c101-lecture-7 - Light We can use different terms to...

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2/28/11 1 Light We can use different terms to describe light: L Color L Wavelength L Frequency Light is composed of electromagnetic waves that travel through some medium. The properties of the medium determine how light travels through it. In a vacuum, light waves travel at a speed of 3.00 x 10 8 m/s or 186,000 miles/s. The speed of light in a vacuum is a constant that is tremendously important in nature and science—it is given the symbol c. Light (con t.) Because light behaves like a wave, we can describe it in one of two ways—by its wavelength or by its frequency. λ = wavelength—distance between two adjacent wave crests. λ has units of distance—frequently nanometers (nm). ν = frequency—how many times the wave goes up and down in a period of time. ν has units of inverse time (1/s Hz[hertz]). λ Light (con t.) If you know either the frequency or the wavelength, you can calculate the other quantity through the relationship: c = λ - ν c = speed of light (3.00 x 10 8 m/s) λ = wavelength (m) ν = frequency (s -1 ) A particle of light is called a photon. Examples Diode laser pointer: λ = 670 nm 670 nm = 670 x 10 -9 m ν = ν = 4.3 x 10 13 Hz Hz 10 x 4.48 m 10 x s m 10 x 3.00 c 14 9 - 1 - 8 = = λ 670 nm 6980 m 6.98 m 10 x 6.98 s 10 x 4.3 s m 10 x 3.00 c 6 - 1 - 13 1 - 8 = μ = = = ν = λ Light (con t.) The type of light (ultraviolet, visible, infrared, x-ray, etc.) is defined by either its frequency or wavelength: 10 3 m 10 2 Hz wavelength frequency gamma rays x-rays ultraviolet infrared microwave radio waves 10 -5 nm 10 -3 nm 1 nm 400 nm 700 nm 10 3 nm 10 6 nm 1 m 10 24 Hz 10 16 Hz 10 12 Hz 10 10 Hz 10 8 Hz 10 6 Hz 10 4 Hz 10 22 Hz 10 20 Hz 10 18 Hz visible light 7 x 10 14 Hz 4 x 10 14 Hz Light (con t.) The energy of light can be determined either from its wavelength or frequency: ν = λ = h E or c h E Planck s constant: h = 6.626 x 10 -34 J s
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2/28/11 2 Examples 4.3 x 10 13 Hz ( ν ) light: E = (6.626 x 10 -34 J s)(4.3 x 10 13 s -1 ) = 2.85 x 10 -20 J = (2.85 x 10 -20 J) (6.022 x 10 23 mol -1 ) = 17.2 kJ mol -1 1 mole = 6.022 x 10 23 things (atoms, molecules, photons, etc.) 670 nm ( λ ) diode laser: E = (6.626 x 10 -34 J s)(3.00 x 10 8 m s -1 ) = 2.97 x 10 -19 J (670 x 10 -9 m) = (2.97 x 10 -19 J) (6.022 x 10 23 mol -1 ) = 179 kJ mol -1 L Atoms and molecules absorb and emit light in the ultraviolet (UV), visible (vis), infrared (IR), and microwave ( μ wave) regions of the electromagnetic spectrum. L Absorption or emission of light in the UV and visible regions involves movement of electrons in the atom or molecule. L One reason UV light is so damaging is that the light has enough energy to break chemical bonds—biological and chemical systems L E ( λ = 300 nm) = 399 kJ mol L Average C-H bond energy = 380 kJ mol -1 Hydrogen Atom Spectrum It was known for a long time that the spectrum of the hydrogen atom displayed a series of discrete lines: Hydrogen Atom Spectrum It was known for a long time that the spectrum of the hydrogen atom displayed a series of discrete lines: The Balmer Series was found to obey the formula: ... 5, 4, 3, n m 10 x 1.0974 R n 1 - 2 1 R c 1 1 - 7 H 2 2 H = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ν = λ Hydrogen Atom Spectrum ... 7, 6, 5, n , m 10 x 1.0974 R , n 1 - 4 1 R c 1 1 - 7 H 2 2 H = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ν = λ
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