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General Properties of Electromagnetic Radiation

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Title: General Properties of Electromagnetic Radiation


1
General Properties of ElectromagneticRadiation
2
  • 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).

3
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.

4
  • 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.

5
Wave Properties of Electromagnetic Radiation
6
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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8
  • 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.

9
  • 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.
10
  • 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

11
  • 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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13
  • 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

14
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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16
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 ?)

17
Mathematic Description of a Wave
w angular frequency 2pn
Y A sin(2??t f), n is the regular
frequency
Douglas A. Skoog, et al. Principles of
Instrumental Analysis, Thomson, 2007
18
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)

19
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.

20
Constructive Interference
21
  • 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.

22
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.
23
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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25
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.

26
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.

27
 
 
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29
Diffraction Pattern From Multiple Slits
Douglas A. Skoog, et al. Principles of
Instrumental Analysis, Thomson, 2007
30
Diffraction Pattern From Multiple Slits
Douglas A. Skoog, et al. Principles of
Instrumental Analysis, Thomson, 2007
31
Diffraction Pattern From Multiple Slits
CF BC sin ? n? n is an integer called order
of interference
Douglas A. Skoog, et al. Principles of
Instrumental Analysis, Thomson, 2007
32
Coherence of Radiationto 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.

33
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.

34
  • 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.

35
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.

36
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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38
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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40
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

41
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

42
Quantum Mechanical Description ofRadiation
  • 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.

43
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.

46
  • 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.

47
  • 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

48
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.

49
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
  • 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).

50
  • 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 hn
  • Therefore, we can generally state that
  • DE hn

51
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??????? ?????? ????????
  • 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.

52
  • 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.

53
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
molecules
54
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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56
Black Body Radiation (Heated ??? ??????? ??????
??????? ????? ??????
  • (Heated solids to incandescence)
  • Gives continuum of radiation called black body
    radiation.
  • Properties
  • Dependent on the temperature ?max ?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.
    ????? ???? ?????? ??? ??? ????? ??????? ???? ???
    ??????? ?????? ????? ??????

57
Increasing ??
58
The Uncertainty Principle????? ??? ??????
????????
  • Werner Heisenberg, in 1927
  • ?????? ???? ?????? ?????????? ?? ??? ??????
    ????? ????? ?? ?????
  • ???? ???? ????????? ?????? ??? ??? ????
  • (???? ??? ?? ????? ??????? ?????)
  • 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.

59
  • 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/ ? ?

60
Multiply both sides by h
61
  • Example
  • The mean lifetime of the excited state when
    irradiating mercury vapor with a pulse of 253.7
    nm radiation is 210-8 s. Calculate the value of
    the width of the emission line .
  • ?Solution
  • Line width can be measured from Uncertainty from
    ?.

62
?? c?-2? ?
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