{"id":2393,"date":"2018-04-11T23:52:47","date_gmt":"2018-04-12T03:52:47","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/light\/"},"modified":"2019-05-13T14:39:23","modified_gmt":"2019-05-13T18:39:23","slug":"light","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/light\/","title":{"raw":"8.1 Electromagnetic Energy","rendered":"8.1 Electromagnetic Energy"},"content":{"raw":"<div class=\"section\" id=\"ball-ch08_s01\" lang=\"en\">\r\n<div class=\"learning_objectives editable block\" id=\"ball-ch08_s01_n01\">\r\n<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this module, you will be able to:\r\n<ul>\r\n \t<li>Describe light with its frequency and wavelength.<\/li>\r\n \t<li>Describe light as a particle of energy.<span style=\"color: #333333;background-color: #ffffff\">\u00a0<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\nOur last \u201cpicture\u201d of the atom consisted of a nucleus containing protons and neutrons (constituting most of the atom\u2019s mass), surrounded by a sea of electrons. The limitations of this model are that it doesn\u2019t show how the electrons are arranged or how they move. It turns out that this <em>electronic structure\u00a0<\/em>is the primary factor controlling how an atom behaves.\r\n\r\nTo get a more complete view of the atom, we need more experimental evidence and interpretation. One of the main ways to investigate electrons in atoms is to use <em>light\u00a0<\/em>with two techniques; 1) by shining a light on the atoms and seeing what happens to the light (absorption spectroscopy), and 2) by heating the atoms and seeing what kind of light is given off (emission spectroscopy). Clearly, we will need to start with an understanding of the nature of light. We will then move on to describe and interpret experiments with light that give us our understanding of what electrons in atoms are doing. Finally, we see how the properties of electrons are related to the way the atoms behave.\r\n<p id=\"ball-ch08_s01_p01\" class=\"para editable block\">What we know as light is more properly called <em class=\"emphasis\">electromagnetic radiation<\/em>. We know from experiments that light acts as a wave. As such, it can be described as having a frequency and a wavelength.<\/p>\r\n<p class=\"para editable block\">The <span class=\"margin_term\"><a class=\"glossterm\">wavelength<\/a><\/span>\u00a0of light is the distance between corresponding points in two adjacent light cycles.\u00a0 Wavelength is typically represented by \u03bb, the lowercase Greek letter <em class=\"emphasis\">lambda<\/em>, and\u00a0has units of length (meters, centimeters, etc.).\u00a0 Figure 1\u00a0shows how wavelength is defined.<\/p>\r\n\r\n<div class=\"figure large medium-height editable block\" id=\"ball-ch08_s01_f01\">\r\n\r\n[caption id=\"attachment_4846\" align=\"aligncenter\" width=\"373\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength.png\" alt=\"\" width=\"373\" height=\"154\" class=\"wp-image-4846 size-full\" \/><\/a> <strong>Figure 1.<\/strong> The wavelength of light is the distance between corresponding points in two adjacent light cycles.[\/caption]\r\n<p id=\"fs-idp150592048\">The <span class=\"margin_term\"><a class=\"glossterm\">frequency<\/a><\/span>\u00a0of light is the number of cycles of light that pass a given point in one second.\u00a0 Frequency is represented by \u03bd, the lowercase Greek letter <em class=\"emphasis\">nu, <\/em>and\u00a0has units of <em class=\"emphasis\">per second<\/em>, written as s<sup class=\"superscript\">\u22121<\/sup> and sometimes called a <em class=\"emphasis\">hertz<\/em> (Hz). \u00a0 The amplitude (a) corresponds to the magnitude of the wave's displacement and so, in <a href=\"#CNX_Chem_06_01_Frequency\" class=\"autogenerated-content\">Figure 2<\/a>, this corresponds to one-half the height between the peaks and troughs. The amplitude is related to the intensity of the wave, which for light is the brightness, and for sound is the loudness.<\/p>\r\n\r\n<figure id=\"CNX_Chem_06_01_Frequency\"><figcaption>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"1300\"]<a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_Frequency.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_Frequency-2.jpg\" alt=\"This figure includes 5 one-dimensional sinusoidal waves in two columns. The column on the left includes three waves, and the column on the right includes two waves. In each column, dashed vertical line segments extend down the left and right sides of the column. A right pointing arrow extends from the left dashed line to the right dashed line in both columns and is labeled, \u201cDistance traveled in 1 second.\u201d The waves all begin on the left side at a crest. The wave at the upper left shows 3 peaks to the right of the starting point. A bracket labeled, \u201clambda subscript 1,\u201d extends upward from the second and third peaks. Beneath this wave is the label, \u201cnu subscript 1 equals 4 cycles per second equals 3 hertz.\u201d The wave below has six peaks to the right of the starting point with a bracket similarly connecting the third and fourth peaks which is labeled, \u201clambda subscript 2.\u201d Beneath this wave is the label, \u201cnu subscript 2 equals 8 cycles per second equals 6 hertz\u201d The third wave in the column has twelve peaks to the right of the starting point with a bracket similarly connecting the seventh and eighth peaks which is labeled, \u201clambda subscript 3.\u201d Beneath this wave is the label, \u201cnu subscript 3 equals 12 cycles per second equals 12 hertz.\u201d All waves in this column appear to have the same vertical distance from peak to trough. In the second column, the two waves are similarly shown, but lack the lambda labels. The top wave in this column has a greater vertical distance between the peaks and troughs and is labeled, \u201cHigher amplitude.\u201d The wave beneath it has a lesser distance between the peaks and troughs and is labeled, \u201cLower amplitude.\u201d\" width=\"1300\" height=\"633\" \/><\/a> <strong>Figure 2.<\/strong> One-dimensional sinusoidal waves show the relationship among wavelength, frequency, and speed. The wave with the shortest wavelength has the highest frequency. Amplitude is one-half the height of the wave from peak to trough.[\/caption]\r\n\r\n<\/figcaption><\/figure>\r\n<p class=\"para\">Light acts as a wave and can be described by a wavelength \u03bb and a frequency \u03bd.<\/p>\r\n\r\n<\/div>\r\n<p id=\"ball-ch08_s01_p02\" class=\"para editable block\">One property of waves is that their speed is equal to their wavelength times their frequency. That means we have<\/p>\r\n<p style=\"text-align: center\"><span class=\"informalequation block\">speed = \u03bb\u03bd<\/span><\/p>\r\n<p style=\"text-align: center\">m\/s = m x s<sup>-1<\/sup><\/p>\r\n<p id=\"ball-ch08_s01_p03\" class=\"para editable block\">For light, however, speed is actually a universal constant when light is traveling through a vacuum (or, to a very good approximation, air). The measured speed of light (<em class=\"emphasis\">c<\/em>) in a vacuum is 2.9979 \u00d7 10<sup class=\"superscript\">8<\/sup> m\/s, or about 3.00 \u00d7 10<sup class=\"superscript\">8<\/sup> m\/s. Thus, we have<\/p>\r\n<p style=\"text-align: center\"><span class=\"informalequation block\">c = \u03bb\u03bd<\/span><\/p>\r\n<p style=\"text-align: center\">m\/s = m x s<sup>-1<\/sup><\/p>\r\n<p id=\"ball-ch08_s01_p04\" class=\"para editable block\">Because the speed of light is a constant, the wavelength and the frequency of light are related to each other: as one increases, the other decreases and vice versa. We can use this equation to calculate what one property of light has to be when given the other property.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Example 1<\/h3>\r\n<p id=\"ball-ch08_s01_p05\" class=\"para\">What is the frequency of light if its wavelength is 5.55 \u00d7 10<sup class=\"superscript\">\u22127<\/sup> m?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\r\n<p id=\"ball-ch08_s01_p06\" class=\"para\">We use the equation that relates the wavelength and frequency of light with its speed. We have<\/p>\r\n<span class=\"informalequation\">3.00\u00d710<sup>8<\/sup>m\/s = (5.55\u00d710<sup>-7<\/sup>m)\u03bd<\/span>\r\n<p id=\"ball-ch08_s01_p07\" class=\"para\">We divide both sides of the equation by 5.55 \u00d7 10<sup class=\"superscript\">\u22127<\/sup> m and get<\/p>\r\n<span class=\"informalequation\">\u03bd = 5.41\u00d710<sup>14<\/sup>\u00a0s<sup>-1<\/sup><\/span>\r\n<p id=\"ball-ch08_s01_p08\" class=\"para\">Note how the m units cancel, leaving s in the denominator. A unit in a denominator is indicated by a \u22121 power\u2014s<sup class=\"superscript\">\u22121<\/sup>\u2014and read as \u201cper second.\u201d<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\r\n<p id=\"ball-ch08_s01_p09\" class=\"para\">What is the wavelength of light if its frequency is 1.55 \u00d7 10<sup class=\"superscript\">10<\/sup> s<sup class=\"superscript\">\u22121<\/sup>?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\r\n<p id=\"ball-ch08_s01_p10\" class=\"para\">0.0194 m, or 19.4 mm<\/p>\r\n\r\n<\/div>\r\n<figure id=\"CNX_Chem_06_01_emspectrum\"><figcaption><\/figcaption><\/figure>\r\n<div class=\"textbox shaded\" id=\"fs-idm80944240\">\r\n<h3>Example 2<\/h3>\r\n<p id=\"fs-idp152169520\">A sodium streetlight gives off yellow light that has a wavelength of 589 nm (1 nm = 1 \u00d7 10<sup>\u22129<\/sup> m). What is the frequency of this light?<\/p>\r\n&nbsp;\r\n<p id=\"fs-idm59714720\"><strong>Solution<\/strong>\r\nWe can rearrange the equation <em>c<\/em> = <em>\u03bb\u03bd<\/em> to solve for the frequency:<\/p>\r\n\r\n<div class=\"equation\" id=\"fs-idp41492256\" style=\"text-align: center\">$latex \\nu = \\frac{c}{\\lambda}$<\/div>\r\n<p id=\"fs-idm79802192\">Since <em>c<\/em> is expressed in meters per second, we must also convert 589 nm to meters.<\/p>\r\n\r\n<div class=\"equation\" id=\"fs-idm52369072\" style=\"text-align: center\">$latex \\nu = (\\frac{2.998 \\times 10^8 \\;\\rule[0.25ex]{0.5em}{0.1ex}\\hspace{-0.5em}\\text{ms}^{-1}}{589 \\;\\rule[0.25ex]{1em}{0.1ex}\\hspace{-1em}\\text{nm}})(\\frac{1 \\times 10^9 \\;\\rule[0.25ex]{1em}{0.1ex}\\hspace{-1em}\\text{nm}}{1\\;\\rule[0.25ex]{0.5em}{0.1ex}\\hspace{-0.5em}\\text{m}}) = 5.09 \\times 10^{14}\\text{s}^{-1}$<\/div>\r\n&nbsp;\r\n<p id=\"fs-idm82969184\"><em><strong>Test Yourself<\/strong><\/em>\r\nOne of the frequencies used to transmit and receive cellular telephone signals in the United States is 850 MHz. What is the wavelength in meters of these radio waves?<\/p>\r\n<em><strong>Answer<\/strong><\/em>\r\n\r\n0.353 m = 35.3 cm\r\n\r\n<\/div>\r\n<p id=\"ball-ch08_s01_p11\" class=\"para editable block\">Light also behaves like a package of energy. It turns out that for light, the energy of the \u201cpackage\u201d of energy is proportional to its frequency. (For most waves, energy is proportional to wave amplitude, or the height of the wave.) The mathematical equation that relates the energy (<em class=\"emphasis\">E<\/em>) of light to its frequency is<\/p>\r\n<p style=\"text-align: center\"><span class=\"informalequation block\">E = h\u03bd<\/span><\/p>\r\n<p id=\"ball-ch08_s01_p12\" class=\"para editable block\">where \u03bd is the frequency of the light, and <em class=\"emphasis\">h<\/em> is a constant called <span class=\"margin_term\"><a class=\"glossterm\">Planck\u2019s constant<\/a><\/span>. Its value is 6.626 \u00d7 10<sup class=\"superscript\">\u221234<\/sup> J\u00b7s \u2014 a very small number that is another fundamental constant of our universe, like the speed of light. The units on Planck\u2019s constant may look unusual, but these units are required so that the algebra works out.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Example 3<\/h3>\r\n<p id=\"ball-ch08_s01_p13\" class=\"para\">What is the energy of light if its frequency is 1.55 \u00d7 10<sup class=\"superscript\">10<\/sup> s<sup class=\"superscript\">\u22121<\/sup>?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\r\n<p id=\"ball-ch08_s01_p14\" class=\"para\">Using the formula for the energy of light, we have<\/p>\r\n<span class=\"informalequation\"><span class=\"mathphrase\"><em class=\"emphasis\">E<\/em> = (6.626 \u00d7 10<sup class=\"superscript\">\u221234<\/sup> J\u00b7s)(1.55 \u00d7 10<sup class=\"superscript\">10<\/sup> s<sup class=\"superscript\">\u22121<\/sup>)<\/span><\/span>\r\n<p id=\"ball-ch08_s01_p15\" class=\"para\">Seconds are in the numerator and the denominator, so they cancel, leaving us with joules, the unit of energy. So<\/p>\r\n<span class=\"informalequation\"><span class=\"mathphrase\"><em class=\"emphasis\">E<\/em> = 1.03 \u00d7 10<sup class=\"superscript\">\u221223<\/sup> J<\/span><\/span>\r\n<p id=\"ball-ch08_s01_p16\" class=\"para\">This is an extremely small amount of energy\u2014but this is for only one light wave.<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\r\n<p id=\"ball-ch08_s01_p17\" class=\"para\">What is the frequency of a light wave if its energy is 4.156 \u00d7 10<sup class=\"superscript\">\u221220<\/sup> J?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\r\n<p id=\"ball-ch08_s01_p18\" class=\"para\">6.27 \u00d7 10<sup class=\"superscript\">13<\/sup> s<sup class=\"superscript\">\u22121<\/sup><\/p>\r\n\r\n<\/div>\r\n<p id=\"ball-ch08_s01_p19\" class=\"para editable block\">Because a light wave behaves like a little particle of energy, light waves have a particle-type name: the <span class=\"margin_term\"><a class=\"glossterm\">photon<\/a><\/span>. It is not uncommon to hear light described as photons.<\/p>\r\n<p id=\"ball-ch08_s01_p20\" class=\"para editable block\">Wavelengths, frequencies, and energies of light span a wide range; the entire range of possible values for light is called the <span class=\"margin_term\"><a class=\"glossterm\">electromagnetic spectrum<\/a><\/span>. We are mostly familiar with visible light, which is light having a wavelength range between about 400 nm and 700 nm. Light can have much longer and much shorter wavelengths than this, with corresponding variations in frequency and energy. <a class=\"xref\" href=\"#ball-ch08_s01_f02\">Figure 3 \"The Electromagnetic Spectrum\"<\/a> shows the entire electromagnetic spectrum and how certain regions of the spectrum are labelled. You may already be familiar with some of these regions; they are all light\u2014with different frequencies, wavelengths, and energies.<\/p>\r\n\r\n<div class=\"figure large editable block\" id=\"ball-ch08_s01_f02\">\r\n\r\n[caption id=\"attachment_4683\" align=\"aligncenter\" width=\"600\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Electromagnetic-Spectrum.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Electromagnetic-Spectrum-1.png\" alt=\"Electromagnetic Spectrum\" width=\"600\" height=\"381\" class=\"wp-image-4683 size-full\" \/><\/a> <strong>Figure 3.<\/strong> The Electromagnetic Spectrum \u00a0The electromagnetic spectrum, with its various regions labelled. The borders of each region are approximate.[\/caption]\r\n\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3>Example 4<\/h3>\r\n<p class=\"Indent\">Using Figure 3, determine which category of EM radiation has more energetic photons, UV or IR.<\/p>\r\n&nbsp;\r\n<p class=\"Solution\"><strong>Solution\u00a0\u00a0 <\/strong><\/p>\r\n<p class=\"Indentpoints\">Looking at Figure 3 we see that IR radiation has LONGER wavelengths. Applying the property that the energy of a photon is inversely proportional to the wavelength of the light, we can conclude that the IR light has LESS energetic photons.<\/p>\r\n&nbsp;\r\n<p class=\"SelfTest\"><em><strong>Test Yourself<\/strong><\/em><\/p>\r\n<p class=\"Indent\">Which light has carries less energy in its photons, light with a frequency of 4.0 x 10<sup>13<\/sup>s<sup>-1<\/sup>or light with a frequency of 1.0 x 10<sup>14<\/sup>s<sup>-1<\/sup>?<\/p>\r\n&nbsp;\r\n\r\n<em><strong>Answer<\/strong><\/em>\r\n<p class=\"Answers\">The lower frequency light of 4.0 x 10<sup>13<\/sup>s<sup>-1<\/sup>would have the lower energy photons.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Technology and the Electromagnetic Spectrum<\/h3>\r\n<p id=\"fs-idm80411056\">Figure 4 shows the <strong>electromagnetic spectrum<\/strong>, the range of all types of electromagnetic radiation. Each of the various colors of visible light has specific frequencies and wavelengths associated with them, and you can see that visible light makes up only a small portion of the electromagnetic spectrum.<\/p>\r\nBecause the technologies developed to work in various parts of the electromagnetic spectrum are different, for reasons of convenience and historical legacies, different units are typically used for different parts of the spectrum. For example, radio waves are usually specified as frequencies (typically in units of MHz), while the visible region is usually specified in wavelengths (typically in units of nm or angstroms).\r\n<figure id=\"CNX_Chem_06_01_emspectrum\"><figcaption>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"1280\"]<a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_emspectrum.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_emspectrum-2.jpg\" alt=\"The figure includes a portion of the electromagnetic spectrum which extends from gamma radiation at the far left through x-ray, ultraviolet, visible, infrared, terahertz, and microwave to broadcast and wireless radio at the far right. At the top of the figure, inside a grey box, are three arrows. The first points left and is labeled, \u201cIncreasing energy E.\u201d A second arrow is placed just below the first which also points left and is labeled, \u201cIncreasing frequency nu.\u201d A third arrow is placed just below which points right and is labeled, \u201cIncreasing wavelength lambda.\u201d Inside the grey box near the bottom is a blue sinusoidal wave pattern that moves horizontally through the box. At the far left end, the waves are short and tightly packed. They gradually lengthen moving left to right across the figure, resulting in significantly longer waves at the right end of the diagram. Beneath the grey box are a variety of photos aligned above the names of the radiation types and a numerical scale that is labeled, \u201cWavelength lambda ( m ).\u201d This scale runs from 10 superscript negative 12 meters under gamma radiation increasing by powers of ten to a value of 10 superscript 3 meters at the far right under broadcast and wireless radio. X-ray appears around 10 superscript negative 10 meters, ultraviolet appears in the 10 superscript negative 8 to 10 superscript negative 7 range, visible light appears between 10 superscript negative 7 and 10 superscript negative 6, infrared appears in the 10 superscript negative 6 to 10 superscript negative 5 range, teraherz appears in the 10 superscript negative 4 to 10 superscript negative 3 range, microwave infrared appears in the 10 superscript negative 2 to 10 superscript negative 1 range, and broadcast and wireless radio extend from 10 to 10 superscript 3 meters. Labels above the scale are placed to indicate 1 n m at 10 superscript negative 9 meters, 1 micron at 10 superscript negative 6 meters, 1 millimeter at 10 superscript negative 3 meters, 1 centimeter at 10 superscript negative 2 meters, and 1 foot between 10 superscript negative 1 meter and 10 superscript 0 meters. A variety of images are placed beneath the grey box and above the scale in the figure to provide examples of related applications that use the electromagnetic radiation in the range of the scale beneath each image. The photos on the left above gamma radiation show cosmic rays and a multicolor PET scan image of a brain. A black and white x-ray image of a hand appears above x-rays. An image of a patient undergoing dental work, with a blue light being directed into the patient's mouth is labeled, \u201cdental curing,\u201d and is shown above ultraviolet radiation. Between the ultraviolet and infrared labels is a narrow band of violet, indigo, blue, green, yellow, orange, and red colors in narrow, vertical strips. From this narrow band, two dashed lines extend a short distance above to the left and right of an image of the visible spectrum. The image, which is labeled, \u201cvisible light,\u201d is just a broader version of the narrow bands of color in the label area. Above infrared are images of a television remote and a black and green night vision image. At the left end of the microwave region, a satellite radar image is shown. Just right of this and still above the microwave region are images of a cell phone, a wireless router that is labeled, \u201cwireless data,\u201d and a microwave oven. Above broadcast and wireless radio are two images. The left most image is a black and white medical ultrasound image. A wireless AM radio is positioned at the far right in the image, also above broadcast and wireless radio.\" width=\"1280\" height=\"822\" \/><\/a> <strong>Figure 4.<\/strong> Portions of the electromagnetic spectrum are shown in order of decreasing frequency and increasing wavelength. Examples of some applications for various wavelengths include positron emission tomography (PET) scans, X-ray imaging, remote controls, wireless Internet, cellular telephones, and radios. (credit \u201cCosmic ray\": modification of work by NASA; credit \u201cPET scan\": modification of work by the National Institute of Health; credit \u201cX-ray\": modification of work by Dr. Jochen Lengerke; credit \u201cDental curing\": modification of work by the Department of the Navy; credit \u201cNight vision\": modification of work by the Department of the Army; credit \u201cRemote\": modification of work by Emilian Robert Vicol; credit \u201cCell phone\": modification of work by Brett Jordan; credit \u201cMicrowave oven\": modification of work by Billy Mabray; credit \u201cUltrasound\": modification of work by Jane Whitney; credit \u201cAM radio\": modification of work by Dave Clausen)[\/caption]\r\n\r\n<\/figcaption><\/figure>\r\n<\/div>\r\n<div id=\"fs-idm41062080\" class=\"textbox shaded\">\r\n<h3 class=\"title\">Wireless Communication<\/h3>\r\n<p class=\"title\">Many valuable technologies operate in the radio (3 kHz-300 GHz) frequency region of the electromagnetic spectrum (Figure 5).<\/p>\r\n\r\n<figure id=\"CNX_Chem_06_01_RadioCell\"><figcaption>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"1200\"]<a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_RadioCell.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_RadioCell-2.jpg\" alt=\"This figure consists of three cell phone tower images. The first involves a structure that uses a significant degree of scaffolding. The second image includes a tower with what appears to be a base that is essentially a large pole that branches out at the very top. The third image shows a cell phone tower that appears to be disguised as a palm tree.\" width=\"1200\" height=\"530\" \/><\/a> <strong>Figure 5.<\/strong> Radio and cell towers are typically used to transmit long-wavelength electromagnetic radiation. Increasingly, cell towers are designed to blend in with the landscape, as with the Tucson, Arizona, cell tower (right) disguised as a palm tree. (credit left: modification of work by Sir Mildred Pierce; credit middle: modification of work by M.O. Stevens)[\/caption]\r\n\r\n<\/figcaption><\/figure>\r\n<p id=\"fs-idm82699072\">At the low frequency (low energy, long wavelength) end of this region are AM (amplitude modulation) radio signals (540-2830 kHz) that can travel long distances. FM (frequency modulation) radio signals are used at higher frequencies (87.5-108.0 MHz). In AM radio, the information is transmitted by varying the amplitude of the wave (<a href=\"#CNX_Chem_06_01_AMFM\" class=\"autogenerated-content\">Figure 6<\/a>). In FM radio, by contrast, the amplitude is constant and the instantaneous frequency varies.<\/p>\r\n\r\n<figure id=\"CNX_Chem_06_01_AMFM\"><figcaption>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"1200\"]<a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_AMFM.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_AMFM-2.jpg\" alt=\"This figure shows 3 wave diagrams. The first wave diagram is in black and shows two crests, indicates a consistent distance from peak to trough, and has one trough in its span across the page. The label, \u201cSignal,\u201d appears to the right. Just below this, a wave diagram is shown in red. The wave includes sixteen crests, but the distance from the peaks to troughs of consecutive waves varies moving across the page. The peak to trough distance is greatest in the region below the peaks of the black wave diagram, and the distance from peak to trough is similarly least below the trough of the black wave diagram. This red wave diagram is labeled, \u201cA M.\u201d The third wave diagram is shown in blue. The distance from peak to trough of consecutive waves is constant across the page, but the peaks and troughs are more closely packed in the region below the peaks of the black wave diagram at the top of the figure. The peaks and troughs are relatively widely spaced below the trough region of the black wave diagram. This blue wave diagram is labeled \u201cF M.\u201d\" width=\"1200\" height=\"703\" \/><\/a> <strong>Figure 6.<\/strong> This schematic depicts how amplitude modulation (AM) and frequency modulation (FM) can be used to transmit a radio wave.[\/caption]\r\n\r\n<\/figcaption><\/figure>\r\n<p id=\"fs-idp85909232\">Other technologies also operate in the radio-wave portion of the electromagnetic spectrum. For example, 4G cellular telephone signals are approximately 880 MHz, while Global Positioning System (GPS) signals operate at 1.228 and 1.575 GHz, local area wireless technology (Wi-Fi) networks operate at 2.4 to 5 GHz, and highway toll sensors operate at 5.8 GHz. The frequencies associated with these applications are convenient because such waves tend not to be absorbed much by common building materials.<\/p>\r\n\r\n<\/div>\r\n<h2 id=\"fs-idp67580224\">\u00a0Key Concepts and Summary<\/h2>\r\n<\/div>\r\n<div class=\"key_takeaways editable block\" id=\"ball-ch08_s01_n04\">\r\n<div><section id=\"fs-idm37883664\" class=\"summary\">Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, <em>c<\/em>, of 2.998 \u00d7 10<sup>8<\/sup> m s<sup>\u22121<\/sup>. This radiation shows wavelike behavior, which can be characterized by a frequency, <em>\u03bd<\/em>, and a wavelength, <em>\u03bb. \u00a0<\/em>The frequency and wavelength of light are related by the speed of light, a constant,\u00a0such that <em>c<\/em> = <em>\u03bb\u03bd<\/em>. \u00a0\u00a0Light acts like a particle of energy, whose value is related to the frequency of light.<\/section><section id=\"fs-idp8373504\" class=\"key-equations\">\r\n<h2>Key Equations<\/h2>\r\n<ul id=\"fs-idp136605408\">\r\n \t<li><em>c<\/em> = <em>\u03bb\u03bd<\/em><\/li>\r\n \t<li>$latex E = h\\nu = \\frac{hc}{\\lambda}$, where <em>h<\/em> = 6.626 \u00d7 10<sup>\u221234<\/sup> J\u00b7s<\/li>\r\n<\/ul>\r\n<div class=\"key_takeaways editable block\" id=\"ball-ch08_s01_n04\">\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Exercises<\/h3>\r\n<div class=\"qandaset block\" id=\"ball-ch08_s01_qs01\">\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s01_qs01_qd01_p1\" class=\"para\">1. Describe the characteristics of a light wave.<\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">2. What is the frequency of light if its wavelength is 7.33 \u00d7 10<\/span><sup class=\"superscript\">\u22125<\/sup><span style=\"font-size: 1em\"> m?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">3. What is the frequency of light if its wavelength is 733 nm?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">4. What is the wavelength of light if its frequency is 8.19 \u00d7 10<\/span><sup class=\"superscript\">14<\/sup><span style=\"font-size: 1em\"> s<\/span><sup class=\"superscript\">\u22121<\/sup><span style=\"font-size: 1em\">?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">5. What is the wavelength of light if its frequency is 1.009 \u00d7 10<\/span><sup class=\"superscript\">6<\/sup><span style=\"font-size: 1em\"> Hz?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">6. What is the energy of a photon if its frequency is 5.55 \u00d7 10<\/span><sup class=\"superscript\">13<\/sup><span style=\"font-size: 1em\"> s<\/span><sup class=\"superscript\">\u22121<\/sup><span style=\"font-size: 1em\">?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">7. What is the energy of a photon if its wavelength is 5.88 \u00d7 10<\/span><sup class=\"superscript\">\u22124<\/sup><span style=\"font-size: 1em\"> m?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">8. FM-95, an FM radio station, broadcasts at a frequency of 9.51 \u00d7 10<\/span><sup>7<\/sup><span style=\"font-size: 1em\"> s<\/span><sup>\u22121<\/sup><span style=\"font-size: 1em\"> (95.1 MHz). What is the wavelength of these radio waves in meters?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">9. One of the radiographic devices used in a dentist's office emits an X-ray of wavelength 2.090 \u00d7 10<\/span><sup>\u221211<\/sup><span style=\"font-size: 1em\"> m. What is the energy, in joules, and frequency of this X-ray?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">10. RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?<\/span><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<b>Answers<\/b>\r\n\r\n1. Light has a wavelength and a frequency.\r\n\r\n2. 4.09 \u00d7 10<sup class=\"superscript\">12<\/sup> s<sup class=\"superscript\">\u22121<\/sup>\r\n\r\n3. 4.09 \u00d7 10<sup class=\"superscript\">14<\/sup> s<sup class=\"superscript\">\u22121<\/sup>\r\n\r\n4. 3.66 \u00d7 10<sup class=\"superscript\">\u22127<\/sup> m\r\n\r\n5. 297 m\r\n\r\n6. 3.68 \u00d7 10<sup class=\"superscript\">\u221220<\/sup> J\r\n\r\n7. 3.38 \u00d7 10<sup class=\"superscript\">\u221222<\/sup> J\r\n\r\n8. 3.15 m\r\n\r\n9.\u00a0<em>E<\/em> = 9.502 \u00d7 10<sup>\u221215<\/sup> J; <em>\u03bd<\/em> = 1.434 \u00d7 10<sup>19<\/sup> s<sup>\u22121<\/sup>\r\n\r\n10.\u00a0Red: 660 nm; 4.54 \u00d7 10<sup>14<\/sup> Hz; 3.01 \u00d7 10<sup>\u221219<\/sup> J. Green: 520 nm; 5.77 \u00d7 10<sup>14<\/sup> Hz; 3.82 \u00d7 10<sup>\u221219<\/sup> J. Blue: 440 nm; 6.81 \u00d7 10<sup>14<\/sup> Hz; 4.51 \u00d7 10<sup>\u221219<\/sup> J. Somewhat different numbers are also possible.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<div>\r\n<h2>Glossary<\/h2>\r\n<strong>amplitude:<\/strong>\u00a0extent of the displacement caused by a wave (for sinusoidal waves, it is one-half the difference from the peak height to the trough depth, and the intensity is proportional to the square of the amplitude)\r\n\r\n<strong>continuous spectrum:\u00a0<\/strong>electromagnetic radiation given off in an unbroken series of wavelengths (e.g., white light from the sun)\r\n\r\n<strong>electromagnetic radiation:\u00a0<\/strong>energy transmitted by waves that have an electric-field component and a magnetic-field component\r\n\r\n<strong>electromagnetic spectrum:\u00a0<\/strong>range of energies that electromagnetic radiation can comprise, including radio, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays; since electromagnetic radiation energy is proportional to the frequency and inversely proportional to the wavelength, the spectrum can also be specified by ranges of frequencies or wavelengths\r\n\r\n<strong>frequency (<em>\u03bd<\/em>):\u00a0<\/strong>number of wave cycles (peaks or troughs) that pass a specified point in space per unit time\r\n\r\n<strong>hertz (Hz):\u00a0<\/strong>the unit of frequency, which is the number of cycles per second, s<sup>\u22121<\/sup>\r\n\r\n<strong>intensity:\u00a0<\/strong>property of wave-propagated energy related to the amplitude of the wave, such as brightness of light or loudness of sound\r\n\r\n<strong>photon:\u00a0<\/strong>smallest possible packet of electromagnetic radiation, a particle of light\r\n\r\n<strong>wave:\u00a0<\/strong>oscillation that can transport energy from one point to another in space\r\n\r\n<strong>wavelength (<em>\u03bb<\/em>):\u00a0<\/strong>distance between two consecutive peaks or troughs in a wave\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"section\" id=\"ball-ch08_s01\" lang=\"en\">\n<div class=\"learning_objectives editable block\" id=\"ball-ch08_s01_n01\">\n<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this module, you will be able to:<\/p>\n<ul>\n<li>Describe light with its frequency and wavelength.<\/li>\n<li>Describe light as a particle of energy.<span style=\"color: #333333;background-color: #ffffff\">\u00a0<\/span><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>Our last \u201cpicture\u201d of the atom consisted of a nucleus containing protons and neutrons (constituting most of the atom\u2019s mass), surrounded by a sea of electrons. The limitations of this model are that it doesn\u2019t show how the electrons are arranged or how they move. It turns out that this <em>electronic structure\u00a0<\/em>is the primary factor controlling how an atom behaves.<\/p>\n<p>To get a more complete view of the atom, we need more experimental evidence and interpretation. One of the main ways to investigate electrons in atoms is to use <em>light\u00a0<\/em>with two techniques; 1) by shining a light on the atoms and seeing what happens to the light (absorption spectroscopy), and 2) by heating the atoms and seeing what kind of light is given off (emission spectroscopy). Clearly, we will need to start with an understanding of the nature of light. We will then move on to describe and interpret experiments with light that give us our understanding of what electrons in atoms are doing. Finally, we see how the properties of electrons are related to the way the atoms behave.<\/p>\n<p id=\"ball-ch08_s01_p01\" class=\"para editable block\">What we know as light is more properly called <em class=\"emphasis\">electromagnetic radiation<\/em>. We know from experiments that light acts as a wave. As such, it can be described as having a frequency and a wavelength.<\/p>\n<p class=\"para editable block\">The <span class=\"margin_term\"><a class=\"glossterm\">wavelength<\/a><\/span>\u00a0of light is the distance between corresponding points in two adjacent light cycles.\u00a0 Wavelength is typically represented by \u03bb, the lowercase Greek letter <em class=\"emphasis\">lambda<\/em>, and\u00a0has units of length (meters, centimeters, etc.).\u00a0 Figure 1\u00a0shows how wavelength is defined.<\/p>\n<div class=\"figure large medium-height editable block\" id=\"ball-ch08_s01_f01\">\n<figure id=\"attachment_4846\" aria-describedby=\"caption-attachment-4846\" style=\"width: 373px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength.png\" alt=\"\" width=\"373\" height=\"154\" class=\"wp-image-4846 size-full\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength.png 373w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength-300x124.png 300w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength-65x27.png 65w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength-225x93.png 225w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Wavelength-350x145.png 350w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/a><figcaption id=\"caption-attachment-4846\" class=\"wp-caption-text\"><strong>Figure 1.<\/strong> The wavelength of light is the distance between corresponding points in two adjacent light cycles.<\/figcaption><\/figure>\n<p id=\"fs-idp150592048\">The <span class=\"margin_term\"><a class=\"glossterm\">frequency<\/a><\/span>\u00a0of light is the number of cycles of light that pass a given point in one second.\u00a0 Frequency is represented by \u03bd, the lowercase Greek letter <em class=\"emphasis\">nu, <\/em>and\u00a0has units of <em class=\"emphasis\">per second<\/em>, written as s<sup class=\"superscript\">\u22121<\/sup> and sometimes called a <em class=\"emphasis\">hertz<\/em> (Hz). \u00a0 The amplitude (a) corresponds to the magnitude of the wave&#8217;s displacement and so, in <a href=\"#CNX_Chem_06_01_Frequency\" class=\"autogenerated-content\">Figure 2<\/a>, this corresponds to one-half the height between the peaks and troughs. The amplitude is related to the intensity of the wave, which for light is the brightness, and for sound is the loudness.<\/p>\n<figure id=\"CNX_Chem_06_01_Frequency\"><figcaption>\n<figure style=\"width: 1300px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_Frequency.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_Frequency-2.jpg\" alt=\"This figure includes 5 one-dimensional sinusoidal waves in two columns. The column on the left includes three waves, and the column on the right includes two waves. In each column, dashed vertical line segments extend down the left and right sides of the column. A right pointing arrow extends from the left dashed line to the right dashed line in both columns and is labeled, \u201cDistance traveled in 1 second.\u201d The waves all begin on the left side at a crest. The wave at the upper left shows 3 peaks to the right of the starting point. A bracket labeled, \u201clambda subscript 1,\u201d extends upward from the second and third peaks. Beneath this wave is the label, \u201cnu subscript 1 equals 4 cycles per second equals 3 hertz.\u201d The wave below has six peaks to the right of the starting point with a bracket similarly connecting the third and fourth peaks which is labeled, \u201clambda subscript 2.\u201d Beneath this wave is the label, \u201cnu subscript 2 equals 8 cycles per second equals 6 hertz\u201d The third wave in the column has twelve peaks to the right of the starting point with a bracket similarly connecting the seventh and eighth peaks which is labeled, \u201clambda subscript 3.\u201d Beneath this wave is the label, \u201cnu subscript 3 equals 12 cycles per second equals 12 hertz.\u201d All waves in this column appear to have the same vertical distance from peak to trough. In the second column, the two waves are similarly shown, but lack the lambda labels. The top wave in this column has a greater vertical distance between the peaks and troughs and is labeled, \u201cHigher amplitude.\u201d The wave beneath it has a lesser distance between the peaks and troughs and is labeled, \u201cLower amplitude.\u201d\" width=\"1300\" height=\"633\" \/><\/a><figcaption class=\"wp-caption-text\"><strong>Figure 2.<\/strong> One-dimensional sinusoidal waves show the relationship among wavelength, frequency, and speed. The wave with the shortest wavelength has the highest frequency. Amplitude is one-half the height of the wave from peak to trough.<\/figcaption><\/figure>\n<\/figcaption><\/figure>\n<p class=\"para\">Light acts as a wave and can be described by a wavelength \u03bb and a frequency \u03bd.<\/p>\n<\/div>\n<p id=\"ball-ch08_s01_p02\" class=\"para editable block\">One property of waves is that their speed is equal to their wavelength times their frequency. That means we have<\/p>\n<p style=\"text-align: center\"><span class=\"informalequation block\">speed = \u03bb\u03bd<\/span><\/p>\n<p style=\"text-align: center\">m\/s = m x s<sup>-1<\/sup><\/p>\n<p id=\"ball-ch08_s01_p03\" class=\"para editable block\">For light, however, speed is actually a universal constant when light is traveling through a vacuum (or, to a very good approximation, air). The measured speed of light (<em class=\"emphasis\">c<\/em>) in a vacuum is 2.9979 \u00d7 10<sup class=\"superscript\">8<\/sup> m\/s, or about 3.00 \u00d7 10<sup class=\"superscript\">8<\/sup> m\/s. Thus, we have<\/p>\n<p style=\"text-align: center\"><span class=\"informalequation block\">c = \u03bb\u03bd<\/span><\/p>\n<p style=\"text-align: center\">m\/s = m x s<sup>-1<\/sup><\/p>\n<p id=\"ball-ch08_s01_p04\" class=\"para editable block\">Because the speed of light is a constant, the wavelength and the frequency of light are related to each other: as one increases, the other decreases and vice versa. We can use this equation to calculate what one property of light has to be when given the other property.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Example 1<\/h3>\n<p id=\"ball-ch08_s01_p05\" class=\"para\">What is the frequency of light if its wavelength is 5.55 \u00d7 10<sup class=\"superscript\">\u22127<\/sup> m?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\n<p id=\"ball-ch08_s01_p06\" class=\"para\">We use the equation that relates the wavelength and frequency of light with its speed. We have<\/p>\n<p><span class=\"informalequation\">3.00\u00d710<sup>8<\/sup>m\/s = (5.55\u00d710<sup>-7<\/sup>m)\u03bd<\/span><\/p>\n<p id=\"ball-ch08_s01_p07\" class=\"para\">We divide both sides of the equation by 5.55 \u00d7 10<sup class=\"superscript\">\u22127<\/sup> m and get<\/p>\n<p><span class=\"informalequation\">\u03bd = 5.41\u00d710<sup>14<\/sup>\u00a0s<sup>-1<\/sup><\/span><\/p>\n<p id=\"ball-ch08_s01_p08\" class=\"para\">Note how the m units cancel, leaving s in the denominator. A unit in a denominator is indicated by a \u22121 power\u2014s<sup class=\"superscript\">\u22121<\/sup>\u2014and read as \u201cper second.\u201d<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\n<p id=\"ball-ch08_s01_p09\" class=\"para\">What is the wavelength of light if its frequency is 1.55 \u00d7 10<sup class=\"superscript\">10<\/sup> s<sup class=\"superscript\">\u22121<\/sup>?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\n<p id=\"ball-ch08_s01_p10\" class=\"para\">0.0194 m, or 19.4 mm<\/p>\n<\/div>\n<figure id=\"CNX_Chem_06_01_emspectrum\"><figcaption><\/figcaption><\/figure>\n<div class=\"textbox shaded\" id=\"fs-idm80944240\">\n<h3>Example 2<\/h3>\n<p id=\"fs-idp152169520\">A sodium streetlight gives off yellow light that has a wavelength of 589 nm (1 nm = 1 \u00d7 10<sup>\u22129<\/sup> m). What is the frequency of this light?<\/p>\n<p>&nbsp;<\/p>\n<p id=\"fs-idm59714720\"><strong>Solution<\/strong><br \/>\nWe can rearrange the equation <em>c<\/em> = <em>\u03bb\u03bd<\/em> to solve for the frequency:<\/p>\n<div class=\"equation\" id=\"fs-idp41492256\" style=\"text-align: center\">[latex]\\nu = \\frac{c}{\\lambda}[\/latex]<\/div>\n<p id=\"fs-idm79802192\">Since <em>c<\/em> is expressed in meters per second, we must also convert 589 nm to meters.<\/p>\n<div class=\"equation\" id=\"fs-idm52369072\" style=\"text-align: center\">[latex]\\nu = (\\frac{2.998 \\times 10^8 \\;\\rule[0.25ex]{0.5em}{0.1ex}\\hspace{-0.5em}\\text{ms}^{-1}}{589 \\;\\rule[0.25ex]{1em}{0.1ex}\\hspace{-1em}\\text{nm}})(\\frac{1 \\times 10^9 \\;\\rule[0.25ex]{1em}{0.1ex}\\hspace{-1em}\\text{nm}}{1\\;\\rule[0.25ex]{0.5em}{0.1ex}\\hspace{-0.5em}\\text{m}}) = 5.09 \\times 10^{14}\\text{s}^{-1}[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<p id=\"fs-idm82969184\"><em><strong>Test Yourself<\/strong><\/em><br \/>\nOne of the frequencies used to transmit and receive cellular telephone signals in the United States is 850 MHz. What is the wavelength in meters of these radio waves?<\/p>\n<p><em><strong>Answer<\/strong><\/em><\/p>\n<p>0.353 m = 35.3 cm<\/p>\n<\/div>\n<p id=\"ball-ch08_s01_p11\" class=\"para editable block\">Light also behaves like a package of energy. It turns out that for light, the energy of the \u201cpackage\u201d of energy is proportional to its frequency. (For most waves, energy is proportional to wave amplitude, or the height of the wave.) The mathematical equation that relates the energy (<em class=\"emphasis\">E<\/em>) of light to its frequency is<\/p>\n<p style=\"text-align: center\"><span class=\"informalequation block\">E = h\u03bd<\/span><\/p>\n<p id=\"ball-ch08_s01_p12\" class=\"para editable block\">where \u03bd is the frequency of the light, and <em class=\"emphasis\">h<\/em> is a constant called <span class=\"margin_term\"><a class=\"glossterm\">Planck\u2019s constant<\/a><\/span>. Its value is 6.626 \u00d7 10<sup class=\"superscript\">\u221234<\/sup> J\u00b7s \u2014 a very small number that is another fundamental constant of our universe, like the speed of light. The units on Planck\u2019s constant may look unusual, but these units are required so that the algebra works out.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Example 3<\/h3>\n<p id=\"ball-ch08_s01_p13\" class=\"para\">What is the energy of light if its frequency is 1.55 \u00d7 10<sup class=\"superscript\">10<\/sup> s<sup class=\"superscript\">\u22121<\/sup>?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\n<p id=\"ball-ch08_s01_p14\" class=\"para\">Using the formula for the energy of light, we have<\/p>\n<p><span class=\"informalequation\"><span class=\"mathphrase\"><em class=\"emphasis\">E<\/em> = (6.626 \u00d7 10<sup class=\"superscript\">\u221234<\/sup> J\u00b7s)(1.55 \u00d7 10<sup class=\"superscript\">10<\/sup> s<sup class=\"superscript\">\u22121<\/sup>)<\/span><\/span><\/p>\n<p id=\"ball-ch08_s01_p15\" class=\"para\">Seconds are in the numerator and the denominator, so they cancel, leaving us with joules, the unit of energy. So<\/p>\n<p><span class=\"informalequation\"><span class=\"mathphrase\"><em class=\"emphasis\">E<\/em> = 1.03 \u00d7 10<sup class=\"superscript\">\u221223<\/sup> J<\/span><\/span><\/p>\n<p id=\"ball-ch08_s01_p16\" class=\"para\">This is an extremely small amount of energy\u2014but this is for only one light wave.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\n<p id=\"ball-ch08_s01_p17\" class=\"para\">What is the frequency of a light wave if its energy is 4.156 \u00d7 10<sup class=\"superscript\">\u221220<\/sup> J?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\n<p id=\"ball-ch08_s01_p18\" class=\"para\">6.27 \u00d7 10<sup class=\"superscript\">13<\/sup> s<sup class=\"superscript\">\u22121<\/sup><\/p>\n<\/div>\n<p id=\"ball-ch08_s01_p19\" class=\"para editable block\">Because a light wave behaves like a little particle of energy, light waves have a particle-type name: the <span class=\"margin_term\"><a class=\"glossterm\">photon<\/a><\/span>. It is not uncommon to hear light described as photons.<\/p>\n<p id=\"ball-ch08_s01_p20\" class=\"para editable block\">Wavelengths, frequencies, and energies of light span a wide range; the entire range of possible values for light is called the <span class=\"margin_term\"><a class=\"glossterm\">electromagnetic spectrum<\/a><\/span>. We are mostly familiar with visible light, which is light having a wavelength range between about 400 nm and 700 nm. Light can have much longer and much shorter wavelengths than this, with corresponding variations in frequency and energy. <a class=\"xref\" href=\"#ball-ch08_s01_f02\">Figure 3 &#8220;The Electromagnetic Spectrum&#8221;<\/a> shows the entire electromagnetic spectrum and how certain regions of the spectrum are labelled. You may already be familiar with some of these regions; they are all light\u2014with different frequencies, wavelengths, and energies.<\/p>\n<div class=\"figure large editable block\" id=\"ball-ch08_s01_f02\">\n<figure id=\"attachment_4683\" aria-describedby=\"caption-attachment-4683\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Electromagnetic-Spectrum.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Electromagnetic-Spectrum-1.png\" alt=\"Electromagnetic Spectrum\" width=\"600\" height=\"381\" class=\"wp-image-4683 size-full\" \/><\/a><figcaption id=\"caption-attachment-4683\" class=\"wp-caption-text\"><strong>Figure 3.<\/strong> The Electromagnetic Spectrum \u00a0The electromagnetic spectrum, with its various regions labelled. The borders of each region are approximate.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3>Example 4<\/h3>\n<p class=\"Indent\">Using Figure 3, determine which category of EM radiation has more energetic photons, UV or IR.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"Solution\"><strong>Solution\u00a0\u00a0 <\/strong><\/p>\n<p class=\"Indentpoints\">Looking at Figure 3 we see that IR radiation has LONGER wavelengths. Applying the property that the energy of a photon is inversely proportional to the wavelength of the light, we can conclude that the IR light has LESS energetic photons.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"SelfTest\"><em><strong>Test Yourself<\/strong><\/em><\/p>\n<p class=\"Indent\">Which light has carries less energy in its photons, light with a frequency of 4.0 x 10<sup>13<\/sup>s<sup>-1<\/sup>or light with a frequency of 1.0 x 10<sup>14<\/sup>s<sup>-1<\/sup>?<\/p>\n<p>&nbsp;<\/p>\n<p><em><strong>Answer<\/strong><\/em><\/p>\n<p class=\"Answers\">The lower frequency light of 4.0 x 10<sup>13<\/sup>s<sup>-1<\/sup>would have the lower energy photons.<\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Technology and the Electromagnetic Spectrum<\/h3>\n<p id=\"fs-idm80411056\">Figure 4 shows the <strong>electromagnetic spectrum<\/strong>, the range of all types of electromagnetic radiation. Each of the various colors of visible light has specific frequencies and wavelengths associated with them, and you can see that visible light makes up only a small portion of the electromagnetic spectrum.<\/p>\n<p>Because the technologies developed to work in various parts of the electromagnetic spectrum are different, for reasons of convenience and historical legacies, different units are typically used for different parts of the spectrum. For example, radio waves are usually specified as frequencies (typically in units of MHz), while the visible region is usually specified in wavelengths (typically in units of nm or angstroms).<\/p>\n<figure id=\"CNX_Chem_06_01_emspectrum\"><figcaption>\n<figure style=\"width: 1280px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_emspectrum.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_emspectrum-2.jpg\" alt=\"The figure includes a portion of the electromagnetic spectrum which extends from gamma radiation at the far left through x-ray, ultraviolet, visible, infrared, terahertz, and microwave to broadcast and wireless radio at the far right. At the top of the figure, inside a grey box, are three arrows. The first points left and is labeled, \u201cIncreasing energy E.\u201d A second arrow is placed just below the first which also points left and is labeled, \u201cIncreasing frequency nu.\u201d A third arrow is placed just below which points right and is labeled, \u201cIncreasing wavelength lambda.\u201d Inside the grey box near the bottom is a blue sinusoidal wave pattern that moves horizontally through the box. At the far left end, the waves are short and tightly packed. They gradually lengthen moving left to right across the figure, resulting in significantly longer waves at the right end of the diagram. Beneath the grey box are a variety of photos aligned above the names of the radiation types and a numerical scale that is labeled, \u201cWavelength lambda ( m ).\u201d This scale runs from 10 superscript negative 12 meters under gamma radiation increasing by powers of ten to a value of 10 superscript 3 meters at the far right under broadcast and wireless radio. X-ray appears around 10 superscript negative 10 meters, ultraviolet appears in the 10 superscript negative 8 to 10 superscript negative 7 range, visible light appears between 10 superscript negative 7 and 10 superscript negative 6, infrared appears in the 10 superscript negative 6 to 10 superscript negative 5 range, teraherz appears in the 10 superscript negative 4 to 10 superscript negative 3 range, microwave infrared appears in the 10 superscript negative 2 to 10 superscript negative 1 range, and broadcast and wireless radio extend from 10 to 10 superscript 3 meters. Labels above the scale are placed to indicate 1 n m at 10 superscript negative 9 meters, 1 micron at 10 superscript negative 6 meters, 1 millimeter at 10 superscript negative 3 meters, 1 centimeter at 10 superscript negative 2 meters, and 1 foot between 10 superscript negative 1 meter and 10 superscript 0 meters. A variety of images are placed beneath the grey box and above the scale in the figure to provide examples of related applications that use the electromagnetic radiation in the range of the scale beneath each image. The photos on the left above gamma radiation show cosmic rays and a multicolor PET scan image of a brain. A black and white x-ray image of a hand appears above x-rays. An image of a patient undergoing dental work, with a blue light being directed into the patient's mouth is labeled, \u201cdental curing,\u201d and is shown above ultraviolet radiation. Between the ultraviolet and infrared labels is a narrow band of violet, indigo, blue, green, yellow, orange, and red colors in narrow, vertical strips. From this narrow band, two dashed lines extend a short distance above to the left and right of an image of the visible spectrum. The image, which is labeled, \u201cvisible light,\u201d is just a broader version of the narrow bands of color in the label area. Above infrared are images of a television remote and a black and green night vision image. At the left end of the microwave region, a satellite radar image is shown. Just right of this and still above the microwave region are images of a cell phone, a wireless router that is labeled, \u201cwireless data,\u201d and a microwave oven. Above broadcast and wireless radio are two images. The left most image is a black and white medical ultrasound image. A wireless AM radio is positioned at the far right in the image, also above broadcast and wireless radio.\" width=\"1280\" height=\"822\" \/><\/a><figcaption class=\"wp-caption-text\"><strong>Figure 4.<\/strong> Portions of the electromagnetic spectrum are shown in order of decreasing frequency and increasing wavelength. Examples of some applications for various wavelengths include positron emission tomography (PET) scans, X-ray imaging, remote controls, wireless Internet, cellular telephones, and radios. (credit \u201cCosmic ray&#8221;: modification of work by NASA; credit \u201cPET scan&#8221;: modification of work by the National Institute of Health; credit \u201cX-ray&#8221;: modification of work by Dr. Jochen Lengerke; credit \u201cDental curing&#8221;: modification of work by the Department of the Navy; credit \u201cNight vision&#8221;: modification of work by the Department of the Army; credit \u201cRemote&#8221;: modification of work by Emilian Robert Vicol; credit \u201cCell phone&#8221;: modification of work by Brett Jordan; credit \u201cMicrowave oven&#8221;: modification of work by Billy Mabray; credit \u201cUltrasound&#8221;: modification of work by Jane Whitney; credit \u201cAM radio&#8221;: modification of work by Dave Clausen)<\/figcaption><\/figure>\n<\/figcaption><\/figure>\n<\/div>\n<div id=\"fs-idm41062080\" class=\"textbox shaded\">\n<h3 class=\"title\">Wireless Communication<\/h3>\n<p class=\"title\">Many valuable technologies operate in the radio (3 kHz-300 GHz) frequency region of the electromagnetic spectrum (Figure 5).<\/p>\n<figure id=\"CNX_Chem_06_01_RadioCell\"><figcaption>\n<figure style=\"width: 1200px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_RadioCell.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_RadioCell-2.jpg\" alt=\"This figure consists of three cell phone tower images. The first involves a structure that uses a significant degree of scaffolding. The second image includes a tower with what appears to be a base that is essentially a large pole that branches out at the very top. The third image shows a cell phone tower that appears to be disguised as a palm tree.\" width=\"1200\" height=\"530\" \/><\/a><figcaption class=\"wp-caption-text\"><strong>Figure 5.<\/strong> Radio and cell towers are typically used to transmit long-wavelength electromagnetic radiation. Increasingly, cell towers are designed to blend in with the landscape, as with the Tucson, Arizona, cell tower (right) disguised as a palm tree. (credit left: modification of work by Sir Mildred Pierce; credit middle: modification of work by M.O. Stevens)<\/figcaption><\/figure>\n<\/figcaption><\/figure>\n<p id=\"fs-idm82699072\">At the low frequency (low energy, long wavelength) end of this region are AM (amplitude modulation) radio signals (540-2830 kHz) that can travel long distances. FM (frequency modulation) radio signals are used at higher frequencies (87.5-108.0 MHz). In AM radio, the information is transmitted by varying the amplitude of the wave (<a href=\"#CNX_Chem_06_01_AMFM\" class=\"autogenerated-content\">Figure 6<\/a>). In FM radio, by contrast, the amplitude is constant and the instantaneous frequency varies.<\/p>\n<figure id=\"CNX_Chem_06_01_AMFM\"><figcaption>\n<figure style=\"width: 1200px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/opentextbc.ca\/chemistry\/wp-content\/uploads\/sites\/150\/2016\/05\/CNX_Chem_06_01_AMFM.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_06_01_AMFM-2.jpg\" alt=\"This figure shows 3 wave diagrams. The first wave diagram is in black and shows two crests, indicates a consistent distance from peak to trough, and has one trough in its span across the page. The label, \u201cSignal,\u201d appears to the right. Just below this, a wave diagram is shown in red. The wave includes sixteen crests, but the distance from the peaks to troughs of consecutive waves varies moving across the page. The peak to trough distance is greatest in the region below the peaks of the black wave diagram, and the distance from peak to trough is similarly least below the trough of the black wave diagram. This red wave diagram is labeled, \u201cA M.\u201d The third wave diagram is shown in blue. The distance from peak to trough of consecutive waves is constant across the page, but the peaks and troughs are more closely packed in the region below the peaks of the black wave diagram at the top of the figure. The peaks and troughs are relatively widely spaced below the trough region of the black wave diagram. This blue wave diagram is labeled \u201cF M.\u201d\" width=\"1200\" height=\"703\" \/><\/a><figcaption class=\"wp-caption-text\"><strong>Figure 6.<\/strong> This schematic depicts how amplitude modulation (AM) and frequency modulation (FM) can be used to transmit a radio wave.<\/figcaption><\/figure>\n<\/figcaption><\/figure>\n<p id=\"fs-idp85909232\">Other technologies also operate in the radio-wave portion of the electromagnetic spectrum. For example, 4G cellular telephone signals are approximately 880 MHz, while Global Positioning System (GPS) signals operate at 1.228 and 1.575 GHz, local area wireless technology (Wi-Fi) networks operate at 2.4 to 5 GHz, and highway toll sensors operate at 5.8 GHz. The frequencies associated with these applications are convenient because such waves tend not to be absorbed much by common building materials.<\/p>\n<\/div>\n<h2 id=\"fs-idp67580224\">\u00a0Key Concepts and Summary<\/h2>\n<\/div>\n<div class=\"key_takeaways editable block\" id=\"ball-ch08_s01_n04\">\n<div>\n<section id=\"fs-idm37883664\" class=\"summary\">Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, <em>c<\/em>, of 2.998 \u00d7 10<sup>8<\/sup> m s<sup>\u22121<\/sup>. This radiation shows wavelike behavior, which can be characterized by a frequency, <em>\u03bd<\/em>, and a wavelength, <em>\u03bb. \u00a0<\/em>The frequency and wavelength of light are related by the speed of light, a constant,\u00a0such that <em>c<\/em> = <em>\u03bb\u03bd<\/em>. \u00a0\u00a0Light acts like a particle of energy, whose value is related to the frequency of light.<\/section>\n<section id=\"fs-idp8373504\" class=\"key-equations\">\n<h2>Key Equations<\/h2>\n<ul id=\"fs-idp136605408\">\n<li><em>c<\/em> = <em>\u03bb\u03bd<\/em><\/li>\n<li>[latex]E = h\\nu = \\frac{hc}{\\lambda}[\/latex], where <em>h<\/em> = 6.626 \u00d7 10<sup>\u221234<\/sup> J\u00b7s<\/li>\n<\/ul>\n<div class=\"key_takeaways editable block\" id=\"ball-ch08_s01_n04\">\n<div class=\"bcc-box bcc-info\">\n<h3>Exercises<\/h3>\n<div class=\"qandaset block\" id=\"ball-ch08_s01_qs01\">\n<div class=\"question\">\n<p id=\"ball-ch08_s01_qs01_qd01_p1\" class=\"para\">1. Describe the characteristics of a light wave.<\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">2. What is the frequency of light if its wavelength is 7.33 \u00d7 10<\/span><sup class=\"superscript\">\u22125<\/sup><span style=\"font-size: 1em\"> m?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">3. What is the frequency of light if its wavelength is 733 nm?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">4. What is the wavelength of light if its frequency is 8.19 \u00d7 10<\/span><sup class=\"superscript\">14<\/sup><span style=\"font-size: 1em\"> s<\/span><sup class=\"superscript\">\u22121<\/sup><span style=\"font-size: 1em\">?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">5. What is the wavelength of light if its frequency is 1.009 \u00d7 10<\/span><sup class=\"superscript\">6<\/sup><span style=\"font-size: 1em\"> Hz?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">6. What is the energy of a photon if its frequency is 5.55 \u00d7 10<\/span><sup class=\"superscript\">13<\/sup><span style=\"font-size: 1em\"> s<\/span><sup class=\"superscript\">\u22121<\/sup><span style=\"font-size: 1em\">?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">7. What is the energy of a photon if its wavelength is 5.88 \u00d7 10<\/span><sup class=\"superscript\">\u22124<\/sup><span style=\"font-size: 1em\"> m?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">8. FM-95, an FM radio station, broadcasts at a frequency of 9.51 \u00d7 10<\/span><sup>7<\/sup><span style=\"font-size: 1em\"> s<\/span><sup>\u22121<\/sup><span style=\"font-size: 1em\"> (95.1 MHz). What is the wavelength of these radio waves in meters?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">9. One of the radiographic devices used in a dentist&#8217;s office emits an X-ray of wavelength 2.090 \u00d7 10<\/span><sup>\u221211<\/sup><span style=\"font-size: 1em\"> m. What is the energy, in joules, and frequency of this X-ray?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">10. RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?<\/span><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><b>Answers<\/b><\/p>\n<p>1. Light has a wavelength and a frequency.<\/p>\n<p>2. 4.09 \u00d7 10<sup class=\"superscript\">12<\/sup> s<sup class=\"superscript\">\u22121<\/sup><\/p>\n<p>3. 4.09 \u00d7 10<sup class=\"superscript\">14<\/sup> s<sup class=\"superscript\">\u22121<\/sup><\/p>\n<p>4. 3.66 \u00d7 10<sup class=\"superscript\">\u22127<\/sup> m<\/p>\n<p>5. 297 m<\/p>\n<p>6. 3.68 \u00d7 10<sup class=\"superscript\">\u221220<\/sup> J<\/p>\n<p>7. 3.38 \u00d7 10<sup class=\"superscript\">\u221222<\/sup> J<\/p>\n<p>8. 3.15 m<\/p>\n<p>9.\u00a0<em>E<\/em> = 9.502 \u00d7 10<sup>\u221215<\/sup> J; <em>\u03bd<\/em> = 1.434 \u00d7 10<sup>19<\/sup> s<sup>\u22121<\/sup><\/p>\n<p>10.\u00a0Red: 660 nm; 4.54 \u00d7 10<sup>14<\/sup> Hz; 3.01 \u00d7 10<sup>\u221219<\/sup> J. Green: 520 nm; 5.77 \u00d7 10<sup>14<\/sup> Hz; 3.82 \u00d7 10<sup>\u221219<\/sup> J. Blue: 440 nm; 6.81 \u00d7 10<sup>14<\/sup> Hz; 4.51 \u00d7 10<sup>\u221219<\/sup> J. Somewhat different numbers are also possible.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<div>\n<h2>Glossary<\/h2>\n<p><strong>amplitude:<\/strong>\u00a0extent of the displacement caused by a wave (for sinusoidal waves, it is one-half the difference from the peak height to the trough depth, and the intensity is proportional to the square of the amplitude)<\/p>\n<p><strong>continuous spectrum:\u00a0<\/strong>electromagnetic radiation given off in an unbroken series of wavelengths (e.g., white light from the sun)<\/p>\n<p><strong>electromagnetic radiation:\u00a0<\/strong>energy transmitted by waves that have an electric-field component and a magnetic-field component<\/p>\n<p><strong>electromagnetic spectrum:\u00a0<\/strong>range of energies that electromagnetic radiation can comprise, including radio, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays; since electromagnetic radiation energy is proportional to the frequency and inversely proportional to the wavelength, the spectrum can also be specified by ranges of frequencies or wavelengths<\/p>\n<p><strong>frequency (<em>\u03bd<\/em>):\u00a0<\/strong>number of wave cycles (peaks or troughs) that pass a specified point in space per unit time<\/p>\n<p><strong>hertz (Hz):\u00a0<\/strong>the unit of frequency, which is the number of cycles per second, s<sup>\u22121<\/sup><\/p>\n<p><strong>intensity:\u00a0<\/strong>property of wave-propagated energy related to the amplitude of the wave, such as brightness of light or loudness of sound<\/p>\n<p><strong>photon:\u00a0<\/strong>smallest possible packet of electromagnetic radiation, a particle of light<\/p>\n<p><strong>wave:\u00a0<\/strong>oscillation that can transport energy from one point to another in space<\/p>\n<p><strong>wavelength (<em>\u03bb<\/em>):\u00a0<\/strong>distance between two consecutive peaks or troughs in a wave<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":330,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"8.1 Electromagnetic Energy","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"chapter-type":[],"contributor":[],"license":[54],"class_list":["post-2393","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-sa"],"part":2362,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2393","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/users\/330"}],"version-history":[{"count":20,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2393\/revisions"}],"predecessor-version":[{"id":4847,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2393\/revisions\/4847"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/parts\/2362"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2393\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/media?parent=2393"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapter-type?post=2393"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/contributor?post=2393"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/license?post=2393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}