{"id":1611,"date":"2017-10-12T13:20:13","date_gmt":"2017-10-12T13:20:13","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/?post_type=chapter&#038;p=1611"},"modified":"2017-11-20T19:26:56","modified_gmt":"2017-11-20T19:26:56","slug":"spectroscopy-and-the-electromagnetic-spectrum","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/chapter\/spectroscopy-and-the-electromagnetic-spectrum\/","title":{"raw":"Spectroscopy and the Electromagnetic Spectrum","rendered":"Spectroscopy and the Electromagnetic Spectrum"},"content":{"raw":"<div class=\"elm-header\">\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Objectives<\/h3>\r\n<div id=\"elm-main-content\" class=\"elm-content-container\">\r\n<div>\r\n<div id=\"skills\">\r\n\r\nAfter completing this section, you should be able to\r\n<ol>\r\n \t<li>write a brief paragraph discussing the nature of electromagnetic radiation.<\/li>\r\n \t<li>write the equations that relate energy to frequency, frequency to wavelength and energy to wavelength, and perform calculations using these relationships.<\/li>\r\n \t<li>describe, in general terms, how absorption spectra are obtained.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"elm-main-content\" class=\"elm-content-container\">\r\n<div>\r\n<div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3 class=\"boxtitle\">Key Terms<\/h3>\r\nMake certain that you can define, and use in context, the key terms below.\r\n<ul>\r\n \t<li>electromagnetic radiation<\/li>\r\n \t<li>electromagnetic spectrum<\/li>\r\n \t<li>hertz (Hz)<\/li>\r\n \t<li>infrared spectroscopy<\/li>\r\n \t<li>photon<\/li>\r\n \t<li>quantum<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div id=\"note\">\r\n<div class=\"textbox\">\r\n<h3 class=\"boxtitle\">Study Notes<\/h3>\r\nFrom your studies in general chemistry or physics, you should be familiar with the idea that electromagnetic radiation is a form of energy that possesses wave character and travels through space at a speed of 3.00 \u00d7 10<sup>8<\/sup>m \u00b7 s<sup>\u22121<\/sup>. However, such radiation also displays some of the properties of particles, and on occasion it is more convenient to think of electromagnetic radiation as consisting of a stream of particles called <em>photons<\/em>.\r\n\r\nIn spectroscopy, the frequency of the electromagnetic radiation being used is usually expressed in <em>hertz<\/em> (<em>Hz<\/em>), that is, cycles per second. Note that 1 Hz = s<sup>\u22121<\/sup>.\r\n\r\nA <em>quantum<\/em> is a small, definite quantity of electromagnetic radiation whose energy is directly proportional to its frequency. (The plural is \u201cquanta.\u201d) If you wish, you can read about the properties of <a href=\"https:\/\/chem.libretexts.org\/Core\/Physical_and_Theoretical_Chemistry\/Spectroscopy\/Fundamentals_of_Spectroscopy\/Electromagnetic_Radiation\" target=\"_blank\" rel=\"internal noopener\">electromagnetic radiation<\/a> and the relationships among wavelength, frequency and energy, or refer to your general chemistry textbook if you still have it.\r\n\r\nNote also that in SI units, Planck\u2019s constant is 6.626 \u00d7 10<sup>\u221234<\/sup>J \u00b7 s.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"section_1\">\r\n<h3 class=\"editable\">The electromagnetic spectrum<\/h3>\r\nElectromagnetic radiation, as you may recall from a previous chemistry or physics class, is composed of electrical and magnetic waves which oscillate on perpendicular planes. Visible light is electromagnetic radiation. So are the gamma rays that are emitted by spent nuclear fuel, the x-rays that a doctor uses to visualize your bones, the ultraviolet light that causes a painful sunburn when you forget to apply sun block, the infrared light that the army uses in night-vision goggles, the microwaves that you use to heat up your frozen burritos, and the radio-frequency waves that bring music to anybody who is old-fashioned enough to still listen to FM or AM radio.\r\n\r\nJust like ocean waves, electromagnetic waves travel in a defined direction. While the speed of ocean waves can vary, however, the speed of electromagnetic waves \u2013 commonly referred to as the speed of light \u2013 is essentially a constant, approximately 300 million meters per second. This is true whether we are talking about gamma radiation or visible light. Obviously, there is a big difference between these two types of waves \u2013 we are surrounded by the latter for more than half of our time on earth, whereas we hopefully never become exposed to the former to any significant degree.\u00a0 The different properties of the various types of electromagnetic radiation are due to differences in their wavelengths, and the corresponding differences in their energies: <em>shorter wavelengths correspond to higher energy.\u00a0 <\/em>\r\n\r\n<img class=\"internal default aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05153404\/image001.png\" alt=\"image002.png\" width=\"391\" height=\"120\" \/>\r\n\r\nHigh-energy radiation (such as gamma- and x-rays) is composed of very short waves \u2013 as short as 10<sup>-16<\/sup> meter from crest to crest.\u00a0 Longer waves are far less energetic, and thus are less dangerous to living things.\u00a0 Visible light waves are in the range of 400 \u2013 700 nm (nanometers, or 10<sup>-9<\/sup> m), while radio waves can be several hundred meters in length.\r\n\r\nThe notion that electromagnetic radiation contains a quantifiable amount of energy can perhaps be better understood if we talk about light as a stream of <em>particles<\/em>, called <strong>photons<\/strong>, rather than as a wave. (Recall the concept known as \u2018wave-particle duality\u2019:\u00a0 at the quantum level, wave behavior and particle behavior become indistinguishable, and very small particles have an observable \u2018wavelength\u2019). If we describe light as a stream of photons, the energy of a particular wavelength can be expressed as:\r\n\r\nE=hc\r\n\r\n<\/div>\r\n<div>\r\n\r\n\u00a0 \u00a0 \u00a0\u03bb<!-- \u03bb -->\r\n\r\nBecause electromagnetic radiation travels at a constant speed, each wavelength corresponds to a given frequency, which is the number of times per second that a crest passes a given point. Longer waves have lower frequencies, and shorter waves have higher frequencies.\u00a0 Frequency is commonly reported in hertz (Hz),\u00a0 meaning \u2018cycles per second\u2019, or \u2018waves per second\u2019. The standard unit for frequency is s<sup>-1<\/sup>.\r\n\r\nWhen talking about electromagnetic waves, we can refer either to wavelength or to frequency - the two values are interconverted using the simple expression:\r\n\r\n<strong>\u03bbv=c<\/strong>\r\n\r\nwhere <span><strong>\u03bd <\/strong><\/span>(the Greek letter \u2018<em>nu\u2019<\/em>) is frequency in s<sup>-1<\/sup>.\u00a0 Visible red light with a wavelength of 700 nm, for example, has a frequency of 4.29 x 10<sup>14<\/sup> Hz, and an energy of 40.9 kcal per mole of photons. The full range of electromagnetic radiation wavelengths is referred to as the <strong>electromagnetic spectrum<\/strong>.\r\n\r\n<img class=\"internal default aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05153407\/image003.png\" alt=\"image004.png\" width=\"554\" height=\"233\" \/>\r\n\r\nNotice in the figure above that visible light takes up just a narrow band of the full spectrum.\u00a0 White light from the sun or a light bulb is a mixture of all of the visible wavelengths.\u00a0 You see the visible region of the electromagnetic spectrum divided into its different wavelengths every time you see a rainbow: violet light has the shortest wavelength, and red light has the longest.\r\n<div>\r\n<div id=\"example\">\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nVisible light has a wavelength range of about 400-700 nm.\u00a0 What is the corresponding frequency range?\u00a0 What is the corresponding energy range, in kcal\/mol of photons?\r\n[reveal-answer q=\"523977\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"523977\"]\r\n\r\nA wavenumber of 3000 cm<sup>-1<\/sup>\u00a0means that 3000 waves fit in one cm (0.01m):\r\n\r\n<img class=\"internal default aligncenter\" src=\"https:\/\/chem.libretexts.org\/@api\/deki\/files\/6452\/image245.png?revision=1\" alt=\"image246.png\" width=\"100\" height=\"47\" \/>\r\n\r\nWe want to find the length of 1 wave, so we divide numerator and denominator by 3000:\r\n\r\n<img class=\"internal default aligncenter\" src=\"https:\/\/chem.libretexts.org\/@api\/deki\/files\/6454\/image247.png?revision=1\" alt=\"image248.png\" width=\"251\" height=\"52\" \/>\r\n\r\nSo 3000 cm<sup>-1<\/sup>\u00a0is equivalent to a wavelength of 3.33 mm.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nwhere E is energy in kcal\/mol,\u00a0 <span><strong>\u03bb<\/strong><\/span> (the Greek letter <em>lambda<\/em>) is wavelength in meters, <em>c<\/em> is 3.00 x 10<sup>8<\/sup> m\/s (the speed of light), and <em>h<\/em> is 9.537 x 10<sup>-14<\/sup> kcal<span>\u2022<\/span>s<span>\u2022<\/span>mol<sup>-1<\/sup>, a number known as Planck\u2019s constant.\r\n\r\n<\/div>\r\n<div id=\"section_2\">\r\n<h3 class=\"editable\">4.1B: Molecular spectroscopy \u2013 the basic idea<\/h3>\r\n<div>\r\n\r\nIn a spectroscopy experiment, electromagnetic radiation of a specified range of wavelengths is allowed to pass through a sample containing a compound of interest. The sample molecules absorb energy from some of the wavelengths, and as a result jump from a low energy \u2018ground state\u2019 to some higher energy \u2018excited state\u2019.\u00a0 Other wavelengths are <em>not<\/em> absorbed by the sample molecule, so they pass on through.\u00a0 A detector on the other side of the sample records which wavelengths were absorbed, and to what extent they were absorbed.\r\n\r\nHere is the key to molecular spectroscopy:\u00a0 <em>a given molecule will specifically absorb only those wavelengths which have energies that correspond to the energy difference of the transition that is occurring.<\/em>\u00a0 Thus, if the transition involves the molecule jumping from ground state A to excited state B, with an energy difference of <span><strong>\u0394<\/strong><\/span>E, the molecule will specifically absorb radiation with\u00a0 wavelength that corresponds to <span><strong>\u0394<\/strong><\/span>E, while allowing other wavelengths to pass through unabsorbed.\r\n\r\n<img class=\"internal default aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05153409\/image005.png\" alt=\"image006.png\" width=\"164\" height=\"140\" \/>\r\n\r\nBy observing which wavelengths a molecule absorbs, and to what extent it absorbs them, we can gain information about the nature of the energetic transitions that a molecule is able to undergo, and thus information about its structure.\r\n\r\nThese generalized ideas may all sound quite confusing at this point, but things will become much clearer as we begin to discuss specific examples.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"section_3\">\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<div id=\"section_3\">\r\n<div id=\"s61717\">\r\n<div id=\"section_15\">\r\n\r\n<b>1.<\/b>Which of the following frequencies\/wavelengths are higher energy\r\n\r\nA.\u00a0 \u03bb = 2.0x10<sup>-6 <\/sup>m or \u03bb = 3.0x10<sup>-9 <\/sup>m\r\n\r\nB.\u00a0 <span>\u03c5<\/span> = 3.0x10<sup>9 <\/sup>Hz or <span>\u03c5<\/span> = 3.0x10<sup>-6 <\/sup>Hz\r\n\r\n<b>2.<\/b>Calculate the energies for the following;\r\n\r\nA. Gamma Ray \u03bb = 4.0x10<sup>-11 <\/sup>m\r\n\r\nB. X-Ray \u03bb = 4.0x10<sup>-9 <\/sup>m\r\n\r\nC. UV light <span>\u03c5<\/span> = 5.0x10<sup>15 <\/sup>Hz\r\n\r\nD. Infrared Radiation \u03bb = 3.0x10<sup>-5 <\/sup>m\r\n\r\nE. Microwave Radiation <span>\u03c5<\/span> = 3.0x10<sup>11 <\/sup>Hz\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"section_3\">\r\n<div id=\"s61717\">\r\n<div id=\"section_16\">\r\n<p id=\"Solutions-61717\">[reveal-answer q=\"558367\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"558367\"]<\/p>\r\n<strong>\u00a0Solutions<\/strong>\r\n\r\n1. A.\u00a0 \u03bb = 3.0x10-9 m\r\n\r\nB.\u00a0 \u03c5 = 3.0x109 Hz\r\n\r\n2.\u00a0 A.\u00a0 4.965x10-15 J\r\n\r\nB.\u00a0 4.965x10-17 J\r\n\r\nC.\u00a0 3.31x10-18 J\r\n\r\nD.\u00a0 6.62x10-21 J\r\n\r\nE.\u00a0 1.99x10-22 J\r\n<p id=\"Solutions-61717\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<strong>Note:<\/strong> You should not try to memorize the relationship between energy and wavelength in the form in which it is given here. Instead, you should be prepared to work from first principles using:\r\n\r\n<em>E<\/em> = <em>hv<\/em>, where <em>h<\/em> = Plank's constant = 6.626 \u00d7 10<sup>\u221234<\/sup>J \u00b7 s.\r\n<em>c<\/em> = <em>\u03bbv<\/em>, where <em>c<\/em> = the speed of light = 3.00 \u00d7 10<sup>8<\/sup>m \u00b7 s<sup>\u22121<\/sup>.\r\nAvogadro\u2019s number = 6.02 \u00d7 10<sup>23<\/sup> mol<sup>\u22121<\/sup>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"section_4\">\r\n<h3 class=\"editable\">Contributors<\/h3>\r\n<ul>\r\n \t<li><a class=\"external\" title=\"http:\/\/science.athabascau.ca\/staff-pages\/dietmark\" href=\"http:\/\/science.athabascau.ca\/staff-pages\/dietmark\" target=\"_blank\" rel=\"external nofollow noopener\">Dr. Dietmar Kennepohl<\/a> FCIC (Professor of Chemistry, <a class=\"external\" title=\"http:\/\/www.athabascau.ca\/\" href=\"http:\/\/www.athabascau.ca\/\" target=\"_blank\" rel=\"external nofollow noopener\">Athabasca University<\/a>)<\/li>\r\n \t<li>Prof. Steven Farmer (<a class=\"external\" title=\"http:\/\/www.sonoma.edu\" href=\"http:\/\/www.sonoma.edu\" target=\"_blank\" rel=\"external nofollow noopener\">Sonoma State University<\/a>)<\/li>\r\n \t<li>William Reusch, Professor Emeritus (<a class=\"external\" title=\"http:\/\/www.msu.edu\/\" href=\"http:\/\/www.msu.edu\/\" target=\"_blank\" rel=\"external nofollow noopener\">Michigan State U.<\/a>), <a class=\"external\" title=\"http:\/\/www.cem.msu.edu\/~reusch\/VirtualText\/intro1.htm\" href=\"http:\/\/www.cem.msu.edu\/%7Ereusch\/VirtualText\/intro1.htm\" target=\"_blank\" rel=\"external nofollow noopener\">Virtual Textbook of\u00a0Organic\u00a0Chemistry<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"elm-header\">\n<div class=\"textbox learning-objectives\">\n<h3>Objectives<\/h3>\n<div id=\"elm-main-content\" class=\"elm-content-container\">\n<div>\n<div id=\"skills\">\n<p>After completing this section, you should be able to<\/p>\n<ol>\n<li>write a brief paragraph discussing the nature of electromagnetic radiation.<\/li>\n<li>write the equations that relate energy to frequency, frequency to wavelength and energy to wavelength, and perform calculations using these relationships.<\/li>\n<li>describe, in general terms, how absorption spectra are obtained.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"elm-main-content\" class=\"elm-content-container\">\n<div>\n<div>\n<div class=\"textbox key-takeaways\">\n<h3 class=\"boxtitle\">Key Terms<\/h3>\n<p>Make certain that you can define, and use in context, the key terms below.<\/p>\n<ul>\n<li>electromagnetic radiation<\/li>\n<li>electromagnetic spectrum<\/li>\n<li>hertz (Hz)<\/li>\n<li>infrared spectroscopy<\/li>\n<li>photon<\/li>\n<li>quantum<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"note\">\n<div class=\"textbox\">\n<h3 class=\"boxtitle\">Study Notes<\/h3>\n<p>From your studies in general chemistry or physics, you should be familiar with the idea that electromagnetic radiation is a form of energy that possesses wave character and travels through space at a speed of 3.00 \u00d7 10<sup>8<\/sup>m \u00b7 s<sup>\u22121<\/sup>. However, such radiation also displays some of the properties of particles, and on occasion it is more convenient to think of electromagnetic radiation as consisting of a stream of particles called <em>photons<\/em>.<\/p>\n<p>In spectroscopy, the frequency of the electromagnetic radiation being used is usually expressed in <em>hertz<\/em> (<em>Hz<\/em>), that is, cycles per second. Note that 1 Hz = s<sup>\u22121<\/sup>.<\/p>\n<p>A <em>quantum<\/em> is a small, definite quantity of electromagnetic radiation whose energy is directly proportional to its frequency. (The plural is \u201cquanta.\u201d) If you wish, you can read about the properties of <a href=\"https:\/\/chem.libretexts.org\/Core\/Physical_and_Theoretical_Chemistry\/Spectroscopy\/Fundamentals_of_Spectroscopy\/Electromagnetic_Radiation\" target=\"_blank\" rel=\"internal noopener\">electromagnetic radiation<\/a> and the relationships among wavelength, frequency and energy, or refer to your general chemistry textbook if you still have it.<\/p>\n<p>Note also that in SI units, Planck\u2019s constant is 6.626 \u00d7 10<sup>\u221234<\/sup>J \u00b7 s.<\/p>\n<\/div>\n<\/div>\n<div id=\"section_1\">\n<h3 class=\"editable\">The electromagnetic spectrum<\/h3>\n<p>Electromagnetic radiation, as you may recall from a previous chemistry or physics class, is composed of electrical and magnetic waves which oscillate on perpendicular planes. Visible light is electromagnetic radiation. So are the gamma rays that are emitted by spent nuclear fuel, the x-rays that a doctor uses to visualize your bones, the ultraviolet light that causes a painful sunburn when you forget to apply sun block, the infrared light that the army uses in night-vision goggles, the microwaves that you use to heat up your frozen burritos, and the radio-frequency waves that bring music to anybody who is old-fashioned enough to still listen to FM or AM radio.<\/p>\n<p>Just like ocean waves, electromagnetic waves travel in a defined direction. While the speed of ocean waves can vary, however, the speed of electromagnetic waves \u2013 commonly referred to as the speed of light \u2013 is essentially a constant, approximately 300 million meters per second. This is true whether we are talking about gamma radiation or visible light. Obviously, there is a big difference between these two types of waves \u2013 we are surrounded by the latter for more than half of our time on earth, whereas we hopefully never become exposed to the former to any significant degree.\u00a0 The different properties of the various types of electromagnetic radiation are due to differences in their wavelengths, and the corresponding differences in their energies: <em>shorter wavelengths correspond to higher energy.\u00a0 <\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal default aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05153404\/image001.png\" alt=\"image002.png\" width=\"391\" height=\"120\" \/><\/p>\n<p>High-energy radiation (such as gamma- and x-rays) is composed of very short waves \u2013 as short as 10<sup>-16<\/sup> meter from crest to crest.\u00a0 Longer waves are far less energetic, and thus are less dangerous to living things.\u00a0 Visible light waves are in the range of 400 \u2013 700 nm (nanometers, or 10<sup>-9<\/sup> m), while radio waves can be several hundred meters in length.<\/p>\n<p>The notion that electromagnetic radiation contains a quantifiable amount of energy can perhaps be better understood if we talk about light as a stream of <em>particles<\/em>, called <strong>photons<\/strong>, rather than as a wave. (Recall the concept known as \u2018wave-particle duality\u2019:\u00a0 at the quantum level, wave behavior and particle behavior become indistinguishable, and very small particles have an observable \u2018wavelength\u2019). If we describe light as a stream of photons, the energy of a particular wavelength can be expressed as:<\/p>\n<p>E=hc<\/p>\n<\/div>\n<div>\n<p>\u00a0 \u00a0 \u00a0\u03bb<!-- \u03bb --><\/p>\n<p>Because electromagnetic radiation travels at a constant speed, each wavelength corresponds to a given frequency, which is the number of times per second that a crest passes a given point. Longer waves have lower frequencies, and shorter waves have higher frequencies.\u00a0 Frequency is commonly reported in hertz (Hz),\u00a0 meaning \u2018cycles per second\u2019, or \u2018waves per second\u2019. The standard unit for frequency is s<sup>-1<\/sup>.<\/p>\n<p>When talking about electromagnetic waves, we can refer either to wavelength or to frequency &#8211; the two values are interconverted using the simple expression:<\/p>\n<p><strong>\u03bbv=c<\/strong><\/p>\n<p>where <span><strong>\u03bd <\/strong><\/span>(the Greek letter \u2018<em>nu\u2019<\/em>) is frequency in s<sup>-1<\/sup>.\u00a0 Visible red light with a wavelength of 700 nm, for example, has a frequency of 4.29 x 10<sup>14<\/sup> Hz, and an energy of 40.9 kcal per mole of photons. The full range of electromagnetic radiation wavelengths is referred to as the <strong>electromagnetic spectrum<\/strong>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal default aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05153407\/image003.png\" alt=\"image004.png\" width=\"554\" height=\"233\" \/><\/p>\n<p>Notice in the figure above that visible light takes up just a narrow band of the full spectrum.\u00a0 White light from the sun or a light bulb is a mixture of all of the visible wavelengths.\u00a0 You see the visible region of the electromagnetic spectrum divided into its different wavelengths every time you see a rainbow: violet light has the shortest wavelength, and red light has the longest.<\/p>\n<div>\n<div id=\"example\">\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Visible light has a wavelength range of about 400-700 nm.\u00a0 What is the corresponding frequency range?\u00a0 What is the corresponding energy range, in kcal\/mol of photons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q523977\">Show Answer<\/span><\/p>\n<div id=\"q523977\" class=\"hidden-answer\" style=\"display: none\">\n<p>A wavenumber of 3000 cm<sup>-1<\/sup>\u00a0means that 3000 waves fit in one cm (0.01m):<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal default aligncenter\" src=\"https:\/\/chem.libretexts.org\/@api\/deki\/files\/6452\/image245.png?revision=1\" alt=\"image246.png\" width=\"100\" height=\"47\" \/><\/p>\n<p>We want to find the length of 1 wave, so we divide numerator and denominator by 3000:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal default aligncenter\" src=\"https:\/\/chem.libretexts.org\/@api\/deki\/files\/6454\/image247.png?revision=1\" alt=\"image248.png\" width=\"251\" height=\"52\" \/><\/p>\n<p>So 3000 cm<sup>-1<\/sup>\u00a0is equivalent to a wavelength of 3.33 mm.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>where E is energy in kcal\/mol,\u00a0 <span><strong>\u03bb<\/strong><\/span> (the Greek letter <em>lambda<\/em>) is wavelength in meters, <em>c<\/em> is 3.00 x 10<sup>8<\/sup> m\/s (the speed of light), and <em>h<\/em> is 9.537 x 10<sup>-14<\/sup> kcal<span>\u2022<\/span>s<span>\u2022<\/span>mol<sup>-1<\/sup>, a number known as Planck\u2019s constant.<\/p>\n<\/div>\n<div id=\"section_2\">\n<h3 class=\"editable\">4.1B: Molecular spectroscopy \u2013 the basic idea<\/h3>\n<div>\n<p>In a spectroscopy experiment, electromagnetic radiation of a specified range of wavelengths is allowed to pass through a sample containing a compound of interest. The sample molecules absorb energy from some of the wavelengths, and as a result jump from a low energy \u2018ground state\u2019 to some higher energy \u2018excited state\u2019.\u00a0 Other wavelengths are <em>not<\/em> absorbed by the sample molecule, so they pass on through.\u00a0 A detector on the other side of the sample records which wavelengths were absorbed, and to what extent they were absorbed.<\/p>\n<p>Here is the key to molecular spectroscopy:\u00a0 <em>a given molecule will specifically absorb only those wavelengths which have energies that correspond to the energy difference of the transition that is occurring.<\/em>\u00a0 Thus, if the transition involves the molecule jumping from ground state A to excited state B, with an energy difference of <span><strong>\u0394<\/strong><\/span>E, the molecule will specifically absorb radiation with\u00a0 wavelength that corresponds to <span><strong>\u0394<\/strong><\/span>E, while allowing other wavelengths to pass through unabsorbed.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"internal default aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1518\/2017\/10\/05153409\/image005.png\" alt=\"image006.png\" width=\"164\" height=\"140\" \/><\/p>\n<p>By observing which wavelengths a molecule absorbs, and to what extent it absorbs them, we can gain information about the nature of the energetic transitions that a molecule is able to undergo, and thus information about its structure.<\/p>\n<p>These generalized ideas may all sound quite confusing at this point, but things will become much clearer as we begin to discuss specific examples.<\/p>\n<\/div>\n<\/div>\n<div id=\"section_3\">\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<div id=\"section_3\">\n<div id=\"s61717\">\n<div id=\"section_15\">\n<p><b>1.<\/b>Which of the following frequencies\/wavelengths are higher energy<\/p>\n<p>A.\u00a0 \u03bb = 2.0&#215;10<sup>-6 <\/sup>m or \u03bb = 3.0&#215;10<sup>-9 <\/sup>m<\/p>\n<p>B.\u00a0 <span>\u03c5<\/span> = 3.0&#215;10<sup>9 <\/sup>Hz or <span>\u03c5<\/span> = 3.0&#215;10<sup>-6 <\/sup>Hz<\/p>\n<p><b>2.<\/b>Calculate the energies for the following;<\/p>\n<p>A. Gamma Ray \u03bb = 4.0&#215;10<sup>-11 <\/sup>m<\/p>\n<p>B. X-Ray \u03bb = 4.0&#215;10<sup>-9 <\/sup>m<\/p>\n<p>C. UV light <span>\u03c5<\/span> = 5.0&#215;10<sup>15 <\/sup>Hz<\/p>\n<p>D. Infrared Radiation \u03bb = 3.0&#215;10<sup>-5 <\/sup>m<\/p>\n<p>E. Microwave Radiation <span>\u03c5<\/span> = 3.0&#215;10<sup>11 <\/sup>Hz<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"section_3\">\n<div id=\"s61717\">\n<div id=\"section_16\">\n<p id=\"Solutions-61717\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q558367\">Show Answer<\/span><\/p>\n<div id=\"q558367\" class=\"hidden-answer\" style=\"display: none\">\n<p><strong>\u00a0Solutions<\/strong><\/p>\n<p>1. A.\u00a0 \u03bb = 3.0&#215;10-9 m<\/p>\n<p>B.\u00a0 \u03c5 = 3.0&#215;109 Hz<\/p>\n<p>2.\u00a0 A.\u00a0 4.965&#215;10-15 J<\/p>\n<p>B.\u00a0 4.965&#215;10-17 J<\/p>\n<p>C.\u00a0 3.31&#215;10-18 J<\/p>\n<p>D.\u00a0 6.62&#215;10-21 J<\/p>\n<p>E.\u00a0 1.99&#215;10-22 J<\/p>\n<p id=\"Solutions-61717\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><strong>Note:<\/strong> You should not try to memorize the relationship between energy and wavelength in the form in which it is given here. Instead, you should be prepared to work from first principles using:<\/p>\n<p><em>E<\/em> = <em>hv<\/em>, where <em>h<\/em> = Plank&#8217;s constant = 6.626 \u00d7 10<sup>\u221234<\/sup>J \u00b7 s.<br \/>\n<em>c<\/em> = <em>\u03bbv<\/em>, where <em>c<\/em> = the speed of light = 3.00 \u00d7 10<sup>8<\/sup>m \u00b7 s<sup>\u22121<\/sup>.<br \/>\nAvogadro\u2019s number = 6.02 \u00d7 10<sup>23<\/sup> mol<sup>\u22121<\/sup><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"section_4\">\n<h3 class=\"editable\">Contributors<\/h3>\n<ul>\n<li><a class=\"external\" title=\"http:\/\/science.athabascau.ca\/staff-pages\/dietmark\" href=\"http:\/\/science.athabascau.ca\/staff-pages\/dietmark\" target=\"_blank\" rel=\"external nofollow noopener\">Dr. Dietmar Kennepohl<\/a> FCIC (Professor of Chemistry, <a class=\"external\" title=\"http:\/\/www.athabascau.ca\/\" href=\"http:\/\/www.athabascau.ca\/\" target=\"_blank\" rel=\"external nofollow noopener\">Athabasca University<\/a>)<\/li>\n<li>Prof. Steven Farmer (<a class=\"external\" title=\"http:\/\/www.sonoma.edu\" href=\"http:\/\/www.sonoma.edu\" target=\"_blank\" rel=\"external nofollow noopener\">Sonoma State University<\/a>)<\/li>\n<li>William Reusch, Professor Emeritus (<a class=\"external\" title=\"http:\/\/www.msu.edu\/\" href=\"http:\/\/www.msu.edu\/\" target=\"_blank\" rel=\"external nofollow noopener\">Michigan State U.<\/a>), <a class=\"external\" title=\"http:\/\/www.cem.msu.edu\/~reusch\/VirtualText\/intro1.htm\" href=\"http:\/\/www.cem.msu.edu\/%7Ereusch\/VirtualText\/intro1.htm\" target=\"_blank\" rel=\"external nofollow noopener\">Virtual Textbook of\u00a0Organic\u00a0Chemistry<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":44985,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1611","chapter","type-chapter","status-publish","hentry"],"part":29,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1611","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/users\/44985"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1611\/revisions"}],"predecessor-version":[{"id":2138,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1611\/revisions\/2138"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/parts\/29"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapters\/1611\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/media?parent=1611"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/pressbooks\/v2\/chapter-type?post=1611"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/contributor?post=1611"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-mcc-organicchemistry\/wp-json\/wp\/v2\/license?post=1611"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}