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- Key Concepts
- Lambert’s Law of Absorption
- Beer’s Law
- Beer-Lambert Law
- Absorption Cross-Sections
- Photometric quantities
- Spectrophotometer
- The Cary 50 Spectrophotometer
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- If one slab of absorbing material of thickness l reduces the intensity
of a beam of light to half.
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- Beer found that Lambert’s linear decay constant k for a solution of an
absorbing substance is linearly related to its concentration c by a
constant, the absorptivity ε, a characteristic of the absorbing
substance.
- Restatement: The linear decay
constant k is linear in concentration c with a constant of
proportionality ε.
- (August Beer, 1825-1863)
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- Transmittance (T)
- Absorbance (A) (AKA optical density, O.D.)
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- Lambert’s and Beer’s 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.
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- 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.
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- 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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- Attenuation of light by absorption and scattering both obey Lambert’s
Law. Thus we can extend our
treatment of absorption to scattering and extinction. (Recall that extinction is the effect
of absorption + scattering.)
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- Spectrometer: measures I vs λ.
Simply measures the spectrum of the light (e.g. emission
spectroscopy).
- Spectrophotometer: measures I/I0
vs λ.
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 λ selection.
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- Measures absorbance as a function of wavelength
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- Computer controlled acquisition
of absorption spectra
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- 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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- Spectroscopy
- Chemical Analysis: trace
analysis, pH, forensic, in situ monitoring, remote monitoring, geology,
astronomy, ....
- Particle size
- Thin film characterization
- Color matching
- Optics
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