What did Balmer do?physics.gsu.edu/dhamala/Phys2212/Slides/Chapter25.pdf · 37 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Energy is Quantized

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 25. Modern Optics and Matter

WavesThis image of the individual

atoms in a silicon crystal

was made by exploiting the

wave properties of electrons.

Sometimes, electrons act less

like particles and more like

traveling waves. This is an

important result of quantum

physics.

Chapter Goal: To explore

the limits of the wave and

particle models.2


Topics:

• Spectroscopy: Unlocking the Structure of

Atoms

• X-Ray Diffraction

• Photons

• Matter Waves

• Energy is Quantized

Chapter 25. Modern Optics and Matter

Waves

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Chapter 25. Reading Quizzes

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What did Balmer do?

A. Developed the mathematical theory

of atomic transitions.

B. Designed the first atomic spectrometer.

C. Fit the visible lines in the spectrum

of hydrogen to a simple formula.

D. Discovered that x rays are diffracted

by crystals.

E. Proposed a relation between the

frequency of an electromagnetic wave and

the energy of photons.

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What did Balmer do?

A. Developed the mathematical theory

of atomic transitions.

B. Designed the first atomic spectrometer.

C. Fit the visible lines in the spectrum

of hydrogen to a simple formula.

D. Discovered that x rays are diffracted

by crystals.

E. Proposed a relation between the

frequency of an electromagnetic wave and

the energy of photons.

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Light consists of discrete, massless

units called

A. quarks.

B. photons.

C. rotons.

D. muons.

E. phonons.

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Light consists of discrete, massless

units called

A. quarks.

B. photons.

C. rotons.

D. muons.

E. phonons.

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The first evidence for matter waves

was found in the

A. de Broglie experiment.

B. Einstein-Bohr experiment.

C. Millikan experiment.

D. Davisson-Germer experiment.

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The first evidence for matter waves

was found in the

A. de Broglie experiment.

B. Einstein-Bohr experiment.

C. Millikan experiment.

D. Davisson-Germer experiment.

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Which “particles” were seen

in this chapter to undergo

interference and diffraction?

A. Electrons.

B. Protons.

C. Neutrons.

D. Both A and B.

E. Both A and C.

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Which “particles” were seen

in this chapter to undergo

interference and diffraction?

A. Electrons.

B. Protons.

C. Neutrons.

D. Both A and B.

E. Both A and C.

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Chapter 25. Basic Content and Examples

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Spectroscopy: Unlocking the Structure of

Atoms

• Hot, self-luminous objects, such as the sun or an

incandescent lightbulb, emit a continuous spectrum

in which a rainbow is formed by light being emitted at

every possible wavelength.

• In contrast, the light emitted by a gas discharge tube (such

as those used to make neon signs) contains only certain

discrete, individual wavelengths. Such a spectrum is called

a discrete spectrum.

There are two types of spectra, continuous spectra and

discrete spectra:

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The Spectrum of Hydrogen

• Hydrogen is the simplest atom, with one electron orbiting

a proton, and it also has the simplest atomic spectrum.

• The emission lines have wavelengths which correspond to

two integers, m and n.

• Every line in the hydrogen spectrum has a wavelength

given by

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X-Ray Diffraction

The figure shows a simple cubic

lattice of atoms. The crystal structure

of most materials is more complex

than this, but a cubic lattice will help

you understand the ideas of

x-ray diffraction.

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X-Ray Diffraction

• The wave reflecting from any particular plane travels an

extra distance ∆r = 2d cosθ before combining with the

reflection from the plane immediately above it, where d is

the spacing between the atomic planes.

• If ∆r = mλ, these two waves will be in phase when they

recombine.

• Consequently, x rays will strongly reflect from the crystal

when the angle of incidence θm satisfies

Equation 25.3 is called the Bragg condition.

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EXAMPLE 25.1 Analyzing x-ray diffraction

QUESTION:

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The Photon Model of Light

The photon model of light consists of three basic

postulates:

1. Light consists of discrete, massless units called

photons. A photon travels in vacuum at the speed of

light, 3.00 × 108 m/s.

2. Each photon has energy

where f is the frequency of the light and h is a universal

constant called Planck’s constant. The value of Planck’s

constant is h = 6.63 × 10–34 J s.

3. The superposition of a sufficiently large number of

photons has the characteristics of a classical light wave.

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EXAMPLE 25.2 The energy of a photon

QUESTIONS:

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Matter Waves

• In 1927 Davisson and Germer were studying how

electrons scatter from the surface of metals.

• They found that electrons incident normal to the crystal

face at a speed of 4.35 × 106 m/s scattered at ø = 50°.

• This scattering can be interpreted as a mirror-like

reflection from the atomic planes that slice diagonally

through the crystal.

• The angle of incidence on this set of planes is the angle θm

in 2d cos θm = mλ, the Bragg condition for diffraction.

• Davisson and Germer found that the “electron

wavelength” was

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The de Broglie Wavelength

De Broglie postulated that a particle of mass m and

momentum p = mv has a wavelength

where h is Planck’s constant. This wavelength for material

particles is now called the de Broglie wavelength. It

depends inversely on the particle’s momentum, so the

largest wave effects will occur for particles having the

smallest momentum.

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EXAMPLE 25.4 The de Broglie wavelength of

an electron

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an electron

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an electron

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Energy is Quantized

• Consider a particle of mass m confined inside a rigid box

of length L.

• Collisions with the ends of the box are perfectly elastic,

with no loss of kinetic energy.

• Since particles have wave-like properties, we should

consider a wave reflecting back and forth from the ends of

the box.

• The reflections create a standing wave.

• The wavelength of a standing wave is related to the length

L of the confining region by

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Energy is Quantized

Relating wavelength to momentum by using the de Broglie

equation, the discrete values of wavelength of the particle

in the box lead to discrete values of momentum, and

discrete levels of energy

A confined particle can only have certain energies. This is

called the quantization of energy. The number n is called

the quantum number; each value of n characterizes one

energy level of the particle in the box.

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EXAMPLE 25.6 The minimum energy of an

electron

QUESTION:

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electron

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electron

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Chapter 25. Summary Slides

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General Principles

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General Principles

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Important Concepts

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Important Concepts

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Important Concepts

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Applications

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Applications

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Chapter 25. Questions

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The first-order diffraction of

monochromatic x rays from crystal A

occurs at an angle of 20°. The first-order

diffraction of the same x rays from

crystal B occurs at 30°. Which crystal has

the larger atomic spacing?

A. Crystal A

B. Crystal B

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The first-order diffraction of

monochromatic x rays from crystal A

occurs at an angle of 20°. The first-order

diffraction of the same x rays from

crystal B occurs at 30°. Which crystal has

the larger atomic spacing?

A. Crystal A

B. Crystal B

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Does a photon of red light have

more energy or less energy than a

photon of blue light?

A. More energy

B. Less energy

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Does a photon of red light have

more energy or less energy than a

photon of blue light?

A. More energy

B. Less energy

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A proton, an electron and an oxygen

atom each pass at the same speed

through a 1-µm-wide slit. Which will

produce a wider diffraction pattern on a

detector behind the slit?

A.The oxygen atom.

B.The proton.

C.The electron.

D.All three will be the same.

E. None of them will produce a diffraction pattern.

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atom each pass at the same speed

through a 1-µm-wide slit. Which will

produce a wider diffraction pattern on a

detector behind the slit?

A.The oxygen atom.

B.The proton.

C.The electron.

D.All three will be the same.

E. None of them will produce a diffraction pattern.

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atom are each confined in a 1-nm-long

box. Rank in order, from largest to

smallest, the minimum possible

energies of these particles.

A. EO > EC > EH

B. EH > EC > EO

C. EO > EH > EC

D. EC > EO > EH

E. EH > EO > EC

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atom are each confined in a 1-nm-long

box. Rank in order, from largest to

smallest, the minimum possible

energies of these particles.

A. EO > EC > EH

B. EH > EC > EO

C. EO > EH > EC

D. EC > EO > EH

E. EH > EO > EC

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What did Balmer do?physics.gsu.edu/dhamala/Phys2212/Slides/Chapter25.pdf · 37 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Energy is Quantized