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Chapter 2 Principles of Spectroscopy EST 3203 Instrumental Analysis

Rezaul KarimEnvironmental Science and Technology Jessore Science and Technology University

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Principles of Spectroscopy Electromagnetic radiation1;

General and wave properties2;

Energy States of Chemical Species2

Electromagnetic spectrum;

Interaction of light with matter1;

Absorbance of light3

quantitative aspects of Spectro-chemical measurements;

Optical Systems Used in Spectroscopy1

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Reference1. Skoog, Holler & Crouch 2007,

Principles of Instrumental Analysis, Brooks Cole Cengage Learning, USA.

2. James W Robinson, 1995. Undergraduate instrumental analysis, Marcel Dekker, Inc. NY

3. Daniel C. Harris , 2010, Quantitative Chemical Analysis , 8th edition, W. H. Freeman and Company 41 Madison Avenue New York.

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What is spectroscopy? Spectroscopy is the science that deals with

the interactions of various types ofradiation with matter.

Spectrometry and spectrometric methodsrefer to the measurement of the intensityof radiation with a photoelectric transduceror other type of electronic device.

It is based on atomic and molecularspectroscopy.

The most widely used spectrometric methodsare based on electromagnetic radiation(EMR).

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Processes in Spectroscopy Absorption:The process by which the energy of the light is

transferred to the atom or molecule raising them from the ground state to an excited state

Fluorescence:The absorbed energy is rapidly lost to the

surroundings by collisions within the system and relax back to the ground state.

Emission:If the substances (atoms or molecules) are heated to

high temperatures (in a flame or in an electric discharge) the electrons are exited to higher energy levels. Later, they relax to the ground state with the emission of radiation.

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What is Light? / EMR Light is a form of energy Light travels through space at extremely

high velocities ◦ The speed of light (c) ~ 3 x 1010 cm/sec or

186,000 miles per second

Light is classified as electromagnetic radiation (EMR)

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General Properties EMR is a type of energy that takes several

forms e.g. light and radiant heat. The properties of electromagnetic radiation

are conveniently described by means of a classical sinusoidal wave model

which embodies such characteristics as wavelength, frequency, velocity, and amplitude.

In contrast to other wave phenomena, such as sound, electromagnetic radiation requires no supporting medium for its transmission and thus passes readily through a vacuum.

The energy of a photon is proportional to the frequency of the radiation.

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Sinusoidal wave model electric and magnetic fields that undergo in-phase,

sinusoidal oscillations at right angles to each other and to the direction of propagation.

The abscissa of this plot is either time as the radiation passes a fixed point in space or distance when time is held constant.

In this figure, the electric field is in the xy plane, and the magnetic field is in the xz plane.

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Wave properties The time in

seconds required for the passage of successive maxima or minima through a fixed point in space is called the period p of the radiation.

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Wavelength () is the linear distance between any two equivalent points on successive waves (e.g., successive maxima or minima).

Other way, , is the crest-to-crest distance between waves.

Amplitude is the vertical distance from the midline of a wave to the peak or trough.

Frequency (v) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s)◦ 106 s-1 = 106 Hz or 1 MHz

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Wave number ῡ, which is defined as the reciprocal of the wavelength in centimeters,

The unit for ῡ is cm-1

it is directly proportional to the frequency, and thus the energy, of radiation.

Thus, we can write, ῡ = kv where the proportionality constant k

depends on the medium and is equal to the reciprocal of the velocity

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The power P of radiation is the energy of the beam that reaches a given area per second,

The intensity I is the power per unit solid angle.

These quantities are related to the square of the amplitude A .

The energy of a photon depends on its frequency (v)

Ephoton = hv

h = Planck’s constant

h = 6.63 x 10-27 erg sec or 6.63 x 10-34 Js

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Electromagnetic spectrum

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the spectrum of visible light

,

colour

regionwavelength (nm)

violet 380 - 435

blue 435 - 500

cyan 500 - 520

green 520 - 565

yellow 565 - 590

orange 590 - 625

red 625 - 740

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The main colour regions of the spectrum are approximately:

Common Wavelength Symbols and Units

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Diffraction All types of electromagnetic radiation exhibit

diffraction a process in which a parallel beam of

radiation is bent as it passes by a sharp barrier or through a narrow opening.

Diffraction is a wave property that can be observed not only for electromagnetic radiation but also for mechanical or acoustical waves.

For example, diffraction is easily demonstrated in the laboratory by mechanically generating waves of constant frequency in a tank of water.

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Refraction When radiation passes at an angle through

the interface between two transparent media that have different densities, ◦ an abrupt change in direction, or refraction, of the

beam is observed as a consequence of a difference in velocity of the radiation in the two media.

When the beam passes from a less dense to a more dense environment, the bending is toward the normal to the interface.

Bending away from the normal occurs when the beam passes from a more dense to a less dense medium.

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Reflection When radiation crosses an interface

between media that differ in refractive index, reflection always occurs.

The fraction of reflected radiation becomes greater with increasing differences in refractive index.

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Scattering A very small fraction of the radiation is

transmitted at all angles from the original path and that the intensity of this scattered radiation increases with particle size.

Rayleigh Scattering

Scattering by Large Molecules Raman Scattering

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QUANTUM-MECHANICALPROPERTIES OF RADIATION When electromagnetic radiation is

emitted or absorbed, a permanent transfer of energy from the emitting object or to the absorbing medium occurs.

To describe these phenomena, it is necessary to treat electromagnetic radiation not as a collection of waves but

rather as a stream of discrete particles called photons or quanta.

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The photo-electric effect The first observation of the photoelectric

effect was made in 1887 by Heinrich Hertz, who reported that a spark jumped more readily between two charged spheres when their surfaces were illuminated with light.

Between the time of this observation and the theoretical explanation of the photoelectric effect by Einstein in 1905, several important studies of the photo-electric effect were performed with what is now known as a vacuum phototube.

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Einstein's explanation of the photo-electric effect was both simple and elegant

In 1916, Millikan's systematic studies confirmed the details of Einstein's theoretical conclusions.

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The results When light of constant frequency is focused on

the anode at low applied negative potential, the photocurrent is directly proportional to the intensity of the incident radiation.

The magnitude of the stopping voltage depends on the frequency of the radiation impinging on the photocathode.

The stopping voltage depends on the chemical composition of the coating on the photocathode.

The stopping voltage is independent of the intensity of the incident radiation.

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These observations suggest that electromagnetic radiation is a form of energy that releases electrons from metallic surfaces and imparts to these electrons sufficient kinetic energy to cause them to travel to a negatively charged electrode.

The number of photoelectrons released is proportional to the intensity of the incident beam. KEm = hv – ω

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Einstein had proposed the relationship between frequency v of light and energy E as embodied by the now famous equation:

Ephoton = hvh = Planck’s constant; 6.63 x 10-27

erg sec or 6.63 x 10-34 Js Wavelength by substitution:

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E = h = hC

V = Wave Number (cm-1)

Wave Length

C = Velocity of Radiation = 3 x 1010

cm/sec.

= Frequency of Radiation (cycles/sec)

The relation between frequency and wavelength is

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V = C

E = h = h

C

C

=

C

=

By how many kilojoules per mole is the energy of O2

increased when it absorbs ultraviolet radiation with a wavelength of 147 nm?◦ How much is the energy of CO2 increased when it absorbs infrared

radiation with a wavenumber of 2300 cm-1?

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Try yourself: What is the wavelength, wave number, and name of radiation with an energy of 100 kJ/mol?

(Answer: 1.20 ᵘm, 8.36 103 c m-1, infrared)

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E = h = hC

Energy States of Chemical Species The quantum theory was first proposed

in 1900 by Max Planck, a German physicist, to explain the properties of radiation emitted by heated bodies.

The theory was later extended to rationalize other types of emission and absorption processes.

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Two important postulates Atoms, ions, and molecules can exist only in

certain discrete states, characterized by definite amounts of energy.◦ When a species changes its state.◦ it absorbs or emits an amount of energy exactly

equal to the energy difference between the states.

When atoms. ions. or molecules absorb or emit radiation in making the transition from one energy state to another, the frequency v or the wavelength λ of the radiation is related to the energy difference between the states by the equation. E1-E0= hv

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The lowest energy state of an atom or molecule is its ground state.

Higher energy states are termed excited states.

Generally. at room temperature chemical species are in their ground state.

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interaction of light and matter Spectroscopists use the interactions of radiation

with matter to obtain information about a sample.

Several of the chemical elements were discovered by spectroscopy.

The sample is usually stimulated by applying energy in the form of heat, electrical energy, light, particles, or a chemical reaction.

Prior to applying the stimulus, the analyte is predominantly in its lowest energy state, or ground state.

The stimulus then causes some of the analytespecies to undergo a transition to a higher energy, or excited state.

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the analyte is stimulated by heal or electrical energy or by a chemical reaction. ◦ Emission speclroscopy usually involves methods in

which the stimulus is heat or electrical energy, and ◦ chemiluminescence spectroscopy refers to excitation

of the analyte by a chemical reaction. In both cases, measurement of the radiant power

emitted as the analyte returns to the ground state can give information about its identity and concentration.

The results of such a measurement are often expressed graphically by a spectrum,

which is a plot of the emitted radiation as a function of frequency or wavelength.

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When the sample is stimulated by application of an external electromagnetic radiation source, several processes are possible.

For example, the radiation can be reflected, scattered or absorbed.

When some of the incident radiation is absorbed, it promotes some of the analyte species to an excited state,

In adsorption spectroscopy, we measure the amount of light absorbed as a function of wavelength.◦ This can give both qualitative and quantitative

information about the sample

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Sample

Incident Radiation P0

Transmitted Radiation, P

E1 = hv1

E2 = hv2

Emission of Radiation Electromagnetic radiation is produced when excited

particles (atoms, ions, or molecules) relax to lower energy levels by giving up their excess energy as photons.

Excitation can be brought about by a variety of means including◦ bombardment with electrons or other elementary particles,

which generally leads to the. Emission of X-radiation:◦ exposure to an electric current, an ac spark. or an

intense heat source (flame, dc are, or furnace), producing ultraviolet, visible, or infrared radiation;

◦ irradiation with a beam of electromagnetic radiation, which produces fluorcseence radiation;

◦ an exothermic chemical reaction that produces chemiluminescence.

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Radiation from an excited source is conveniently characterized by means of an emission spectrum, which usually takes the form of a plot of the relative power of the emitted radiation as a function of wavelength or frequency.

Three types of spectra:

The line spectrum is made up of a series of sharp, well-defined peaks caused by excitation of individual atoms.

The band spectrum consists of several groups of lines so closely spaced that they are not completely resolved.

the continuum portion of the spectrum is responsible for the increase in the background that is evident above about 350 nm.

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Absorption of Radiation When radiation passes through a layer of

solid, liquid, or gas, certain frequencies may be selectively removed by absorption, a process in which electromagnetic energy is transferred to the atoms, ions, or molecules composing the sample.

Absorption promotes those particles from their normal room temperature state, or ground state, to one or more higher-energy excited states.

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According to quantum theory, atoms, molecules, and ions have only a limited number of discrete energy levels;◦ for absorption of radiation to occur, the energy

of the exciting photon must exactly match the energy difference between the ground state and one of the excited states of the absorbing species.

a study of the frequencies of absorbed radiation provides a means of characterizing the constituents of a sample of matter.

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Atomic Absorption The passage of polychromatic ultraviolet or visible

radiation through a medium that consists of mono atomic particles, such as gaseous mercury or sodium, results in the absorption of but a few well-defined frequencies.◦ The relative simplicity of such spectra is due to the

small number of possible energy states for the absorbing particles.

Excitation can occur only by an electronic process in which one or more of the electrons of the atom are raised to a higher energy level.

Ultraviolet and visible radiation have enough energy to cause transitions of the outermost, or bonding, electrons only.

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Molecular Absorption Absorption spectra for polyatomic molecules,

particularly in the condensed state, are considerably more complex than atomic spectra because the number of energy states of molecules is generally enormous when compared with the number of energy states for isolated atoms.

The energy E associated with the bands of a moleculc is made up of three components. ◦ E = Etrans+Erot+Evib

That

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Relaxation proceses Ordinarily, the lifetime of an atom or

molecule excited by absorption of radiation is brief because there are several relaxation processes that permit its return to the ground state.◦ Non-radiative Relaxation

◦ Fluorescence and Phosphorescence Relaxation

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non radiative relaxation involves the loss of energy in a series of small steps, the excitation energy being converted to kinetic energy by collision with other molecules.

A minute increase in the temperature of the system results.

Relaxation can also occur by emission of fluorescence radiation.

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Fluorescence and phosphorescence are analytically important emission processes in which species are excited by absorption of a beam of EMR, radiant emission then occurs as the excited species return to the ground state.

Fluorescence occurs more rapidly than phosphorescence.

Is generally complete after about 10-5 S from the time of excitation.

Phosphorescence emission takes place over periods longer than 10-5 S and may indeed continue for minutes or even hours after irradiation has ceased.

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Molecular fluorescence is caused by irradiation of molecules in solution or in the gas phase.

Phosphorescence occurs when an excited molecule relaxes to a metastable excited electronic state (called the triplet state), which has an average lifetime of greater than about 10-5 s.

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Some of the important types of transitions

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In conclusion When light strikes a sample of matter, the light

may be ◦ absorbed by the sample, ◦ transmitted through the sample, ◦ reflected off the surface of the sample, or◦ scattered by the sample.

Samples can also emit light after absorbing incident light; such a process is called luminescence. There are different kinds of luminescence, called ◦ fluorescence or ◦ phosphorescence depending on the specific

process that occurs

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Absorbance of light When a molecule absorbs a photon, the

energy of the molecule increases; promoted to an excited state.◦ microwave radiation stimulates rotation of

molecules when it is absorbed. ◦ Infrared radiation stimulates vibrations. ◦ Visible and ultraviolet radiation promote

electrons to higher energy orbitals. ◦ X-rays and short-wavelength ultraviolet

radiation break chemical bonds and ionize molecules.

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The Uncertainty Principle The uncertainty principle was first

proposed in 1927 by Werner Heisenberg, who postulated that nature places limits on the precision with which certain pairs of physical measurements can be made.

The uncertainty principle has important and widespread implications in instrumental analysis.

It is readily derived from the principle of superposition.

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If the energy E of a particle or system of particles - photons, electrons, neutrons, or protons, for example - is measured for an exactly known period of time ∆t, then this energy is uncertain by at least h/∆ t.

Therefore, the energy of a particle can be known with zero uncertainty only if it is observed for an infinite period.

For finite periods, the energy measurement can never be more precise than hl∆t.

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Quantitative aspects All four require the measurement of

radiant power P, which is the energy of a beam of radiation that reaches a given area per second.

In modern instruments, radiant power is determined with a radiation detector that converts radiant energy into an electrical signal S.

Generally S is a voltage or a current that ideally is directly proportional to radiant power.

That is, S = kP

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Emission, Luminescence,and Scattering Methods the power of the radiation emitted by an

analyte after excitation is ordinarily directly proportional to the analyte concentration c (Pe= kc).

Combining this equation with Equation gives S = K’c.

where k' is a constant that can be evaluated by exciting analyte radiation in one or more standards and by measuring S.

An analogous relationship also applies for luminescence and scattering methods.

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Absorption Methods Irradiance, P, is the energy per second per unit

area of the light beam.

◦ P0, irradiance of beam entering sample; ◦ P, irradiance of beam emerging from sample; ◦ b, length of path through sample

Two terms, which are widely used in absorption spectrometry and are related to the ratio of P0 and P, are transmittance and absorbance.

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Transmittance T, is defined as the fraction of the

original light that passes through the sample.◦ Transmittance: T= P/P0

Therefore, T has the range 0 to 1. The percent transmittance is simply 100T and ranges between 0 and 100%.

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Absorbance◦ Absorbance: A= - log(P/P0) = -log T◦ When no light is absorbed, P =P0 and A= 0.

If 90% of the light is absorbed, 10% is transmitted and P = P0/10.

This ratio gives A=1. If only 1% of the light is transmitted, A =2. Absorbance is sometimes called optical

density. Absorbance is directly proportional to the

concentration, c, of the light-absorbing species in the sample

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Beer’s law: A= ϵbc◦ Where, Absorbance: A, dimensionless ◦ Path lengh, b; expressed in centimeters◦ molar absorptivity (or extinction coefficient, ϵ, M-1 cm-1

The heart of spectrophotometry is called the Beer-Lambert law, or simply Beer’s law.

Molar absorptivity is the characteristic of a substance that tells how much light is absorbed at a particular wavelength.

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Math Find the absorbance and transmittance

of a 0.002 40 M solution of a substance with a molar absorptivity of 313 M-1 cm-

1in a cell with a 2.00-cm pathlength

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Solution Absorbance, A= ϵbc

=(313 M-1 cm-1)(2.00 cm)(0.002 40 M)

= 1.50

Transmittance is obtained by raising 10 to the power equal to the expression on each side of the equation:

T = 10 logT; T = 10–A = 10–1.50 = 0.0316 Just 3.16% of the incident light

emerges from this solution.

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Try yourself: The transmittance of a 0.010 M solution of a compound in a 0.100-cmpathlength cell is T 8.23%. Find the absorbance (A) and the molar absorptivity (ε).

(Answer: 1.08, 1.08 103 M-1 cm-1)

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Deviations from Beer’s Law /When Beer’s Law Fails Beer’s law states that absorbance is

proportional to the concentration of the absorbing species.

It applies to monochromatic radiation, and it works very well for dilute solutions (≤ 0.01 M) of most substances.

There are several possible reasons for deviation from linearity at high concentrations.

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Measuring Absorbance

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i. We do not measure the incident irradiance, P0 , directly. Rather, the irradiance of light passing through a reference cuvet containing pure solvent (or a reagent blank) is defined as P0.

ii. This cuvet is then removed and replaced by an identical one containing sample.

iii. The irradiance of light striking the detector after passing through the sample is the quantity P.

iv. Knowing both P and P0 allows T or A to be determined.

the wavelength of maximum absorbance◦ at the maximum The sensitivity of the analysis is greatest; that is,

we get the maximum response for a given concentration of analyte.

The curve is relatively flat, so there is little variation in absorbance if the monochromatordrifts a little or if the width of the transmitted band changes slightly.

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Example: Measuring Benzene in Hexane Pure hexane has negligible ultraviolet

absorbance above a wavelength of 200 nm.

A solution prepared by dissolving 25.8 mg of benzene (C6H6, FM 78.11) in hexane and diluting to 250.0 mL had an absorption peak at 256 nm and an absorbance of 0.266 in a 1.000-cm cell.

Find the absorptivity of benzene at this wavelength.

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Solution: The concentration of benzene is [C6H6] = (0.025 8 g)/(78.11 g/mol)/0.250 0 L

= 1.32x103 MWe find the molar absorptivity from Beer’s

law: Molar absorptivity ε =A /bc = (0.266)/(1.00

cm)(1.32x103 M) = 201.3 M-1 cm-1

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Try yourself A sample of hexane contaminated with

benzene had an absorbance of 0.070 at 256 nm in a cuvet with a 5.000-cm pathlength. Find the concentration of benzene in mg/L.

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OPTICAL SYSTEMS USED IN SPECTROSCOPY

The essential components of a spectrophotometer include:◦ 1- A stable source of radiant energy◦ 2- A system of lenses, mirrors, and slits which

define, collimate (make parallel) and focus the beam.◦ 3- Wavelength Selectors to resolve the

radiation into component wavelengths or bands of wavelength.◦ 4- A transparent container to hold the sample.◦ 5- Radiation detector◦ 6- Readout system (meter, recorder or

computer).

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optics / optical configuration / optical layout

:

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The specific arrangement of these components: double beam spectrometer

Radiation Sources An ideal radiation source for spectroscopy

should have the following characteristics:1. The source must emit radiation over the entire

wavelength range to be studied.2. The intensity of radiation over the entire

wavelength range must be high enough.3. The intensity of the source should not vary

significantly at different wavelengths.4. The intensity of the source should not

fluctuate over long time intervals.5. The intensity of the source should not

fluctuate over short time intervals..

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Continuum sources Continuum sources emit radiation over a wide

range of wavelengths and the intensity of emission varies slowly as a function of wavelength.◦ the tungsten filament lamp which produces visible

radiation◦ the deuterium lamp for the UV region, ◦ high pressure mercury or xenon arc lamps for the UV

region, and ◦ heated solid ceramics or heated wires for the IR region

of the spectrum. Continuum sources are used for most molecular

absorption and fluorescence spectrometric instruments.

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Line sources Line sources emit only a few discrete

wavelengths of light, and the intensity is a strong function of the wavelength. ◦ hollow cathode lamps and electrodeless

discharge lamps, used in the UV and visible regions for AAS and atomic fluorescence spectrometry, ◦ sodium or mercury vapor lamps (similar

to the lamps now used in street lamps) for lines in the UV and visible regions, and lasers.

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Wavelength Selectors These are devices which resolve wide band

polychromatic radiation from the source into narrow bands or, even better, monochromatic radiation.

There are two types of resolving devices ◦ filters and ◦ mono-chromators.

Filters prepared from special materials allow transmission of only limited wavelength regions while absorbing most of the radiation of other wavelengths. ◦ absorption filters and ◦ interference filters.

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Absorption filters Absorption filters can be as simple as a

piece of colored glass that isolate various ranges of visible light.

These filters are stable, simple, and cheap, so they are excellent for use in portable spectrometers designed to be carried into the field.

The transmission range may be 50–300 nm for typical absorption filters.

Absorption filters are limited to the visible region of the spectrum and the X-ray region.

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interference filter the interference filter is constructed of

multiple layers of different materials. The wavelengths transmitted are

controlled by the thickness. Interference filters can be constructed for

transmission of light in the IR, visible, and UV regions of the spectrum.

The wavelength ranges transmitted are generally 1–10 nm,

The amount of light transmitted is generally higher than for absorption filters.

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Monochromators Monochromators resolve poly-chromatic into its

individual wavelengths and isolate these wavelengths into very narrow bands.

The components of a monochromator include: i. an entrance slit which admits polychromatic radiation

from the source; ii. a collimating device either a lens or a mirror; iii. a dispersing device, either a prism or grating which

resolve the radiation into small bands of wavelengths emerging at

iv. different angles; v. A focusing lens or mirror; vi. An exit slit.

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Sample Containers The cells or cuvettes that hold the

samples must be made of material that is transparent to radiation in the spectral region of interest.

Quartz or fused silica ultraviolet region (< 350 nm).

Plastic containers - visible region. Crystalline sodium chloride (NaCl) -

infrared region.

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Cuvets Cuvet has flat,

fused-silica (SiO2) faces. UV- visible

1.000-cm pathlength

visible - Glass is IR measurements -

NaCl or KBr. Far-IR region,

polyethylene is a transparent window

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Radiation Detectors Phototubes Photomultiplier tube Photoconductivity detectors Thermal detectors

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Processors and readout The electronic signal generated by any

radiation detector must be translated into a form that can be interpreted.

This process is typically accomplished with amplifiers, ammeters, potentiometers and potentiometer recorders.

Amplifiers◦ The amplifier takes an “input” signal from the

circuit of the sensing component and, through a series of electronic operations, produces an “output” signal which in many times larger than the “input”. ◦ The amplification factor (ratio of output to input)

is called “the gain” of the amplifier.

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Readout devices Several types of readout devices are

found. For example, the digital meters, the

scale of potentiometers, cathode ray tubes and computers.

The instrument is calibrated so that there are 100 units on the meter from (It=0) to (I = I0) and these units are linear with respect to It.

When an absorbing sample is substituted for the “blank”, the detector response will show between 0 and 100 units on the meter.

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