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The energy of the electromagnetic spectrum moves through space as waves that have three associated variables frequency, wavelength, and amplitude The frequency, n, is the number of waves that pass a point per second Wavelength, l, is the distance between two identical points on a wave Amplitude is the height of the wave and is related to the intensity (or brightness, for visible light) of the wave Figure 102 shows the wavelength and amplitude of a wave The energy associated with a certain frequency of light is related by the equation: E = hn where h is Planck s constant = 663 10
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In developing the quantum mechanical model of the atom, it was found that the electrons can have only certain distinct quantities of energy associated with them, and that in order for the atom to change its energy it has to absorb or emit a certain amount of energy The energy that is emitted or absorbed is really the difference in the two energy states and can be calculated by: E = hn
8 All electromagnetic radiation travels at about the same speed in a vacuum, 30 10 m/s This constant is called the speed of light (c) The product of the frequency and the wavelength is the speed of light:
c = nl Let s apply some of the relationships What wavelength of radiation has photons of 19 energy 783 10 J
Wavelength l
Amplitude
Wavelength and amplitude of a wave
Spectroscopy, Light, and Electrons 139
Answer: Using the equations E = hn we get n = E/h Inserting the appropriate values: n = E/h = 783 10 Then: l = c/n = (30 108 m/s)/(118 1015s 1) = 25 10 7m This answer could have been calculated more quickly by combining the original two equations to give: l = hc / E
and and
c = nl l = c /n
J/663 10 34 Js = 118 1015 s 1
Wave Properties of Matter
The concept that matter possesses both particle and wave properties was first postulated by de Broglie in 1925 He introduced the equation l = h/mv, which indicates a mass (m) moving with a certain velocity (v) would have a specific wavelength (l) associated with it (Note that this v is the velocity not the frequency) If the mass is very large (a locomotive), the associated wavelength is insignificant However, if the mass is very small (an electron), the wavelength is measurable The denominator may be replaced with the momentum of the particle (p = mv)
Atomic Spectra
Late in the 19th century scientists discovered that when the vapor of an element was heated it gave off a line spectrum, a series of fine lines of colors instead of a continuous spectrum like a rainbow This was used in the developing quantum mechanical model as evidence that the energy of the electrons in an atom was quantized, that is, there could only be certain distinct energies (lines) associated with the atom Niels Bohr developed the first modern atomic model for hydrogen using the concepts of quantized energies The Bohr model postulated a ground state for the electrons in the atom, an energy state of lowest energy, and an excited state, an energy state of higher energy In order for an electron to go from its ground state to an excited state, it must absorb a certain amount of energy If the electron dropped back from that excited state to its ground state, that same amount of energy would be emitted Bohr s model also allowed scientists to develop a method of calculating the energy associated with a particular energy level for the electron in the hydrogen atom: 2 18 10 18 joule n2 where n is the energy state This equation can then be modified to calculate the energy difference between any two energy levels: En = 1 1 E = 2 18 10 18 J 2 2 n final ninitial
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