Transcript 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.
wavenumber is directly proportional to frequency and thus E
 =k
kdepends on medium and = 1/velocity
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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
radio waves 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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Mathematic Description of a Wave
2v
 = angular frequency = 2 =

Y = A sin(2t + ), is the regular frequency
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Douglas A. Skoog, et al. Principles of Instrumental Analysis, Thomson, 2007
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1t+ 1) + 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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Constructive Interference
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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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Diffraction Pattern From Multiple Slits
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Douglas A. Skoog, et al. Principles of Instrumental Analysis, Thomson, 2007
Diffraction Pattern From Multiple Slits
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Douglas A. Skoog, et al. Principles of Instrumental Analysis, Thomson, 2007
Diffraction Pattern From Multiple Slits
CF = BC sin  = n
n is an integer called order of interference
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Douglas A. Skoog, et al. Principles of Instrumental Analysis, Thomson, 2007
Coherence of Radiation
to give diffraction patterns
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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Scattering of Radiation
The fraction of radiation transmitted at all
angles from its original path
• Rayleigh scattering
– Molecules or aggregates of molecules smaller
than 
• Scattering by big molecules
– Used for measuring particle size
• Raman Scattering
– Involves quantized frequency changes
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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: (E= h)
Heated objects (or Excitation): Emission of
electromagnetic radiation as photons after
relaxation .
Explanation:
1. Atoms, ions, and molecules can exist in
certain discrete energy states only.
2. 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
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(energy is quantized).
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:
E= 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:
Electronic Energy States:‫مستويات الطاقة الرئيسية‬
• 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:
‫تساهمية‬
‫روابط‬
‫على‬
‫تحتوي‬
‫التي‬
‫الجزيئات‬
‫في‬
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:
‫تكون واضحة في الجزيئات الغازية النها سهلة الدوران‬
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.
atoms
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molecules
Line Versus Band Spectra
Spectra: Two types: 1) Line Spectra 2) Band Spectra
1) Line Spectra: Resulted from atoms
Atoms have electronic energy levels, absorption or
emission involves transitions between discrete
states with no other possibilities.
2) Band Spectra: Resulted from molecules:
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.
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Black Body Radiation (Heated
‫خاص بالمواد الصلبة المسخنة لدرجة التوهج‬
(Heated solids to incandescence)
Gives:
continuum of radiation called black body
radiation.
Properties:
1.Dependent on the temperature: λmax 1/T
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. ‫بمعنى جميع المواد عند نفس حرارة‬
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‫التسخين تعطي نفس االشارة القصوى للطول الموجي‬
Increasing →
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The Uncertainty Principle
‫قاعدة عدم التأكد آليزنبرج‬
Werner Heisenberg, in 1927:
‫اليمكن قياس كميتين فيزيائيتين في نفس اللحظة بدرجة عالية من الدقة‬
‫ سرعة االلكترون وموضعه عند زمن معين‬:‫مثال‬
)‫(مهمة جدا في أجهزة التحليل اآللي‬
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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Understand the meaning of this principle:
Comparing the two frequencies (Unknown and Known) 1
and 2 by measuring the difference ().
Now let both interfere to give a beat.
The shortest time (t) that can be allowed for the
interaction is the time of formation of one single beat,
( equals to/or larger than the period of one beat which is Pb)
Therefore, we can write:
t  Pb so,  t  1/  
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Multiply both sides by h
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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:
Line width can be measured from Uncertainty from
.
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 = c-2Δ 
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