Spectroscopy
Early Theories and Theorists of the Atom
1. Democritus - Greek Philosopher that proposed the concept of the atom more than two thousand years
ago.
 Matter is composed of empty space through which atoms move.
 Atoms are solid, homogeneous, indestructible, and indivisible.
 Different kinds of atoms have different sizes and shapes.
 The differing properties of matter are due to the size, shape, and movement of atoms.
2. John Dalton - Adapted the theories of Democritus to develop his own Atomic Theory.
 All matter is composed of extremely small particles called atoms.
 All atoms of a given element are identical, having the same size, mass, and chemical properties.
Atoms of specific element are different from those of any other element.
 Atoms cannot be created, divided into smaller particles, or destroyed.
 Different atoms combine in simple whole number ratios to form compounds.
 In a chemical reaction, atoms are separated, combined, or rearranged.
Daltons 3 Main Laws:
Conservation of Mass
Definite Composition
Multiple Proportions
Joseph John Thomson: discovered the electron in a series of experiments designed to study the nature of
electric discharge in a high-vacuum cathode-ray tube
Rays from the cathode (C) pass through a slit in the anode (A) and through a slit in a grounded metal plug
(B). An electrical voltage is established between aluminum plates (D and E), and a scale pasted on the
outside of the end of the tube measures the deflection of the rays.
Ernest Rutherford:
Rutherford's Gold Foil Experiment
> Over 98% of the particles went straight through.
> About 2% of the particles went through but were deflected by large angles.
> About 0.01% of the particles bounced off the gold foil.
Subatomic Particles: the building blocks for atoms
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Nucleus - the center or core of an atom that contains positively charged atoms.
Protons - (p+) Positively charged subatomic particle Discovered by Ernest Rutherford
Electrons - (e-) Negatively charged subatomic particle that surrounds the nucleus. Discovered by J.J.
Thompson, Charged determined by Robert Millikan. (Millikan's Oil-Drop experiment.
 Neutrons - (n) neutral, carries no electrical charge and are contained in the nucleus with the protons.
Discovered by James Chadwick. Rutherford's coworker.
 Isotopes have different atomic masses, yet identical chemical and physical properties
 Isotopes are common in nature and influence the measured atomic masses of large assemblies of atoms
 Different isotopes of the same element have the same name (ex Carbon-12, Carbon-13) Exception
hydrogen, deuterium, tritium
Note: A proton's positive charge is equal to, but opposite to the negative charge of an electron.
Particle
Symbol
Location in the
Atom
Relative
Charge
Relative Mass
Mass (g)
proton
p
nucleus
+1
1
1.673 × 10-24
neutron
n
nucleus
0
1
1.675 × 10-24
electrons
e-
electron cloud
-1
~0
9.110 × 10-28
How Atoms Differ
Atomic Weight (u): The average mass of an atom of an element, usually expressed in atomic mass units. The
terms mass and weight are used interchangeably in this case. The atomic weight given on the periodic table is
a weighted average of isotopic masses found in a typical terrestrial sample of the element.
 Atomic Number (Z) – is equal to number of Protons and Electrons in the atom.
 # of Neutrons = Mass Number (MW) – Atomic Number.
Isotopes = Atoms of the same element having a different numbers of neutrons due to different atomic
masses. Same Atomic #!
Mass Number
3
235
1H
92U
Atomic Number
Ions = is an atom or group of atoms that has a positive or negative charge. The atomic number still equals
the number of protons, but different number of electrons.
Na+1 = 11+ protons, 12 neutrons, & 10e' {-11 + (+1)} = -10e'
O-2 = 8+ protons, 8 neutrons, & 10e' {-8 + (-2)} = -10e'
Fe+3 = 26+ protons, 30 neutrons, & 23e' {-26 + (+3) = -23e'
Rutherford's Nuclear Model
1. The atom contains a tiny dense center called the nucleus.
 the volume is about 1/10 trillionth the volume of the atom
2. The nucleus is essentially the entire mass of the atom.
3. The nucleus is positively charged & the amount of positive charges of the nucleus balances the negative
charge of the electrons.
4. The electrons move around in the empty space of the atom surrounding the nucleus.
Thomson's Atomic Theory
1. An atom is breakable!
2. An atom has structure
3. Electrons suspended in a positively charged
electric field.
 must have positive charge to balance
negative charge of electrons and make
the atom neutral
4. Mass of atom due to electrons.
5. Atom mostly "empty" space & compared size
of electron to size of atom
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically,
spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a
prism. Later the concept was expanded greatly to comprise any interaction with radiative energy as a
function of its wavelength or frequency. Spectroscopic data is often represented by a spectrum, a plot of
the response of interest as a function of wavelength or frequency
Types of Spectroscopy:
Radiative energy
Types of spectroscopy are distinguished by the type of radiative energy involved in the
interaction. In many applications, the spectrum is determined by measuring changes in the
intensity or frequency of this energy. The types of radiative energy studied include:
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Electromagnetic radiation was the first source of energy used for spectroscopic
studies. Techniques that employ electromagnetic radiation are typically classified by
the wavelength region of the spectrum and include microwave, terahertz, infrared,
near infrared, visible and ultraviolet, x-ray and gamma spectroscopy.
Particles, due to their de Broglie wavelength, can also be a source of radiative
energy and both electrons and neutrons are commonly used. For a particle, its
kinetic energy determines its wavelength.
Acoustic spectroscopy involves radiated pressure waves.
Mechanical methods can be employed to impart radiating energy, similar to
acoustic waves, to solid materials.
Nature of the interaction
Types of spectroscopy can also be distinguished by the nature of the interaction between
the energy and the material. These interactions include
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Absorption occurs when energy from the radiative source is absorbed by the
material. Absorption is often determined by measuring the fraction of energy
transmitted through the material; absorption will decrease the transmitted portion.
Emission indicates that radiative energy is released by the material. A material's
blackbody spectrum is a spontaneous emission spectrum determined by its
temperature. Emission can also be induced by other sources of energy such as
flames or sparks or electromagnetic radiation in the case of fluorescence.
Elastic scattering and reflection spectroscopy determine how incident radiation is
reflected or scattered by a material. Crystallography employs the scattering of high
energy radiation, such as x-rays and electrons, to examine the arrangement of atoms
in proteins and solid crystals.
Impedance spectroscopy studies the ability of a medium to impede or slow the
transmittance of energy. For optical applications, this is characterized by the index
of refraction.
Inelastic scattering phenomena involve an exchange of energy between the radiation
and the matter that shifts the wavelength of the scattered radiation. These include
Raman and Compton scattering.
Coherent or resonance spectroscopy are techniques where the radiative energy
couples two quantum states of the material in a coherent interaction that is
sustained by the radiating field. The coherence can be disrupted by other
interactions, such as particle collisions and energy transfer, and so often require
high intensity radiation to be sustained. Nuclear magnetic resonance (NMR)
spectroscopy is a widely used resonance method and ultrafast laser methods are also
now possible in the infrared and visible spectral regions.
Frequency and Wavelength
We know that frequency is the number of Oscillations per second and Wavelength is the
distance between two points of same phase. From the wavelength equation we can deduce
that the frequency and wavelength of a wave are inversely proportional to each other
which means that the wave whose wavelength is more has less frequency and vice-verso.
v = f λ where f = frequency of the wave
v = Speed of the wave
λ = Wavelength of the wave.
Wavelength of Sound
Sound is originally compression wave in a medium like air. The higher the frequency,
shorter the distance takes place between each successive rarefaction or compression in the
incoming sound wave. This distance is referred as Wavelength.
We know that the Wavelength of a sound depends on the frequency of the sound
source. That is Sound from the same source will have the same speed in either medium.
The Formula for Wavelength of Sound is given by
λ = v f where v is the velocity and f is the frequency.
Sound travels more faster in water therefore the wavelength will be longer.
Sound travels at about 750 mil/hr, Hence the compression waves between 100 Hz and
20,000 Hz have wavelengths that range between several feet to a fraction of an inch.
Energy to Wavelength
Energy, wavelength of the wave is related to each other by the following equation:
E = hc λ where h = planck’s constant = 6.6×10−34 J-s,
c = Speed of light = 3×108 m/s,
λ = Wavelength of Light.
We will use above equation to convert Wavelength to Energy or Energy Wavelength or
Energy to Wavelength as the other two quantities are constant.
Wavelength Spectrum
The electromagnetic waves are represented by the Electromagnetic spectrum. This
spectrum gives us the wavelength of various waves at different frequency.
We can call this spectrum as wavelength spectrum.
The below figure shows different waves (or rays) with their wavelength on x-axis.
1.
2.
3.
4.
5.
6.
Microwave radio frequencies -> 108 nm - 3 x 109 Hz
UHF frequencies -> 109 nm - 3 x 108 Hz
VHF frequencies -> 1010 nm - 3 x 107 Hz
AM Broadcast radio frequencies -> 3 x 1011 nm - 1000 kHz
Audio frequencies -> 1014 nm - 3000 Hz
Electrical power frequency -> 5 x 1015 nm - 60 Hz.
Beer’s Law
Absorption spectra of chemical species (atoms, molecules, or ions) are generated when a beam of
electromagnetic energy (i.e. light) is passed through a sample, and the chemical species absorbs a
portion of the photons of electromagnetic energy passing through the sample. A classic example of
this phenomenon is responsible for our perception of color. Consider the situation where a beam of
white light (i.e. sunlight) passes through a sample solution containing chlorophyll (the compound
responsible for the color of leaves). The chlorophyll molecules absorb only a few select photons in the
blue and red regions of the visible portion of the electromagnetic spectrum. The energies of these
absorbed photons cause electrons in the chlorophyll molecule to be excited, and in the plant cell the
energy of these excited electrons is used to drive the conversion of carbon dioxide and water to
glucose. More important for our purposes is the fact that when the red and blue photons that
chlorophyll absorbs are subtracted from white light, the resulting beam of light leaving the solution
appears green to our eye, and this is why leaves appear green to us.
If we could measure the total number of photons of all colors that enter the sample and compare that
with the total number of photons of all colors that leave the sample, we would find fewer photons
exiting the sample than entering the sample. This is consistent with the fact that the chlorophyll
molecules absorbed some of the photons from the beam of white light that entered the solution.
A spectrophotometer is an instrument designed to make this measurement. Using some very well
understood electronics, this device effectively “counts” the number of photons that enters a sample and
compares it with the number of photons that exits a sample. In addition, the instrument is able to take
white light and separate it into its constituent colors (i.e. somewhat a prism), allowing the user to
examine the absorption of light of individual wavelengths with nearly 1 nm resolution.
In optics, that portion of physics that deals with the properties of light, the measurement of the number
of photons delivered at a point in a given unit of time is called the Intensity, I. (Higher intensity could
be thought of as “brighter” and lower intensity could be thought of as “dimmer”; hence high intensity
light will be bright and low intensity light will be dim.) If we measure the intensity of the beam of
light entering our sample (Io) and compare it with the intensity of the beam of light exiting our sample
(I) we can take the ratio I/Io to get an indication of what fraction of the light entering the sample was
found exiting the sample. This ratio is called the Transmittance:
Transmittance: T I Io
We can convert this ratio into a percentage by multiplying by 100 to get Percent Transmittance (%T):
% Transmittance: %T I Io 100
Thus if the intensity of the light exiting our sample is 76 and the intensity of the light entering our
sample is 100, then the Transmittance would be 0.76 and the % Transmittance would be 76%,
indicating that 76% of the photons entering our sample are finding their way out of our sample.
For our purposes it is mathematically convenient to define a new concept, Absorbance (A):
Absorbance: A log10 I Io
Absorbance is a direct measure of how much light is absorbed by our sample. If you play with the
formula in your calculator you will find that absorbance can take on values between 0 (at 100%
Transmittance) and about 2.0 (at 1% Transmittance); thus large values of absorbance are associated
with very little light passing entirely through the sample and small values of absorbance (i.e. those
approaching 0) are associated with most of the light passing entirely through the sample.
The Beer-Lambert Law:
Consider a solution of a chemical species that absorbs light of a particular wavelength. We could
imagine two interesting situations. First, if we pass a beam of light of the appropriate wavelength
through a fairly dilute solution, we could imagine that the photons will encounter a small number of
the absorbing chemical species, so we might expect a high % transmittance and a low absorbance.
Alternatively, if we pass the same beam of light through a highly concentrated solution, we could
imagine that the photons will encounter a large number of the absorbing chemical species, and we
might expect a low % transmittance and a high absorbance. Thus absorbance is proportional to the
concentration of the sample. Secondly, we could imagine that if we allow the beam of light to
encounter the solution for a long period of time we might expect to see a low % transmittance and a
high absorbance; whereas, if the beam were allowed to encounter the solution for a short period of
time we might expect to see a high % transmittance and a low absorbance. Since light travels at a
constant speed, c = 3.0 x 108 m/s, this implies that the absorbance should also be proportional to the
path length of the beam through the sample.
When the path length is measured in centimeters, and the concentration of the absorbing species
is measured in Molarity, the proportionality constant is called the Molar Absorptivity, having
units of M-1cm-1, and our proportionality reduces to the
Beer-Lambert Law:
This technique is used not only by chemists but by scientists of many fields. The Beer-Lambert
law allows you, the scientist, to measure the absorbance of a particular sample and to deduce the
concentration of the solution from that measurement! In effect, you can measure the
concentration of a particular chemical species in a solution as long as you know the species
absorbs light of a particular wavelength.
Beer Lamberts Law
A=εbc
A - absorbance (-)
ε - molar absorbtivity with units of L mol-1 cm-1
b - path length of the sample (cuvette)
c - Concentration of the compound in solution, expressed in mol L-1
Transmittance, T = I / I0, %T = 100 T
Absorbance,
A = log10 I0 / I
A = log10 1 / T
A = 2 - log10 %T