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General Properties of ElectromagneticRadiation

- 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).

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.

- 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.

Wave Properties of Electromagnetic Radiation

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.

- 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.

- 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

- 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

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 ?)

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

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)

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.

Constructive Interference

- 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.

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.

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.

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

Douglas A. Skoog, et al. Principles of

Instrumental Analysis, Thomson, 2007

Diffraction Pattern From Multiple Slits

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

Douglas A. Skoog, et al. Principles of

Instrumental Analysis, Thomson, 2007

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.

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.

- 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.

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.

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

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

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.

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.

- 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.

- 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

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.

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).

- 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

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.

- 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.

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

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 ??? ??????? ??????

??????? ????? ??????

- (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.

????? ???? ?????? ??? ??? ????? ??????? ???? ???

??????? ?????? ????? ??????

Increasing ??

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.

- 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/ ? ?

Multiply both sides by h

- 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

?.

?? c?-2? ?