{"id":399,"date":"2016-01-11T20:00:14","date_gmt":"2016-01-11T20:00:14","guid":{"rendered":"https:\/\/opentextbc.ca\/introductorychemistryclone\/chapter\/light-2\/"},"modified":"2020-07-28T23:03:17","modified_gmt":"2020-07-28T23:03:17","slug":"light","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introductorychemistryclone\/chapter\/light\/","title":{"raw":"Light","rendered":"Light"},"content":{"raw":"[latexpage]\r\n
\r\n

Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n
    \r\n \t
  1. Describe light with its frequency and wavelength.<\/li>\r\n \t
  2. Describe light as a particle of energy.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nWhat we know as light is more properly called electromagnetic radiation<\/i>. We know from experiments that light acts as a wave. As such, it can be described as having a frequency and a wavelength. The [pb_glossary id=\"1762\"]wavelength[\/pb_glossary]\u00a0of light is the distance between corresponding points in two adjacent light cycles, and the [pb_glossary id=\"1763\"]frequency[\/pb_glossary]\u00a0of light is the number of cycles of light that pass a given point in one second. Wavelength is typically represented by \u03bb, the lowercase Greek letter lambda<\/i>, while frequency is represented by \u03bd, the lowercase Greek letter nu<\/i> (although it looks like a Roman \u201cvee,\u201d it is actually the Greek equivalent of the letter \u201cen\u201d). Wavelength has units of length (metres, centimetres, etc.), while frequency has units of per second<\/i>, written as s\u22121<\/sup> and sometimes called a hertz<\/i> (Hz). Figure 8.21 \"Characteristics of Light Waves\" shows how these two characteristics are defined.\r\n
    \r\n\r\n[caption id=\"attachment_397\" align=\"aligncenter\" width=\"450\"]\"Diagrams<\/a> Figure 8.21 \"Characteristics of Light Waves.\" Light acts as a wave and can be described by a wavelength \u03bb and a frequency \u03bd.[\/caption]\r\n\r\nOne property of waves is that their speed is equal to their wavelength times their frequency. That means we have:\r\n\r\n\\[\\text{speed}=\\lambda\\nu\\]\r\n\r\nFor light, however, speed is actually a universal constant when light is travelling through a vacuum (or, to a very good approximation, air). The measured speed of light (c<\/i>) in a vacuum is 2.9979 \u00d7 108<\/sup> m\/s, or about 3.00 \u00d7 108<\/sup> m\/s. Thus, we have:\r\n\r\n\\[c=\\lambda \\nu\\]\r\n\r\nBecause 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.\r\n
    \r\n

    Example 8.7<\/p>\r\n\r\n<\/header>\r\n

    \r\n

    Problem<\/h1>\r\nWhat is the frequency of light if its wavelength is 5.55 \u00d7 10\u22127<\/sup> m?\r\n

    Solution<\/h2>\r\nWe use the equation that relates the wavelength and frequency of light with its speed. We have:\r\n\r\n\\[3.00\\times 10^8\\text{ m\/s}=(5.55\\times 10^{-7}\\text{ m})\\nu\\]\r\n\r\nWe divide both sides of the equation by 5.55 \u00d7 10\u22127<\/sup> m and get:\r\n\r\n\\[\\nu = 5.41\\times 10^{14}\\text{ s}^{-1}\\]\r\n\r\nNote how the m units cancel, leaving s in the denominator. A unit in a denominator is indicated by a \u22121 power \u2014 s\u22121<\/sup> \u2014 and read as \u201cper second.\u201d\r\n

    Test Yourself<\/h1>\r\nWhat is the wavelength of light if its frequency is 1.55 \u00d7 1010<\/sup> s\u22121<\/sup>?\r\n

    Answer<\/h2>\r\n0.0194 m, or 19.4 mm\r\n\r\n<\/div>\r\n<\/div>\r\nLight 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 (E<\/i>) of light to its frequency is:\r\n\r\n\\[E=h\\nu\\]\r\n\r\nWhere \u03bd is the frequency of the light, and h<\/i> is a constant called [pb_glossary id=\"1765\"]Planck\u2019s constant[\/pb_glossary]. Its value is 6.626 \u00d7 10\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.\r\n
    \r\n

    Example 8.8<\/p>\r\n\r\n<\/header>\r\n

    \r\n

    Problem<\/h1>\r\nWhat is the energy of light if its frequency is 1.55 \u00d7 1010<\/sup> s\u22121<\/sup>?\r\n

    Solution<\/h2>\r\nUsing the formula for the energy of light, we have:\r\n\r\n\\[E=(6.626\\times 10^{-34}\\text{ J}\\cdot \\text{s})(1.55\\times 10^{10}\\text{ s}^{-1})\\]\r\n\r\nSeconds are in the numerator and the denominator, so they cancel, leaving us with joules, the unit of energy. So:\r\n\r\n\\[E=1.03\\times 10^{-23}\\text{ J}\\]\r\n\r\nThis is an extremely small amount of energy \u2014 but this is for only one light wave.\r\n

    Test Yourself<\/h1>\r\nWhat is the frequency of a light wave if its energy is 4.156 \u00d7 10\u221220<\/sup> J?\r\n

    Answer<\/h2>\r\n6.27 \u00d7 1013<\/sup> s\u22121<\/sup>\r\n\r\n<\/div>\r\n<\/div>\r\nBecause a light wave behaves like a little particle of energy, light waves have a particle-type name: the [pb_glossary id=\"1766\"]photon[\/pb_glossary]. It is not uncommon to hear light described as photons.\r\n\r\nWavelengths, frequencies, and energies of light span a wide range; the entire range of possible values for light is called the [pb_glossary id=\"1767\"]electromagnetic spectrum[\/pb_glossary]. 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. Figure 8.22 \"The Electromagnetic Spectrum\" 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.\r\n\r\n[caption id=\"attachment_398\" align=\"aligncenter\" width=\"600\"]\"The<\/a> Figure 8.22 \"The Electromagnetic Spectrum.\" The electromagnetic spectrum, with its various regions labelled. The borders of each region are approximate.[\/caption]\r\n\r\n
    \r\n

    Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

    \r\n