Wave-particle duality

Question 1

Monoenergetic electrons used for diffraction so that

Answer 1

electrons have same kinetic energy and so same velocity and so same de Broglie wavelength and so same amount of diffraction

Question 2

Electron beam double slit diffraction: Intensity decreases but time increases so

Answer 2

same number of electrons pass through, images are the same/no change

Question 3

What was de Broglie’s theory

Answer 3

if wave-like like showed particle properties (photons), then particles like electrons should show wave-like properties such as wavelength = h/p = h/mv which relates a wave property (wavelength) to a moving particle property (momentum)

Question 4

Wave nature of electrons

Answer 4

produces interference and diffraction patterns – alternating bands of dark and light. Can only be explained using waves interfering constructively (in phase) or destructively (out of phase)

Question 5

Particle nature of electrons

Answer 5

Electron beams are deflected by an electric field.

Question 6

Wave theory and particle theory model the behaviour of light but do not describe what it actually is

Answer 6

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Question 7

First direct evidence of the wave nature of electrons

Answer 7

low energy electron diffraction by graphite crystals

Question 8

Explain electron diffraction experiment

Answer 8

• Monoenergetic electrons accelerated in a vacuum tube towards graphite crystals
• They interacted and formed a diffraction pattern – concentric circles
• Wave theory predicts the spread of the circles in the diffraction pattern increases if the wavelength increases
• Increasing the accelerating voltage increases the speed of the electrons and caused the circles to squash together because the wavelength decreases so the spread is smaller as described by the de Broglie equation

Question 9

Why doesn’t the wave-nature of particles occur all the time:

Answer 9

Particle diffraction only occurs if the particle interacts with an object of about the same size as its de Broglie wavelength (or with crystal spacing’s of similar size)

Question 10

Estimate of anode voltage needed to produce wavelengths of the order of the size of atom:

Answer 10

• If the size of the atom is roughly 0.1nm, then an anode voltage of around 150V is needed

Question 11

Why are electron beams better at probing structures compared to X-rays:

Answer 11

• Wavelength of electrons can be easily reduced by increasing electron gun’s anode voltage
• This allows electrons to probe structures that are too small to be probed by X-rays
• So more accurate method that X-ray scattering through graphite structures

Question 12

Speed of electrons equation:

Answer 12

• For electrons produced by thermionic emission, the speed v of the electrons depends on the anode potential VA in accordance with the equation ½ mv2 = eV,
• assuming v &laquo_space;c.
• Giving lambda^2 = h^2/2meV

Question 13

Explain the electron diffraction image:

Answer 13

• Concentric circles on a fluorescent screen
• Bright circular rings = constructive interference = maxima
• Larger wavelength = wider ring spacing
• Amount of diffraction determined by: dsinX = nlambda