medium, the
  intensity of a beam of light decreases by the
  same proportion for equal path lengths traveled.
• The linear decay constant a is a characteristic
  of the medium. It has units of reciprocal
  length. a is the path length over which the
  intensity is attenuated to 1/e.

Johann Heinrich Lambert 1728-1777
The distance traveled through the medium is
called the path length.
a
I(x)
x
Photo http//www-history.mcs.st-andrews.ac.uk/hi
story/PictDisplay/Lambert.html
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Lamberts Law of Absorption (base 10)
Typically base 10 is used in photometry.
k is the path length over which the intensity is
attenuated to 1/10.
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Lamberts Law Example

• If one slab of absorbing material of thickness l
  reduces the intensity of a beam of light to half.
  

l
a
Then two slabs of the same absorbing material
will then reduce the intensity of a beam of light
to one quarter.
l
l
a
a
And three slabs will reduce the intensity of a
beam of light to one eight.
l
l
l
a
a
a
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Beers Law

• Beer found that Lamberts linear decay constant k
  for a solution of an absorbing substance is
  linearly related to its concentration c by a
  constant, the absorptivity e, a characteristic of
  the absorbing substance.
• Restatement The linear decay constant k is
  linear in concentration c with a constant of
  proportionality e.
• (August Beer, 1825-1863)

Typical units are k cm-1 c M
(moles/liter) e M-1cm-1
A colored absorber has an absorptivity that is
dependent on wavelength of the light e(?). The
absorptivity is the fundamental property of a
substance. This is the property that contains
the observable spectroscopic information that can
be linked to quantum mechanics (also see
absorption cross section.)
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Photometric Quantities
In photometry we measure the intensity of light
and characterize its change by and object or
substance. This change is typically expresses as
percent transmittance or absorbance.

• Transmittance (T)
• Absorbance (A) (AKA optical density, O.D.)

usually given in percent
Frequently when your primary interest is the
light beam
Used almost exclusively when your interest
concerns the properties of the material
by convention, base 10 logs are used
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Beer-Lambert Law

• Lamberts and Beers Laws are combined to
  describe the attenuation of light by a solution.
  It is easy to see how the two standard
  photometric quantities can be written in terms of
  this law.

Transmittance
Absorbance
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Cross-Sections and Absorptivitythe connection to
single particles and molecules

• The absorption of light by particles (and single
  molecules) is characterized by an absorption
  cross section C. In this model the particle is
  replaced by a perfectly absorbing sphere with a
  cross sectional area C. This cross section is a
  property of the particle and is not related to
  its geometric cross sectional area. The
  concentration of particles per unit volume is N.

typical units are C cm2 N cm-3
The cross section can be directly related to the
molar absorptivity. NA is Avagadros number.
units are C cm2 N cm-3 NA mole-1 e
M-1cm-1
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Efficiency

• The absorption efficiency Q of a particle is the
  ratio of its absorption cross section C to its
  geometric cross section Cgeo.
• Absorption efficiency is dimensionless.

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Extension to Scattering and Extinction

• Attenuation of light by absorption and scattering
  both obey Lamberts Law. Thus we can extend our
  treatment of absorption to scattering and
  extinction. (Recall that extinction is the
  effect of absorption scattering.)

The scattering efficiency can be much larger than
unity. Extinction paradox Qext 2 (Qabs 1
Qsca 1) for an perfectly absorbing particle
very large compared to the wavelength of light.

• Note
• All of these quantities are in general wavelength
  dependent.
• Our discussion has not included the mechanism
  (cause) of absorption and scattering.
• There are many different mechanisms that cause of
  absorption and scattering.

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Instrumentation

• Spectrometer measures I vs ?. Simply measures
  the spectrum of the light (e.g. emission
  spectroscopy).
• Spectrophotometer measures I/I0 vs ?. Measures
  how the sample changes the spectrum of the light
  (e.g. transmission, reflection, scattering,
  fluorescence).
• All spectrophotometers contain a spectrometer.
• -meter the detector is electronic
• -graph light intensity recorded on film
• photometer measures I/I0 without ? selection.

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The Spectrophotometer

• Measures absorbance as a function of wavelength

Components light source, monochromator, sample
cell, detector, optical system.
monochromator
sample cell
detector
slit
diffraction grating
light source
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Cary 50 UV-Vis Spectrophotometer
monochromator

• Computer controlled acquisitionof absorption
  spectra

balance the forces
detector
sample
Can you find the diffraction grating and the slit?
light source
www.varianinc.com
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Making a Measurement with the Cary 50

• First, measure the baseline using a blank sample.
  This is raw I0. The blank sample is the cuvette
  with deionized water (everything but your
  nanoparticles). This corrects for any absorption
  due to the cuvette, water, and variations of the
  light intensity of the light source,
  monochromator, etc.
• Second, measure the zero by inserting the beam
  block. This corrects the instrument for the
  detector background.
• Third, measure your sample. This is the raw I.
  The Cary 50 automatically calculates the
  corrected intensities (I and I0) by subtracting
  the zero from each of the raw intensities.
• Subsequent measurements do not require
  re-measuring the blank and zero, simply repeat
  step 3.

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Applications of Spectrophotometry

• Spectroscopy
• Chemical Analysis trace analysis, pH, forensic,
  in situ monitoring, remote monitoring, geology,
  astronomy, ....
• Particle size
• Thin film characterization
• Color matching
• Optics