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Electrons as Waves

Electrons as Waves. Characteristics of Waves. Wavelength The shortest distance between equivalent points on a continuous wave; either crest to crest or trough to trough Measured in m. Characteristics of Waves. Frequency

beverly-leblanc
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Electrons as Waves

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  1. Electrons as Waves

  2. Characteristics of Waves • Wavelength • The shortest distance between equivalent points on a continuous wave; either crest to crest or trough to trough • Measured in m

  3. Characteristics of Waves • Frequency • the number of waves that pass a given point per second; one hertz (Hz) equals one wave per second

  4. Characteristics of Waves • Amplitude • The wave's height from the origin to crest or origin to trough • Measured in m

  5. The Wave

  6. As shown in the formula, if wavelength increases, frequency decreases. As wavelength decreases, frequency increases.

  7. Electromagnetic Wave Relationship • speed = λ υ • c = speed of light = 3.00 x 108 m/s

  8. Sample Problem • If a gamma ray traveling at the speed of light has a frequency of 2.88 x 1021Hz, what is its wavelength? • speed = λ υ • 3.00 x 108 m/s = λ (2.88 x 1021 Hz) Answer: λ = 1.04 x 10-13 m

  9. Energy • Energy will increase as frequency increases • E = h υ • h is a constant = 6.626 x 10-34Js

  10. Sample Problem • A photon has an energy of 2.93 x 10 -25J. What is its frequency? • E = h υ • 2.93 x 10-25 J = (6.626x10-34Js) υ Answer: υ = 4.42 x 105 Hz or 442,000 Hz

  11. What about in this one? • What is the energy of an ultraviolet photon that has a wavelength of 1.18 x 10-8m? • E = h υ • But wait? Do we have frequency? No? So…Find it! • Speed = c = λ υ • 3.00 x 108m/s = (1.18 x 10-8m) υ • υ = 2.54 x 1016 • Now solve for the energy • E = (6.626 x 10-34 Js) (2.54 x 1016) • E = 1.68 x 10-17 J

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