Download General Properties of Electromagnetic Radiation

General Properties of
Electromagnetic
Radiation
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The electromagnetic radiation is looked at as
sinusoidal waves which are composed of a
combination of two fields. An electric field (which
we will use, in this course, to explain absorption
and emission of radiation by analytes) and a
magnetic field at right angle to the electric field
(which will be used to explain phenomena like
nuclear magnetic resonance in the course of
special topics in analytical chemistry offered to
Chemistry students only).
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The classical wave model
The classical wave model describes
electromagnetic radiation as waves that have a
wavelength, frequency, velocity, and amplitude.
These properties of electromagnetic radiation
can explain classical characteristics of
electromagnetic radiation like reflection,
refraction, diffraction, interference, etc. However,
the wave model can not explain the phenomena
of absorption and emission of radiation.
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We will only deal with the electric field of the
electromagnetic radiation and will thus
refer to an electromagnetic wave as an
electric field having the shape of a
sinusoidal wave. The arrows in the figure
below represent few electric vectors while
the yellow solid sinusoidal wave is the
magnetic field associated with the electric
field of the wave.
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Wave Properties of
Electromagnetic Radiation
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Wave Parameters
1. Wavelength ()
The wavelength of a wave is the distance
between two consecutive maxima or two
consecutive minima on the wave. It can
also be defined as the distance between
two equivalent points on two successive
maxima or minima. This can be seen on
the figure below:
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2. Amplitude (A)
The amplitude of the wave is represented by
the length of the electrical vector at a
maximum or minimum in the wave. In the
figure above, the amplitude is the length of
any of the vertical arrows perpendicular to
the direction of propagation of the wave.
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3. Frequency
The frequency of the wave is directly proportional to the
energy of the wave and is defined as the number of
wavelengths passing a fixed point in space in one
second.
4. Period (p)
The period of the wave is the time in seconds required
for one wavelength to pass a fixed point in space.
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5. Velocity (v)
The velocity of a wave is defined as the
multiplication of the frequency times the
wavelength. This means:
V = 
The velocity of light in vacuum is greater
than its velocity in any other medium
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Since the frequency of the wave is a
constant and is a property of the source,
the decrease in velocity of electromagnetic
radiation in media other than vacuum
should thus be attributed to a decrease in
the wavelength of radiation upon passage
through that medium.
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6. Wavenumber ()
The reciprocal of wavelength in centimeters
is called the wavenumber. This is an
important property especially in the study
of infrared spectroscopy.
 =k
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Electromagnetic Spectrum
The electromagnetic radiation covers a vast
spectrum of frequencies and wavelengths. This
includes the very energetic gamma-rays
radiation with a wavelength range from 0.005 –
1.4 Ao to radiowaves in the wavelength range up
to meters (exceedingly low energy). However,
the region of interest to us in this course is rather
a very limited range from 180-780 nm. This
limited range covers both ultraviolet and visible
radiation.
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Mathematical Description of a
Wave
A sine wave can be mathematically represented by the
equation:
Y = A sin (t + )
Where y is the electric vector at time t, A is the amplitude of
the wave,  is the angular frequency, and is the phase
angle of the wave.
The angular frequency is related to the frequency of
radiation by the relation:
= 2
This makes the wave equation become:
Y = A sin (2t + )
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Superposition of Waves
When two or more waves traverse the same
space, a resultant wave, which is the sum
of all waves, results. Where the resultant
wave can be written as:
Y = A1 sin (2 t+  ) + A2 sin (2t + )
+ ........ + An sin (2nt + n)
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Constructive Interference
The resultant wave would has a greater
amplitude than any of the individual waves
which, in this case, is referred to as
constructive interference. The opposite
could also take place where lower
amplitude is obtained.
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The decrease in the intensity is a result of what is
called a destructive interference. When the
multiple waves have the same wavelength,
maximum constructive interference takes place
when 1 - 2 is equal to zero, 360 deg or multiple
of 360 deg. Also maximum destructive
interference is observed when 1 – 2 is equal to
180 deg, or 180 deg + multiples of 360 deg. A
100% constructive interference can be seen for
interference of yellow and blue shaded waves
resulting in a wave of greater amplitude, brown
shaded.
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The blue and yellow shaded waves interfere to give the brown
shaded wave of less amplitude, a consequence of destructive
interference of the two waves.
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The Period of a Beat
When two waves of the same amplitude but
different frequencies interfere, the
resulting wave exhibit a periodicity and is
referred to as beat (see figure below). The
period of the beat can be defined as the
reciprocal of the frequency difference
between the two waves:
Pb = 1/()
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Fourier Transform
The resultant wave of multiple waves of
different amplitudes and frequencies can
be resolved back to its component waves
by a mathematical process called Fourier
transformation. This mathematical
technique is the basis of several
instrumental techniques like Fourier
transform infrared, Fourier transform
nuclear magnetic resonance, etc.
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Diffraction of Radiation
Diffraction is a characteristic of
electromagnetic radiation. Diffraction is a
process by which a parallel beam of
radiation is bent when passing through a
narrow opening or a pinhole. Therefore,
diffraction of radiation demonstrate its
wave nature. Diffraction is not clear when
the opening is large.
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Coherence of Radiation
Two beams of radiation are said to be
coherent if they satisfy the following
conditions:
1. Both have the same frequency and
wavelength or set of frequencies and
wavelength.
2. Both have the same phase relationships
with time.
3. Both are continuous.
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Transmission of Radiation
As mentioned before, the velocity of radiation in
any medium is less than that in vacuum. The
velocity of radiation is therefore a function of the
refractive index of the medium in which it
propagates. The velocity of radiation in any
medium can be related to the speed of radiation
in vacuum ( c ) by the relation:
ni = c/vi
Where, vi is the velocity of radiation in the medium
I, and ni is the refractive index of medium i.
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The decrease in radiation velocity upon
propagation in transparent media is
attributed to periodic polarization of atomic
and molecular species making up the
medium. By polarization we simply mean
temporary induced deformation of the
electronic clouds of atoms and molecules
as a result of interaction with electric field
of the waves.
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Dispersion of Radiation
If we look carefully at the equation ni = c/vi
and remember that the speed of radiation
in vacuum is constant and independent on
wavelength, and since the velocity of
radiation in medium I is dependent on
wavelength, therefore the refractive index
of a substance should be dependent on
wavelength. The variation of the refractive
index with wavelength is called dispersion.
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Refraction of Radiation
When a beam of radiation hits the interface
between two transparent media that have
different refractive indices, the beam
suffers an abrupt change in direction or
refraction. The degree of refraction is
quantitatively shown by Snell's law where:
n1 sin 1 = n2 sin 2
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Reflection of Radiation
An incident beam hitting transparent
surfaces (at right angles) with a different
refractive index will suffer successive
reflections. This means that the intensity of
emerging beam will always be less than
the incident beam.
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Scattering of Radiation
When a beam of radiation hits a particle,
molecule, or aggregates of particles or
molecules, scattering occurs. The intensity
of scattered radiation is directly
proportional to particle size, concentration,
the square of the polarizability of the
molecule, as well as the fourth power of
the frequency of incident beam. Scattered
radiation can be divided into three
categories:
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Quantum Mechanical Description of
Radiation
All the previously mentioned properties of radiation agrees
with the wave model of radiation. However, some
processes of interest to us, especially in this course, can
not be explained using the mentioned wave properties of
radiation. An example would be the absorption and
emission of radiation by atomic and molecular species.
Also, other phenomena could not be explained by the
wave model and necessitated the suggestion that
radiation have a particle nature. The familiar experiment
by Heinrich Hertz in 1887 is the corner stone of the
particle nature of radiation and is called the photoelectric
effect.
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The Photoelectric Effect
When Millikan used an experimental setup
like the one shown below to study the
photoelectric effect, he observed that
although the voltage difference between
the cathode and the anode was insufficient
to force a spark between the two
electrodes, a spark occurs readily when
the surface of the cathode was illuminated
with light. Look carefully at the
experimental setup:
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It is noteworthy to observe the following points:
1. The cathode was connected to the positive terminal of
the variable voltage source, where it is more difficult to
release electrons from cathode surface.
2. The anode was connected to the negative terminal of the
voltage source which makes it more difficult for the
electron to collide with the anode for the current to pass.
3. The negative voltage was adjusted at a value insufficient
for current to flow. The negative voltage at which the
photocurrent is zero is called the stopping voltage.
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At these conditions, no current flows through the
circuit as no electrons are capable of completing
the circuit by transfer from cathode to anode.
However, upon illumination of the cathode by
radiation of suitable frequency and intensity, an
instantaneous flow of current takes place. If we
look carefully at this phenomenon and try to
explain it using the wave model of radiation, it
would be obvious that none of the wave
characteristics (reflection, refraction,
interference, diffraction, polarization, etc. ) can
be responsible for this type of behavior.
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What actually happened during illumination is that radiation
offered enough energy for electrons to overcome binding
energy and thus be released. In addition, radiation
offered released electrons enough kinetic energy to
transfer to the anode surface and overcome repulsion
forces with the negative anode.
If the energy of the incident beam was calculated per
surface area of an electron, this energy is infinitesimally
small to be able to release electrons rather than giving
electrons enough kinetic energy. When this experiment
was repeated using different frequencies and cathode
coatings the following observations were collected:
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Conclusions
1. The photocurrent is directly proportional to
the intensity of incident radiation.
2. The magnitude of the stopping voltage
depends on both chemical composition of
cathode surface and frequency of incident
radiation.
3. The magnitude of the stopping voltage is
independent on the intensity of incident
radiation.
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Energy States of Chemical
Species
The postulates of quantum theory as
introduced by Max Planck in 1900, intended
to explain emission by heated bodies,
include the following:
1. Atoms, ions, and molecules can exist in
certain discrete energy states only. When
these species absorb or emit energy exactly
equal to energy difference between two
states; they transfer to the new state. Only
certain energy states are allowed (energy is
quantized).
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2. The energy required for an atom, ion,
or a molecule to transfer from a one
energy state to another is related to
the frequency of radiation absorbed
or emitted by the relation:
Efinal – Einitial = h
Therefore, we can generally state that:
E = h
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Types of Energy States
Three types of energy states are usually
identified and used for the explanation of
atomic and molecular spectra:
1. Electronic Energy States: These are present
in all chemical species as a consequence of
rotation of electrons, in certain orbits,
around the positively charged nucleus of
each atom or ion. Atoms and ions exhibit this
type of energy levels only.
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2. Vibrational Energy Levels: These are
associated with molecular species only and
are a consequence of interatomic
vibrations. Vibrational energies are also
quantized, that is, only certain vibrations
are allowed.
3. Rotational Energy Levels: These are
associated with the rotations of molecules
around their center of gravities and are
quantized. Only molecules have vibrational
and rotational energy levels.
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The solid black lines represent electronic energy levels. Arrows
pointing up represent electronic absorption and arrows pointing
down represent electronic emission. Dotted arrows represent
relaxation from higher excited levels to lower electronic levels.
The figure to left represents atomic energy levels while that to
the right represents molecular energy levels.
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Line Versus Band Spectra
Since atoms have electronic energy levels, absorption
or emission involves transitions between discrete
states with no other possibilities. Such transitions
will only result in line spectra. However, since
molecular species contain vibrational and rotational
energy levels associated with electronic levels,
transitions can occur from and to any of these
levels. These unlimited numbers of transitions will
give an absorption or emission continuum, which is
called a band spectrum. Therefore, atoms and ions
always give line spectra while molecular species
give band spectra.
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Black Body Radiation
When solids are heated to incandescence, a
continuum of radiation called black body
radiation is obtained. It is noteworthy to
indicate that the produced emission
continuum is:
1. Dependent on the temperature where as
temperature of the emitting solid is
increased, the wavelength maximum is
decreased.
2. The maximum wavelength emitted is
independent on the material from which the
surface is made.
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The Uncertainty Principle
Werner Heisenberg, in 1927, introduced
the uncertainty principle, which states
that: Nature imposes limits on the
precision with which certain pairs of
physical measurements can be made.
This principle has some important
implications in the field of instrumental
analysis and will be referred to in
several situations throughout the
course.
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To understand the meaning of this
principle, the easiest way is to assume
that an unknown frequency is to be
determined by comparison with a
known frequency. Now let both interfere
to give a beat. The shortest time that
can be allowed for the interaction is the
time of formation of one single beat,
which is Pb. Therefore, we can write:
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Example: The mean lifetime of the
excited state when irradiating mercury
vapor with a pulse of 253.7 nm
radiation is 2*10-8 s. Calculate the value
of the width of the emission line.
ٍSolution:
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