Absorbance of Electromagnetic Radiation

Absorbance of Electromagnetic Radiation

Chapter 2 Ultraviolet and visible spectroscopy Molecular Spectrophotometry Properties of light Electromagnetic radiation and electromagnetic spectrum

Absorption of light Beers law Limitation of Beers law Absorption of light by molecules Instrumentation: Spectrophotometer Applications: Individual species and mixtures Spectrophotometric titration (up to p.524 in the notes) Spectrophotometry It refers to the use of light (electromagnetic radiation) to measure chemical concentrations. Mainly, the fundamental principles of absorption and emission of radiation by molecules or atoms and how these

processes are used in quantitative analysis will be discussed . Electromagnetic radiation Electromagnetic radiation or light, is a form of energy whose behavior is described by the properties of both waves and particles. The optical properties of electromagnetic radiation, such as diffraction and dispersion , are explained best by describing light as a wave. Many of the interactions between electromagnetic radiation and matter, such as absorption and emission are better described by treating light as a particle, or photon.

Wave Properties of EMR consists of oscillating electric and magnetic fields that propagate through space along a linear path and with a constant velocity Oscillations in the electric and magnetic fields are perpendicular to each other, and to the direction of the wave's propagation Plane polarized electromagnetic radiation showing the electric field, the magnetic field and the direction of propagation In a vacuum, EMR travels at the speed of light, c, which is 2.99792 x 108 m/s. EMR moves through a medium other than a vacuum with a velocity, v, less than that of

the speed of light in a vacuum. The difference between v and c is small enough (< 0.1%) that the speed of light to three significant figures, 3.00 x 108 m/s, is sufficiently accurate for most purposes. Characteristics electromagnetic wave The interaction of EMR with matter can be explained using either the electric field or the magnetic field. Only the electric field component will be used to discuss this matter An electromagnetic wave is characterized by several fundamental properties, including its velocity, amplitude, frequency, phase angle, polarization, and direction of propagation.

The interaction of EMR with matter can be explained using either the electric field or the magnetic field. Only the electric field component will be used to discuss this matter Ae is the electric field maximum amplitude Is the distance between successive maxima or successive minima Frequency, , is the number of oscillations in the electric field per unit time. One oscillation/sec = one hertz (HZ) The wavelength of an electromagnetic wave, , is

defined as the distance between successive maxima, or successive minima For ultraviolet and visible electromagnetic radiation the wavelength is usually expressed in nanometers (nm, 109 m) The wavelength for infrared radiation is given in microns (m, 106 m). Wavelength depends on the electromagnetic wave's velocity, where = c/ = v/ (in vacuum) Wave number : = 1/ Power and Intensity of light

Power, P, and Intensity, I, of light give the flux of energy from a source of EMR P is the flux of energy per unit time I is the flux of energy per unit time per area Particle Properties of Electromagnetic Radiation When a sample absorbs electromagnetic radiation it undergoes a change in energy. The interaction between the sample and the electromagnetic radiation is easiest to understand if we assume that: electromagnetic radiation consists of a beam of energetic particles (packets of energy) called photons.

When a photon is absorbed by a sample, it is "destroyed," and its energy is acquired by the sample Particle Properties of Electromagnetic Radiation The energy of a photon, in joules, is related to its frequency, wavelength, or wavenumber by the following equations: E =h = hc

= hc h is Planck's constant, which has a value of 6.626 x 1034 J s. Electromagnetic Spectrum The spectrum is the written records of the EMR EMR is divided into different regions based on the type of atomic or molecular transition that gives rise to the absorption or emission of photons The boundaries describing the electromagnetic spectrum are not rigid, and an overlap between spectral regions is possible. Colors of the visible light

of maximum absorption (nm) 380420 420440 440470 470500 500520 520550 550580 580620 620680 680780 Color absorbed

Violet Violetblue Blue Bluegreen Green Yellowgreen Yellow Orange Red Purple Color observed Greenyellow Yellow

Orange Red Purple Violet Violetblue Blue Bluegreen Green Measuring Photons as a Signal Spectroscopy is divided into two broad classes: 1. Energy is transferred between a photon of electromagnetic radiation and the analyte (Absorption or Emission of radiation 2. Changes in electromagnetic radiation wave characteristics

(changes in amplitude, phase angle, polarization, or direction of propagation. Class 1: Absorption of radiation In absorption spectroscopy the energy carried by a photon is absorbed by the analyte, promoting the analyte from a lowerenergy state (Ground state) to a higherenergy, (or excited) state Absorbing a photon of visible light causes a valence electron in the analyte to move to a higherenergy level. When an analyte absorbs infrared radiation one of its chemical bonds experiences a change in vibrational energy. Energy level diagram showing absorption of a photon

The intensity of photons passing through a sample containing the analyte is attenuated because of absorption. The measurement of this attenuation, which we call absorbance, The energy levels have welldefined values (i.e., they are quantized). Absorption only occurs when the photon's energy matches the difference in energy, E, between two energy levels. A plot of absorbance as a function of the photon's energy (wavelength, , is called an absorbance spectrum Wavelenth at which Absorbance is maximum max

Ultraviolet/visible absorption spectrum for bromothymol blue Class 1 Emission of Radiation Emission of a photon occurs when an analyte in a higherenergy state returns to a lowerenergy state The higherenergy state can be achieved in several ways: including thermal energy, radiant energy from a photon, or by a chemical reaction. Emission following the absorption of a photon is also called photoluminescence, and that following a chemical reaction is called chemiluminescence. Emission (luminescence) Spectrum

Typical Emission Spectrum Various spectroscopic techniques of class 1 Class 2 Changes in the EMR wave characteristics In this class of spectroscopy: the electromagnetic radiation undergoes a change in amplitude, phase angle, polarization, or direction of propagation as a result of its refraction, reflection, scattering, diffraction, or dispersion by the sample. Several representative spectroscopic techniques

are listed in the following table Various spectroscopic techniques of class 2 Sources of Energy All forms of spectroscopy require a source of energy. In absorption and scattering spectroscopy this energy is supplied by photons (EMR or light). Emission and luminescence spectroscopy use thermal, radiant (photon), or chemical energy to promote the analyte to a less stable, higher energy state. Sources of Electromagnetic Radiation

A source of electromagnetic radiation must provide an output that is both intense and stable in the desired region of the electromagnetic spectrum. Sources of electromagnetic radiation are classified as either continuum or line sources. A continuum source emits radiation over a wide range of wavelengths, with a relatively smooth variation in intensity as a function of wavelengths. Line sources emit radiation at a few selected, narrow wavelength ranges Common sources of EMR Emission spectrum from a

continuum emission source Emission spectrum fro ma typical line source Absorbance of Electromagnetic Radiation In absorption spectroscopy a beam of electromagnetic radiation passes through a sample. Much of the radiation is transmitted without a loss in intensity. At selected wavelengths the radiation's intensity is attenuated. The process of attenuation is called absorption. Two general requirements must be met if an analyte is to absorb electromagnetic radiation.

The first requirement is that there must be a mechanism by which the radiation's electric field or magnetic field interacts with the analyte. For ultraviolet and visible radiation, this interaction involves the electronic energy of valence electrons. A chemical bond's vibrational energy is altered by the absorbance of infrared radiation. The second requirement is that the energy of the electromagnetic radiation must exactly equal the difference in energy, AE, between two of the analytes quantized energy states. Molecular Orbital (MO)Theory Review

MO Theory: Electrons in atoms exist in atomic orbitals while electrons in molecules exist in molecular orbitals. Bonding MO: A MO where electrons have a lower energy than they would in isolated atomic orbitals Anitbonding MO: A MO in which electrons have a higher energy than they would in isolated atomic orbitals. Ground State: Refers to the state of lowest energy. Electrons can be promoted from a ground state to a higher excited state by input of energy. Excited State: Any electronic state other than the ground state. )a( Relative Energies of Molecular Orbitals Energy

sigma* * n Compounds containing only sigma bonds have absorptions only in the ultraviolet. These transitions correspond to sigma-sigma* sigma n-sigma* transitions are common Compare the energy of n-sigma*

vs a sigma-sigma* Electronic transition in Formaldehyde Example of Electronic Transitions: Absorptions O C H Formaldehyde H Contains both and

nonbonding electrons (n) Molecular Absorption Molecules undergo three types of quantized transitions when excited by ultraviolet, visible, and infrared radiation. 1. electronic transition The transition of an electron between two orbitals (the energy by the photon must be exactly the same as the energy difference between the two orbital energies) and the absorption process is called electronic absorption Molecular orbital diagram for formaldehyde

In electronic transition, an electron from one molecular orbital moves to another orbital with an increase or decrease in the energy of the molecule The lowest energy electronic transition in formaldehyde involves the promotion of a non-bonding (n) electron to the anti-bonding * orbital Singlet state and triplet stat Singlet state: the state in which the spins are opposed TRiplet state: the state in

which the spins are paired * n S1, 355, UV In general T1 is of lower energy than S1 * n T1, 397, visible vibrational and rotational transitions. 2

Vibration of the atoms of the molecule with respect to one another; Atoms and groups of atoms within molecules can undergo various types of vibrations and each requires a discrete amount of energy to initiate or maintain. Also molecules can rotate around their axes a matter that requires discrete amount of energy. Various Types of Vibrations Vibrations of formaldehyde Thus each molecular energy state is

comprised of an electronic, vibrational and rotational component such that: E total = E electonic + E vibrational + E rotational E electonic > E vibrational > E rotational Energy of a Molecule Emolecule =Eelectronic + Evibrational + Erotational + Espin + Etranslational Our Focus Eelectronic (UV/Vis) Evibrational (IR) Energy of a Molecule Eelectronic --> 105-106 kJ/mole --> UV-Vis UV-Vis range: 200 - 700 nm

Evibrational--> 10 - 40 kJ/mole --> IR Near IR: 800 - 2500 nm (5000 nm) Mid-IR : 5000 nm - 25,000 nm (5 microns - 25 microns) Erotational--> 10 kJ/mole --> microwaves Espin --> 10-3 J/mole --> Radiofrequency Etranslational --> continuous Electronic transitions ?What happens to the absorbed energy

Internal Conversion (IC) Radiationless transition between states with same spin quantum numbers ( S1 S0) Intersystem Crossing (ISC) Radiationless transition between states with different spin quantum numbers ( S1 T1) Fluorescence Radiation transition between states with the same spin quantum number ( S1 S0) Phosphorescence Radiation transition between states with different spin quantum number ( T1 S0) Combined electronic, vibrational, and

rotational transitions When a molecule absorbs light having sufficient energy to cause an electronic transition, vibrational and rotational transitionsthat is, changes in the vibrational and rotational statescan occur as well. The reason why electronic absorption bands are usually very broad is that many different vibrational and rotational levels are available at slightly different energies. Therefore, a molecule could absorb photons with a fairly wide range of energies and still be promoted from the ground electronic state to one particular excited electronic state.

Absorption of Light Beers Law P0 P P T P0 Beers Law P0 = 10,000 P = 5,000

-b- P 5000 T 0.5 P0 10000 Beers Law P0 = 10,000 P = 2,500 --2b--

P 2500 T 0.25 P0 10000 Beers Law P0 = 10,000 P = 1,250 ----3b----

P 1250 T 0.125 P0 10000 Beers Law P0 = 10,000 P = 625 ------4b------ P

625 T 0.0625 P0 10000 Relationship between transmittance and cell thickness Transmittance, T 1 0.5 0.25 0.125 0.0625 0.03125 0.015625

0.0078125 0.00390625 0.001953125 0.000976563 P T P0 1.2 1 Transmittance Thickness, b

0 1 2 3 4 5 6 7 8 9 10 0.8 0.6 0.4

0.2 0

( Thickness, multiples of b ) * Relationship between absorbance and cell thickness Transmittance, T 1

0.5 0.25 0.125 0.0625 0.03125 0.015625 0.0078125 0.00390625 0.001953125 0.000976563 A = -log T 0.000 0.301 0.602

0.903 1.204 1.505 1.806 2.107 2.408 2.709 3.010 P A log T log P0 A abc 3.5

3.0 Absorbance Thickness, b 0 1 2 3 4 5 6 7 8 9 10

2.5 2.0 1.5 1.0 0.5 0.0 0 1 2 3 4 5 6 7 8 9 10 Thickness, multiples of b A absorbance a absorptivity b thickness c concentration

Relation between Absorbance and Transmittance Calculation of absorbance from transmittance T %T A 1 100 0.000 0.9 90 0.046 0.8 80 0.097 0.7

70 0.155 0.6 60 0.222 0.5 50 0.301 0.4 40 0.398 0.3 30 0.523 0.2

20 0.699 0.1 10 1.000 0.075 7.5 1.125 0.05 5 1.301 0.01 1 2.000 0.001

0.1 3.000 80 %T A log T abc A 60 40 20 200 Cell B3=100*A3

Cell C3=-log(A3) 0 100 250 300 350 400 450

1 2 500 Spectroscopy Nomenclature Absorbance and Transmittance Spectra 0 100 100

.8 80 80 .6 %T 60 A 40

40 .2 20 20 200 .4 250 300

350 400 450 500 1 2 200 250 300 350 400 450 500 % Transmission Spectrum

0 200 250 300 350 400 450 50 Absorbance Spectrum A log T abc Absorbance Spectra and Concentration concA 1 .8 .6

.4 concB .2 A 0 200 200 250

250 300 300 350 350 400 400

Absorbance Spectra A log T abc 450 450 500 500 Absorbance and Concentration: Beer's Law When monochromatic EMR passes through an infinitesimally thin layer of sample, of thickness dx,

it experiences a decrease in power of dP. The fractional decrease in power is proportional to the sample's thickness and the analyte's concentration, C Thus, where P is the power incident on the thin layer of sample, and is a proportionality constant. Integrating the left side of equation from P = Po to P = P T, and the right side from x = 0 to x = b, where b is the sample's overall thickness,

gives Converting from ln to log and substituting log po/pT by A (absorbance) gives A = abC Where a is tha anlayte absorptivity with units of cm-1conc-1. When concentration is expressed using molarity the absorptivity is replaced by molar absorptivity The absorptivity and molar absorptivity give, in effect, the probability that the analyte will absorb a photon of given energy. As a result, values for both a and depend on the wavelength of electromagnetic radiation.

Predicting Concentrations from Absorbance Spectra unknown Regression equation slope Intercept Conc of unknown 0.162 0.330 0.499 0.660 0.840 0.539

1.00 Absorbance 30.00 60.00 90.00 120.00 150.00 0.80 0.60 0.40 0.20 0.00

0.00562 -0.0076 97.25978648 Conc, Micro-M Absorption Spectra of Mixtures Containing n components A1 a1 bc1 a1 bc2 a1 bc3 a1 bcn A2 a2 bc1 a2 bc2 a2 bc3 a2 bcn An an bc1 an bc2 an bc3 an bcn

Absorption Spectra of Mixtures Containing n components Constant pathlength A1 k1 c1 k1 c2 k1 c3 k1 cn A2 k2 c1 k2 c2 k2 c3 k2 cn An kn c1 kn c2 kn c3 kn cn Limitations to Beers Law

Ideally, according to Beer's law, a calibration curve of absorbance versus the concentration of analyte in a series of standard solutions should be a straight line with an intercept of 0 and a slope of ab or b. In many cases, calibration curves are found to be nonlinear. Deviations from linearity are divided into three categories: fundamental, chemical, and instrumental. Fundamental Limitations to Beers Law Beer's law Beers law is a limiting law that is valid only for low concentrations of analyte. 1. At higher concentrations the individual particles of analyte are no longer behave independently of one

another The resulting interaction between particles of analyte may change the value of a or . 2. The absorptivity, a, and molar absorptivity, , depend on the sample's refractive index. Since the refractive index varies with the analyte's concentration, the values of a and will change. For sufficiently low concentrations of analyte, the refractive index remains essentially constant, and the calibration curve is linear. Chemical Limitations to Beer's Law Chemical deviations from Beer's law can occur when the absorbing species is involved in an equilibrium

reaction. Consider, as an example, the weak acid, HA. To construct a Beer's law calibration curve, several standards containing known total concentrations of HA, Ctot, are prepared and the absorbance of each is measured at the same wavelength. Since HA is a weak acid, it exists in equilibrium with its conjugate weak base, A If both HA and A- absorb at the selected wavelength, then Beers law is written as where CHA and CA are the equilibrium concentrations of HA and A. Since the weak acid's total concentration, Ctot, is Ctot = CHA + CA

The concentration of HA and A- can be written as Where HA is the fraction of week acid present as HA Thus, Because values of HA may depend on the concentration of HA, equation may not be linear. A Beer's law calibration curve of A versus Ctot will be linear if one of two conditions is met. 1. If the wavelength is chosen such that HA and A are equal, then equation simplifies to A = b Ctot and a linear curve is realized

2. Alternatively, if HA is held constant for all standards, then equation will be a straight line at all wavelengths. Because HA is a weak acid, values of HA change with pH. To maintain a constant value for HA , therefore, we need to buffer each standard solution to the same pH. Depending on the relative values of HA and A, the calibration curve will show a positive or negative deviation from Beer's law if the standards are not buffered to the same pH. Instrumental Limitations to Beer's Law There are two principal instrumental limitations to Beer's

law. 1. Beers law is strictly valid for purely monochromatic radiation; that is, for radiation consisting of only one wavelength. even the best wavelength selector passes radiation with a small, but finite effective bandwidth. Using polychromatic radiation always gives a negative deviation from Beer's law, but is minimized if the value of is essentially constant over the wavelength range passed by the wavelength selector. For this reason, it is preferable to make absorbance measurements at a broad absorption peak. Effect of wavelength on the linearity of a Beers law calibration curve

2. Stray Radiation Stray radiation arises from imperfections within the wavelength selector that allows extraneous light to "leak" into the instrument. Stray radiation adds an additional contribution, Pstray, to the radiant power reaching the detector; thus For small concentrations of analyte, Pstray is significantly smaller than Po and PT, and the absorbance is unaffected by the stray radiation. At higher concentrations of analyte, Pstray is no longer significantly smaller than PT and the absorbance is smaller than expected. The result is a negative deviation

Instrument Designs for Molecular UV/Vis Absorption Filter Photometers Molecular UV/Vis absorption is measured using an absorption or interference filter to isolate a band of radiation. The filter is placed between the source and sample to prevent the sample from decomposing when exposed to highenergy radiation. A filter photometer has a single optical path between the source and detector and is called a singlebeam instrument. The instrument is calibrated to 0% T while using a shutter to block the source radiation from the detector. After removing the shutter, the instrument is

calibrated to 100% T using an appropriate blank. In comparison with other spectroscopic instruments, photometers have the advantage of being relatively inexpensive, rugged, and easy to maintain. Another advantage of a photometer is its portability, making it a useful instrument for conducting spectroscopic analyses in the field. A disadvantage of a photometer is that it cannot be used to obtain an absorption spectrum. Spectrometer/spectrophotometer The simplest spectrophotometer is a singlebeam instrument equipped with a fixedwavelength monochromator,

Singlebeam spectrophotometers are calibrated and used in the same manner as a photometer. One common example of a singlebeam spectropho tometer is the Spectronic20 It has a fixed effective bandwidth of 20 nm. Because its effective bandwidth is fairly large, this instrument is more appropriate for a quantitative analysis than for a qualitative analysis. Other singlebeam spectrophotometers are available with effective bandwidths of 23 nm. Fixedwavelength singlebeam spectrophotometers are not practical for recording spectra since manually adjusting the wavelength and recalibrating the spectrophotometer is timeconsuming.

Block diagram for a single beam fixed wavelength spectrophotometer Double-beam spectrophotometer Double-beam spectrophotometer A chopper is used to control the radiation's path, alternating it between the sample, the blank, and a shutter. The signal processor uses the chopper's known speed of rotation to resolve the signal reaching the detector into that due to the transmission of the blank (Po) and the sample (PT). By including an opaque surface as a shutter it is possible to continuously adjust the 0% T response of the detector.

The effective bandwidth of a doublebeam spectrophotometer is controlled by means of adjustable slits at the entrance and exit of the monochromator. Effective bandwidths of between 0.2 nm and 3.0 nm are common. A scanning monochromator allows for the automated recording of spectra. Doublebeam instruments are useful for both quantitative and qualitative analyses. Diode array spectrophotometer Previous designs use only one detector and can monitor a

single wavelength at a time. A linear photodiode array consists of multiple detectors, or channels, allowing an entire spectrum to be recorded in as little as 0.1 s. the Source radiation passing through the sample is dispersed by a grating. The linear photodiode array is situated at the grating's focal plane, with each diode recording the radiant power over a narrow range of wavelengths. Sample Compartment (Cell) The sample compartment for the instruments provides a lighttight environment that prevents the loss of radiation, as well as the addition of stray radiation.

Samples are normally in the liquid or solution state and are placed in cells constructed with UV/Vistransparent materials, such as quartz, glass, and plastic Quartz or fusedsilica cells are required when working at wavelengths of less than 300 nm where other materials show a significant absorption. The most common cell has a pathlength of 1 cm, although cells with shorter (> I mm) and longer pathlengths (< 10 cm) are available. Cells with a longer pathlength are useful for the analysis of very dilute solutions or for gaseous samples. Typical Uv/Vis Cells

The highest quality cells are constructed in a rectangular shape, allowing the radiation to strike the cell at a 90 angle, where losses to reflection are minimal. These cells, which are usually available in matched pairs having identical optical properties, are the cells of choice for doublebeam instruments.

Fiber optic probes In some circumstances it is desirable to monitor a system without physically removing a sample for analysis. This is often the case, for example, with the online monitoring of industrial production lines or waste lines, With the use of a fiberoptic probe it is possible to analyze samples in situ. A simple example of a remotesensing, fiberoptic probe is shown in the Figure and consists of two bundles of fiberoptic cable. One bundle transmits radiation from the source to the

sample cell, which is designed to allow for the easy flow of sample through it. Radiation from the source passes through the solution, where it is reflected back by a mirror. The second bundle of fiberoptic cable transmits the nonabsorbed radiation to the wavelength selector. Fiber optic probes UV and Visible Detectors UV and Visible Detectors work on the basis of the photoelectric effect: light ejects an electron from a metal surface A vacuum phototube converts a light flux into an electrical current, and is useful for detecting high

levels of light A photomultiplier converts a single photon into a current pulse, and is useful for detecting low levels of light Photodiodes are based on the promotion of electrons from the valence band to the conduction band of semiconductors, and are useful for detecting both high and low levels of light 1 : 7.4 Photo electric effectExperimental setup to show the photoelectric effect

When light shines on a metal surface, the surface emits electrons. For example, you can start a current in a circuit just by shining a light on a metal plate. Why do you think this happens? The answer: It is known that light is made up of electromagnetic waves, and that the waves carry energy. So if a wave of light hit an electron in one of the atoms in the metal, it might transfer enough energy to knock the electron out of its atom. Number of photoelectrons ejected is proportional to light intensity Each metal has a different threshold frequency below which no photoelectrons are produced

A range of energies are produced but the maximum value depends on colour (frequency) Photoelectric Effect Because metals contain free electrons they can absorb UV and visible radiation If the energy of the absorbed photon is greater than the work function of the metal, an electron is ejected into the vacuum Alkali metals are commonly used in detectors Mixtures of alkali metals can give 0 as high as 750 nm 2 : 7.4 metal

Li Na K Rb Cs 2.9 eV

2.75 2.3 2.16 2.14 0 428 nm 451 539

574 579 Vacuum Phototube A metallic surface with a low work function is placed inside an evacuated tube. When light interacts with the metal, electrons are photo-ejected. By placing a 90 V electric potential between the photocathode and anode, the electrons are drawn to the anode. The resultant current is measured by a micro-ammeter. glass tube

h e I photocathode + anode Photomultipliers Photomultiplier A photomultiplier is nothing more than a vacuum

phototube followed by an electron multiplier. h 1 e PC 4 e D1 16 e D2 106 D3 A

D9 I 100 k -1,000 V +0 V The secondary electron emitters are called dynodes and are made from a beryllium alloy. The number of secondary electrons varies from 3 to 5. For an average of 4, the gain of the multiplier shown above is 410 = 106. This is a current of 1.610-13 A per photon. 4 : 7.4

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