C1210 lecture 18

C1210 lecture 18 - Electrons are particles Electrons in...

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• Electrons are particles • Electrons in atoms don’t behave exactly like particles. • Electromagnetic radiation is a wave. • Electrons in atoms also behave like waves, matter waves. • Electrons exhibit “wave-matter duality”; they have characteristics of both… Louis de Broglie “duhBROee” proposed that particles as well as waves have wavelengths: Note that when a particle is massive, its wavelength is immeasurably small. When a particle is small (like an electron) its wavelength may become sufficiently large to interact with other objects and waves. Can we demonstrate that particles can behave like waves? How DO waves behave? m s m kg s s m kg s m kg s J mv h = = = 2 2 λ
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Waves interfere with one another when they overlap. The phases of the waves when they overlap determines how they combine. (a) In phase: constructive interference (b) Out of phase: destructive interference. (c) Light waves passing through two pinholes and interfering.
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Diffraction patterns formed from (a) electrons passing through a Si crystal and (b) electrons passing through a double slit and interfering with each other, like waves.
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A traveling wave moves like a wave in the ocean. The wave moves along the surface, but the water just moves up and down with no net motion after the wave has passed. Types of waves: A standing wave is like a vibrating guitar string. The ends are fixed (nodes) and fixed locations on the string move up and down. We’re going to beat the guitar string analogy to death, so bear with me. .. Ends fixed: entire half- wavelength middle and ends fixed: 2 × frequency, ½ half- wavelength 3 × frequency, half- wavelength 4 × frequency, ¼ half- wavelength
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Generally, where L is the length of the string and λ is the wavelength: = 2 λ n L or, solving for λ : n L 2 = where n is a “quantum number”.
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This note was uploaded on 12/10/2009 for the course CHE 1220 taught by Professor Jespersen during the Spring '09 term at St. John's.

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C1210 lecture 18 - Electrons are particles Electrons in...

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