Transcript General Properties of Electromagnetic Radiation

General Properties of
Electromagnetic
Radiation
Lecture 1
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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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1. Rayleigh Scattering
Rayleigh Scattering is scattering of
electromagnetic radiation by particles
much smaller than the wavelength of the
radiation. Rayleigh Scattering usually
occurs in gasses. The scattering of solar
radiation by earth’s atmosphere is one of
the main reasons why the sky is blue.
Rayleigh Scattering has a strong
dependence on wavelength having a
wavelength^-4 relationship.
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2. Mie scattering
Mie scattering is caused
by dust, smoke, water
droplets, and other
particles in the lower
portion of the
atmosphere. It occurs
when the particles
causing the scattering
are close in dimension
to the wavelengths of
radiation in contact with
them. Mie scattering is
responsible for the
white appearance of the
clouds.
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3. Tyndall Effect (nonspecific scattering)
It occurs in the lower portion of the
atmosphere when the particles are
much larger than the incident radiation.
This type of scattering is not
wavelength dependent and is the
primary cause of haze.
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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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The Uncertainty Principle says that the product
of the unceratinty Δx of the location of a
particle and the uncertainty of the
momentum Δpx can be no smaller than ½h,
where h is Planck's constant divided by 2π;
i.e.,
Δx·Δpx ≥ ½h
It is also true that the product of the
uncertainty in the energy ΔE of a particle and
the uncertainty concering time Δt must be no
smaller than ½h. Thus
ΔE·Δt ≥ ½h
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A Quick Derivation of the Energy-Time Uncertainty
Principle
The energy E of a particle with mass m and velocity v
is ½mv². Its momentum p is mv. Therefore the energy
expressed in terms of momentum is
E = p²/(2m)
The change in energy δE resulting from a change δp in
momentum is given approximately by
δE = pδp/m = (p/m)δp
Thus the uncertainty ΔE in energy is given by
ΔE = pΔp/m = (p/m)Δ
The uncertainty in time Δt is given by
Δt = Δx/v
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