# de broglie wavelengths contents: de broglie wavelengths example 1 whiteboards

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De Broglie wavelengths Contents: de Broglie wavelengths Example 1 Whiteboards Transmission electron microscopes Scanning electron microscopes Scanning tunneling electron microscopes. Louis de Broglie. p = momentum (p = mv) h = Planck’s constant (6.626 x 10 -34 Js) - PowerPoint PPT Presentation

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• De Broglie wavelengths

Contents:de Broglie wavelengthsExample 1WhiteboardsTransmission electron microscopesScanning electron microscopesScanning tunneling electron microscopes

• Louis de BroglieTOCLight is acting as both particle and waveMatter perhaps does alsoE = hf = hc/E = mc2mc2 = hc/mc = p = h/

• Davisson-Germer(Interference)

• TOCExample 1: What is the de Broglie wavelength of a .50 kg ball going 40. m/s?

p = mv = (.50 kg)(40. m/s) = 20. kg m/sp = h/, = h/p = (6.626 x 10-34 Js)/(20. kg m/s)= 3.31 x 10-35 mGolly - nothing is that small (atoms are 10-10 m)How would you observe the wave behaviour of that?

• p = h/p = momentum (p = mv)h = Plancks constant (6.626 x 10-34 Js) = de Broglie wavelengthExample 2: Through what potential must you accelerate an electron so that it has a wavelength of 1.0 nm?

p = h/ = (6.626E-34 Js)/(1.0E-9 m) = 6.626E-25 kg m/sp = mv, v = p/m = (6.626E-25 kg m/s)/(9.11E-31 kg) = 727332.6 m/sVe = 1/2mv2, V = 1/2mv2/e = 1/2(9.11E-31 kg)(727332.6 m/s)2/(1.602E-19 C) = 1.504 VVe = 1/2mv2V = accelerating voltage (V)e = elementary charge (1.602x10-19 C)m = particle mass (kg)v = velocity (m/s)

• Whiteboards: de Broglie Wavelength1 | 2 | 3 | 4 | 5TOC

• 404 nmWm = 9.11 x 10-31 kgp = mvp = h/p = (9.11 x 10-31 kg)(1800 m/s) = 1.6398 x 10-27 kg m/s = h/p = (6.626 x 10-34 Js)/(1.6398 x 10-27 kg m/s)= 404 nmWhat is the de Broglie wavelength of an electron going 1800 m/s? (3)

• 1.10 x 10-27 kg m/sWp = h/p = (6.626 x 10-34 Js)/(600. x 10-9 m) = 1.10 x 10-27 kg m/sWhat is the momentum of a 600. nm photon?

• 3.428E-10 mWp = h/ Ve = 1/2mv2Ve = 1/2mv2, v2 = 2Ve/m, v = (2(12.8 V)(1.602E-19 C)/(9.11E-31 kg)) = 2121739.443 m/sp = h/, = h/p = h/mv = (6.626E-34 Js)/((9.11E-31 kg)(2121739.443 m/s)) = 3.428E-10 mElectrons in a microscope are accelerated through 12.8 V. What de Broglie wavelength will they have?

• 3.25293E-18 VWp = h/ = (6.626E-34 Js)/(.68 m) = 9.74412E-34 kg m/sp = mv, v = p/m = (6.626E-25 kg m/s)/(9.11E-31 kg) = 0.001069607 m/sVe = 1/2mv2, V = 1/2mv2/e = 1/2(9.11E-31 kg)(0.001069607 m/s)2/(1.602E-19 C) = 3.25293E-18 VYou want to use an electron to have the same wavelength as the waves on a violin string. Through what potential do you accelerate them. (violin strings are about 34 cm long, so the fundamental is about .68 m long)

• 1.00 NWfor 1 photon: p = h/for 5 photons: 5p = 5h/p = (6.626 x 10-34 Js)/(620. x 10-9 m) = 1.0687 x 10-27 kg m/stotal p change = (9.36 x 1026 )(1.0687 x 10-27 kg m/s) = 1.00 NA 300. MW 620. nm laser is putting out 9.36 x 1026 photons per second. since F = p/t, and t = 1 second, what is the total thrust of the laser? (2)

• Applications of matter wavesTOCElectron MicroscopesImage resolution = h/pElectric or magnetic lensesGertrude Rempfer (PSU)

• Scanning electron microscope

• Scanning tunneling electron microscopeActually can image atoms and molecules(Novellus)

• Soooo Is/are Light/electrons a wave or particle?????Particle behaviourWave behaviourComplementarity/DualityWave XOR Particle behaviour explains the behavior.Behaviour depends on situation. (Other particle interactions)

• *The fossilized shell of a microscopic ocean animal is magnified 392 times its actual size. The ancient creature, called Radiolarian, lived in the waters off Antarctica and is now used to study such things as climate and ocean circulation. *Spider Web*Cat Hair

*Cat Hair

*Cat Hair

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