1. De Broglie wavelengths
Contents:
de Broglie wavelengths
Example 1
Whiteboards
Transmission electron microscopes
Scanning electron microscopes
Scanning tunneling electron microscopes

2. Louis de Broglie Light is acting as both particle and wave
Matter perhaps does also
E = hf = hc/
E = mc2
mc2 = hc/
mc = p = h/
p = momentum (p = mv)
h = Planck’s constant (6.626 x Js)
 = de Broglie wavelength
TOC

3. Davisson-Germer
(Interference)

4. h = Planck’s constant (6.626 x 10-34 Js)  = de Broglie wavelength
p = momentum (p = mv)
h = Planck’s constant (6.626 x Js)
 = de Broglie wavelength
Example 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/s
p = h/,  = h/p = (6.626 x Js)/(20. kg m/s)
= 3.31 x m
Golly - nothing is that small (atoms are m)
How would you observe the wave behaviour of that?
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5. p = h/ = (6.626E-34 Js)/(1.0E-9 m) = 6.626E-25 kg m/s
p = momentum (p = mv)
h = Planck’s constant
(6.626 x Js)
 = de Broglie wavelength
Ve = 1/2mv2
V = accelerating voltage (V)
e = elementary charge
(1.602x10-19 C)
m = particle mass (kg)
v = velocity (m/s)
Example 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/s
p = mv, v = p/m = (6.626E-25 kg m/s)/(9.11E-31 kg) = m/s
Ve = 1/2mv2, V = 1/2mv2/e =
1/2(9.11E-31 kg)( m/s)2/(1.602E-19 C) = V

6. Whiteboards:
de Broglie Wavelength
1 | 2 | 3 | 4 | 5
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7. What is the de Broglie wavelength of an electron going 1800 m/s? (3)
m = 9.11 x kg
p = mv
p = h/
p = (9.11 x kg)(1800 m/s) = x kg m/s
 = h/p = (6.626 x Js)/( x kg m/s)
= 404 nm W
404 nm

8. What is the momentum of a 600. nm photon?
p = (6.626 x Js)/(600. x 10-9 m) = 1.10 x kg m/s W
1.10 x kg m/s

9. Electrons in a microscope are accelerated through 12. 8 V
Electrons in a microscope are accelerated through 12.8 V. What de Broglie wavelength will they have?
p = h/ Ve = 1/2mv2
Ve = 1/2mv2, v2 = 2Ve/m,
v = √(2(12.8 V)(1.602E-19 C)/(9.11E-31 kg)) = m/s
p = h/,  = h/p = h/mv =
(6.626E-34 Js)/((9.11E-31 kg)( m/s)) = 3.428E-10 m W
3.428E-10 m

10. You 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)
p = h/ = (6.626E-34 Js)/(.68 m) = E-34 kg m/s
p = mv, v = p/m = (6.626E-25 kg m/s)/(9.11E-31 kg)
= m/s
Ve = 1/2mv2, V = 1/2mv2/e =
1/2(9.11E-31 kg)( m/s)2/(1.602E-19 C)
= E-18 V W
E-18 V

11. A 300. MW 620. nm laser is putting out 9. 36 x 1026 photons per second
A 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)
for 1 photon: p = h/
for 5 photons: 5p = 5h/
p = (6.626 x Js)/(620. x 10-9 m) = x kg m/s
total p change = (9.36 x 1026 )( x kg m/s) = 1.00 N W
1.00 N

12. Applications of “matter” waves
Electron Microscopes
Image resolution  
 = h/p
Electric or magnetic lenses
Gertrude Rempfer (PSU)
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14. Scanning electron microscope

18. 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.

22. Spider Web

23. Cat Hair

24. Cat Hair

25. Scanning tunneling electron microscope
Actually can image atoms and molecules
(Novellus)

26. Wave behaviour Particle behaviour
Soooo – Is/are Light/electrons a wave or particle?????
Wave behaviour
Particle behaviour
Complementarity/Duality
Wave XOR Particle behaviour explains the behavior.
Behaviour depends on situation. (Other particle interactions)

27. Cat Hair