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Foundations of Spectroscopy

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Foundations of Spectroscopy FOUNDATIONS OF SPECTROSCOPY Incandescent Bulb Virtual Spectrum 2 1 Diffraction Grating Spectroscope Eye of Human Retina Real Spectrum by DR. STEPHEN THOMPSON MR. JOE STALEY The contents of this module were developed under grant award # P116B-001338 from the Fund for the Improve- ment of Postsecondary Education (FIPSE), United States Department of Education. However, those contents do not necessarily represent the policy of FIPSE and the Department of Education, and you should not assume endorsement by the Federal government. FOUNDATIONS OF SPECTROSCOPY CONTENTS 2 Introduction 3 Electromagnetic Radiation Ruler: The ER Ruler 4 Numbering Electromagnetic Radiation 5 Waves 6 Frequency And Wavelength 7 Questions For The ER Ruler 8 Fundamental Processes 9 Spectroscope 10 Interference: The Principle By Which Light Is Broken Up 11 Diffraction 12 An Atomic Line Emission Spectrum From A Discharge Tube 13 Fluorescent Lights 14 Continuous Emission 15 The Origins Of Band Spectra 16 Origins Of band Spectra 17 The Frank-Condon Principle 18 Band Spectra 19 Lasers 20 Simple Spectra 21 Complex Spectra 22 Spectral Questions FOUNDATIONS OF SPECTROSCOPY INTRODUCTION Spectroscopy is the study of the interaction of electro- Much of the scientifi c knowledge of the structure of the magnetic radiation with matter. When matter is ener- universe, from stars to atoms, is derived from inter- gized (excited) by the application of thermal, electrical, pretations of the interaction of radiation with matter. nuclear or radiant energy, electromagnetic radiation is One example of the power of these techniques is the often emitted as the matter relaxes back to its original determination of the composition, the velocities, and (ground) state. The spectrum of radiation emitted by a the evolutionary dynamics of stars. The source of the substance that has absorbed energy is called an emis- incredible amount of energy produced by the sun is sion spectrum and the science is appropriately called nuclear fusion reactions going on within the hot inte- emission spectroscopy. rior (temperature 40 x 106K). Two fusion cycles, the Another approach often used to study the interaction of carbon cycle and the proton cycle, convert hydrogen electromagnetic radiation with matter is one whereby nuclei into helium nuclei via heavier nuclei, such as a continuous range of radiation (e.g., white light) is carbon 12 and nitrogen 14. The enormous radiation of allowed to fall on a substance; then the frequencies energy from the hot core seethes outwards by convec- absorbed by the substance are examined. The result- tion. This radiation consists of the entire electromag- ing spectrum from the substance contains the original netic spectrum as a continuous spectrum. Towards range of radiation with dark spaces that correspond to the surface of the sun (the photosphere), the different missing, or absorbed, frequencies. This type of spec- elements all absorb at their characteristic frequencies. trum is called an absorption spectrum. In spectroscopy The radiation that shoots into space toward earth is the emitted or absorbed radiation is usually analyzed, a continuous emission spectrum with about 22,000 i.e., separated into the various frequency components, dark absorption lines present in it (Fraunhofer lines), of and the intensity is measured by means of an instru- which about 70% have been identifi ed. These absorp- ment called a spectrometer. tion lines - i.e., missing frequencies - prove that more The resultant spectrum is mainly a graph of intensity than 60 terrestrial elements are certainly present in the of emitted or absorbed radiation versus wavelength or sun. frequency. There are in general three types of spectra: continuous, line, and band. The sun and heated solids produce continuous spectra in which the emitted radia- tion contains all frequencies within a region of the elec- tromagnetic spectrum. A rainbow and light from a light bulb are examples of continuous spectra. Line spectra are produced by excited atoms in the gas phase and contain only certain frequencies, all other frequencies being absent. Each chemical element of the periodic chart has a unique and, therefore, characteristic line spectrum. Band spectra are produced by excited mol- ecules emitting radiation in groups of closely spaced lines that merge to form bands. These categories of emission and absorption spectra contain tremendous amounts of useful information about the structure and composition of matter. Spec- troscopy is a powerful and sensitive form of chemical analysis, as well as a method of probing electronic and nuclear structure and chemical bonding. The key to interpreting this spectral information is the knowledge that certain atomic and molecular processes involve only certain energy ranges. Page 3 shows the regions of the electromagnetic spectrum and the associated energy transitions that occur in atomic and molecular processes. 2 FOUNDATIONS OF SPECTROSCOPY ELECTROMAGNETIC RADIATION RULER: THE ER RULER Energy Level Transition Energy Wavelength Joules nm 10-27 2 34 8 Plank’s constant, h = 6.63 x 10- J s. 4 6 Nuclear and electron spin 6 RF 4 The speed of light, c = 3.0 x 108 m s-1. 10-26 2 1010 25 10- 109 10-24 Wavelength 108 µW -23 10 700 nm Molecular rotations 107 10-22 106 650 nm 10-21 105 Molecular vibrations IR 10-20 600 nm 104 10-19 103 VIS 550 nm Valence electrons 10-18 102 Middle-shell electrons 17 10- UV 500 nm 10 10-16 1 450 nm Inner-shell electrons 10-15 X 10-1 10-14 400 nm 10-2 10-13 10-3 RF = Radio frequency radiation Nuclear 10-12 γ µW = Microwave radiation 4 10- IR = Infrared radiation VIS = Visible light radiation 10-11 10-5 UV = Ultraviolet radiation 6 X = X-ray radiation 4 10-10 2 γ = gamma ray radiation 2 -6 4 10 6 8 3 FOUNDATIONS OF SPECTROSCOPY NUMBERING ELECTROMAGNETIC RADIATION Radiation may be described in one of two ways: either How many meters are in a nanometer? as a stream of energy pulses (photons) or as energy waves sent out from a source at the speed of light. How many megabytes in a gigabyte? How many Scientists use whichever interpretation works best to kilobytes in a terabyte? explain an experiment involving radiation. The photon and wave theories are linked by Plank’s law: What is the frequency of a one nanometer photon? What is its energy? 25 E = hν A rough calculation suggests that there might be 10 stars in the observable universe. How many Yotta where E is the photon energy in Joules (J), ν is the stars is that? frequency of the radiation (Hz or s-1) and h is Plank’s constant (6.63 x 10-34 J s). Could you see a 500 nm speck of dust? Why? You can calculate the kinetic energy, in Joules, of a Wavelength and frequency are related by moving object by multiplying its mass, in kilograms, c = λν times the square of its velocity, in meters per second, and dividing the result by two. What is the kinetic where c is the speed of light (3 x 108 m s-1), λ is the energy of a 1.0 Mgram elephant fl ying at 10 meters wavelength of the radiation (often reported in nm), per second? Of a 10 gram meteoroid moving at and ν is the frequency. Mmeters per second? PREFIXES AND SCIENTIFIC NOTATION Prefi x Symbol Value Notation Some Greek letters which we will use: Yotta Y 1,000,000,000,000,000,000,000,000 1024 α = “alpha”; as in α particle. Zetta Z 1,000,000,000,000,000,000,000 1021 β = “beta”; as in β particle. Exa E 1,000,000,000,000,000,000 1018 γ = “gamma”; as in γ ray. Peta P 1,000,000,000,000,000 1015 δ = “delta”; used with a plus or minus sign tera T 1,000,000,000,000 1012 to represent partial charges in giga G 1,000,000,000 109 polarized molecules. mega M 1,000,000 106 ∆ = “delta”; a capital delta is used for a kilo k 1,000 103 change in a quantity. hecto h 100 102 λ = “lambda”; used for wavelength. deka da 10 101 ν = “nu”; used for frequency. 1.0 100 µ = “mu”; used for the prefi x micro. deci d 0.1 10-1 π = “pi” is the ratio of the circumference of centi c 0.01 10-2 a circle to its diameter. milli m 0.001 10-3 Ω = “omega”; a capital omega is used for micro µ 0.000001 10-6 electrical resistance. nano n 0.000000001 10-9 pico p 0.000000000001 10-12 femto f 0.000000000000001 10-15 atto a 0.000000000000000001 10-18 zepto z 0.000000000000000000001 10-21 yocto y 0.000000000000000000000001 10-24 4 FOUNDATIONS OF SPECTROSCOPY WAVES The fi sherman rises and falls with the passing waves. The (vertical) distance the fi sherman moves through is called the amplitude of the wave. The distance between crests of the wave is called the wavelength. The time it takes for the fi sherman to go from one wave top (crest), down to the bottom (trough) and back up to the top is called the period; its inverse is called the frequency. If the sea is choppy we could say that the number of waves going by the fi sherman in a sec- ond is the frequency. There is a general relationship for all waves that the velocity of the wave is the product of the wavelength times the frequency. v = λν Measure the wavelength and amplitude, in centimeters, of the fi sherman’s wave. If the frequency of the wave is 2.5 Hz, calculate its velocity. 5 FOUNDATIONS OF SPECTROSCOPY FREQUENCY AND WAVELENGTH TIME 0.000 s 0.000 s 0.125 s 0.125 s 0.250 s 0.250 s 0.375 s 0.375 s 0.500s 0.500s 0.625 s 0.625 s 0.750 s 0.750 s 0.875 s 0.875 s 1.000 s 1.000 s Each of the vertical sequences of pictures above shows a wave moving to the right.
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