38 The Atom and the Quantum

38 The Atom and the Quantum

Material particles and light have both wave properties and particle properties.


Atomic structure is revealed by analyzing light. Light has a dual nature, which in turn radically alters our understanding of the atomic world.


38.1

Models

Through the centuries there have been two primary models of light: the particle model and the wave model.


38.1

Models

Nobody knows what an atom’s internal structure looks like, for there is no way to see it with our eyes.

To visualize the processes that occur in the subatomic realm, we construct models.

The planetary model in which electrons orbit the nucleus was suggested by the Danish physicist

Niels Bohr in 1913. It is still useful for understanding the emission of light.


38.1

Models

The planetary model has been replaced by a more complex model in which the electrons are represented as clouds.


38.1

Models

Models help us to understand processes that are difficult to visualize.

A useful model of the atom must be consistent with a model for light.

Most of what we know about atoms we learn from the light and other radiations they emit.

Most light comes from the motion of electrons within the atom.


38.1

Models

There have been two primary models of light: the particle model and the wave model.

• Isaac Newton believed light was composed of tiny particles.

• Christian Huygens believed that light was a wave phenomenon.


38.1

Models

The wave model was reinforced when Thomas

Young demonstrated constructive and destructive interference of light.

Later, James Clerk Maxwell proposed that light is an electromagnetic wave.

The wave model gained further support when

Heinrich Hertz produced radio waves that behaved as Maxwell had predicted.

In 1905, Albert Einstein resurrected the particle theory of light.


38.1

Models

What are the two primary models of light?


38.2

Light Quanta

The energy of a photon is directly proportional to the photon’s frequency.


38.2

Light Quanta

Einstein visualized particles of light as concentrated bundles of electromagnetic energy.

Max Planck had proposed that atoms do not emit and absorb light continuously, but do so in little chunks.

Each chunk was considered a quantum, or a fundamental unit.


38.2

Light Quanta

Planck believed that light existed as continuous waves, but that emission and absorption occurred in quantum chunks.

Einstein went further and proposed that light itself is composed of quanta.

One quantum of light energy is now called a photon.


38.2

Light Quanta

Matter is quantized, equal to some whole-number multiple of the mass of a single atom.

Electric charge is quantized as a multiple of the charge of a single electron.

Other quantities such as energy and angular momentum are quantized.


38.2

Light Quanta

The energy in a light beam is quantized and comes in packets, or quanta; only a whole number of quanta can exist.

• The quanta of electromagnetic radiation are the photons.

• Photons have no rest energy.

• They move at the speed of light so the total energy of a photon is the same as its kinetic energy.


38.2

Light Quanta

The energy of a photon of light is proportional to its vibrational frequency.

• When the energy E of a photon is divided by its frequency f, the quantity that results is known as Planck’s constant, h.

• This quantity is always the same, no matter what the frequency.

• The energy of every photon is therefore E = hf .

• This equation gives the smallest amount of energy that can be converted to light of frequency f.


38.2

Light Quanta

How is the energy of a photon related to its frequency?


38.3

The Photoelectric Effect

The photoelectric effect suggests that light interacts with matter as a stream of particle-like photons.


38.3


Einstein found support for his quantum theory of light in the photoelectric effect.

The photoelectric effect is the ejection of electrons from certain metals when light falls upon them.

These metals are said to be photosensitive .


38.3


Explanation of the Photoelectric Effect

Energy from the light shining on a metal plate gives electrons bound in the metal enough energy to escape.

• High-frequency light, even from a dim source, is capable of ejecting electrons from a photosensitive metal surface.

• Low-frequency light, even from a very bright source, cannot dislodge electrons.

• Since bright light carries more energy than dim light, it was puzzling that dim blue light could dislodge electrons when bright red light could not.


38.3


Einstein explained the photoelectric effect in terms of photons.

• The absorption of a photon by an atom in the metal surface is an all-or-nothing process.

• Only one photon is absorbed by each electron ejected from the metal.

• The number of photons that hit the metal has nothing to do with whether a given electron will be ejected.

• If the energy in the photon is large enough, the electron will be ejected from the metal.


38.3


The intensity of light does not matter. From E = hf , the critical factor is the frequency, or color, of the light.

• Each blue or violet light photon carries enough energy to free an electron from the metal.

• A few photons of blue or violet light can eject a few electrons. Many red or orange photons cannot eject a single electron.

• Only high-frequency photons have the energy needed to pull loose an electron.


38.3


Support for the Particle Model of Light

The energy of a wave is spread out along a broad front.

For the energy of a light wave to be concentrated enough to eject a single electron from a metal surface is unlikely.

The photoelectric effect suggests that light interacts with matter as a stream of particle-like photons.


38.3


The number of photons in a light beam controls the brightness of the whole beam.

The frequency of the light controls the energy of each individual photon.

Experimental verification of Einstein’s explanation was made

11 years later by the American physicist Robert Millikan.

Every aspect of Einstein’s interpretation was confirmed, including the direct proportionality of photon energy to frequency.


38.3

The Photoelectric Effect think!

Will high-frequency light eject a greater number of electrons than low-frequency light?


38.3

The Photoelectric Effect think!

Will high-frequency light eject a greater number of electrons than low-frequency light?

Answer:

Not necessarily. The answer is yes if electrons are ejected by the high-frequency light but not by the low-frequency light, because its photons do not have enough energy. If the light of both frequencies can eject electrons, then the number of electrons ejected depends on the brightness of the light, not on its frequency.


38.3


What does the photoelectric effect suggest about the way light interacts with matter?


38.4

Waves as Particles

Light behaves like waves when it travels in empty space, and like particles when it interacts with solid matter.


38.4


A photograph taken with exceedingly feeble light provides a striking example of the particle nature of light.

The image progresses photon by photon.

Photons seem to strike the film in an independent and random manner.


38.4


What causes light to behave like a wave? Like a particle?


38.5

Particles as Waves

De Broglie suggested that all matter could be viewed as having wave properties.


38.5


If waves can have particle properties, cannot particles have wave properties?

This question was posed by the French physicist Louis de

Broglie and his answer later won the Nobel Prize in physics.

De Broglie suggested that all matter could be viewed as having wave properties.


38.5


All particles —electrons, protons, atoms, marbles, and even humans —have a wavelength: where h is Planck’s constant.


38.5


The wavelength of a particle is called the de Broglie wavelength.

• A particle of large mass and ordinary speed has too small a wavelength to be detected by conventional means.

• A tiny particle—such as an electron—moving at typical speed has a detectable wavelength.


38.5


The wavelength of electrons is smaller than the wavelength of visible light but large enough for noticeable diffraction.

A beam of electrons can be diffracted and undergoes wave interference under the same conditions that light does.


38.5

Particles as Waves a. The diffraction of an electron beam produces an interference pattern.


38.5

Particles as Waves a. The diffraction of an electron beam produces an interference pattern.

b. The fringes produced by a beam of light are very similar to those produced by the beam of electrons.


38.5


An electron microscope uses the wave nature of electrons.

• The wavelength of electron beams is typically thousands of times shorter than the wavelength of visible light.

• The electron microscope is able to distinguish details thousands of times smaller than is possible with optical microscopes.


38.5


What did de Broglie suggest about all matter?


38.6

Electron Waves

According to de Broglie’s theory of matter waves, electron orbits exist only where an electron wave closes in on itself in phase.


38.6

Electron Waves

The planetary model of the atom was useful in explaining the atomic spectra of the elements and why elements emitted only certain frequencies of light.

• An electron has different amounts of energy when it is in different orbits around a nucleus.

• An electron is in a different energy level when it is in a different orbit.

• Electrons in an atom normally occupy the lowest energy levels available.


38.6

Electron Waves

In the Bohr model of the atom, the electron orbits correspond to different energy levels.


38.6

Electron Waves

Bohr Model Explanation of Atomic Spectra

An electron can be boosted to a higher energy level.

• This occurs in gas discharge tubes such as neon signs.

• Electric current boosts electrons of the gas to higher energy levels.

• As the electrons return to lower levels, photons are emitted.

• The energy of a photon is exactly equal to the difference in the energy levels in the atom.


38.6

Electron Waves

The pattern of lines in the spectrum of an element corresponds to electron transitions between the energy levels of the atoms of that element.

By examining spectra, physicists were able to determine the various energy levels in the atom.


38.6

Electron Waves

Why were electrons at discrete distances from the atomic nucleus?

This was resolved by thinking of the electron not as a particle whirling around the nucleus but as a wave.

According to de Broglie’s theory of matter waves, electron orbits exist only where an electron wave closes in on itself in phase.


38.6

Electron Waves

De Broglie’s Theory

The electron wave reinforces constructively in each cycle, like the standing wave on a music string.

The electron is visualized not as a particle located at some point in the atom.

• Its mass and charge are spread throughout a standing wave surrounding the nucleus.

• The wavelength of the electron wave must fit evenly into the circumferences of the orbits.


38.6

Electron Waves

De Broglie suggested electrons have a wavelength. a. Electron orbits exist only when the circumference of the orbit is a whole-number multiple of the wavelength.


38.6

Electron Waves

De Broglie suggested electrons have a wavelength. a. Electron orbits exist only when the circumference of the orbit is a whole-number multiple of the wavelength. b. When the wave does not close in on itself in phase, it undergoes destructive interference.


38.6

Electron Waves

The circumference of the innermost orbit, according to this model, is equal to one wavelength of the electron wave.

The second orbit has a circumference of two electron wavelengths, the third three, and so on.


38.6

Electron Waves

Orbit circumferences are wholenumber multiples of the electron wavelengths, which differ for the various elements.

This results in discrete energy levels, which characterize each element.

Since the circumferences of electron orbits are discrete, the radii of these orbits, and hence the energy levels, are also discrete.


38.6

Electron Waves

In this simplified version of de Broglie’s theory of the atom, the waves are shown only in circular paths around the nucleus. In an actual atom, the standing waves make up spherical and ellipsoidal shells rather than flat, circular ones.


38.6

Electron Waves

This explains why electrons do not spiral closer and closer to the nucleus when photons are emitted.

Since an orbit is described by a standing wave, the circumference of the smallest orbit can be no smaller than one wavelength.

In the modern wave model of the atom, electron waves also move in and out, toward and away from the nucleus.

The electron wave is in three dimensions, an electron “cloud.”


38.6

Electron Waves

How did de Broglie’s theory of matter waves describe electron orbits?


38.7

Relative Sizes of Atoms

The radii of the electron orbits in the Bohr model of the atom are determined by the amount of electric charge in the nucleus.


38.7


The single proton in the hydrogen atom holds one negatively charged electron in an orbit at a particular radius.

In helium, the orbiting electron would be pulled into a tighter orbit with half its former radius since the electrical attraction is doubled.

This doesn’t quite happen because the double-positive charge in the nucleus attracts and holds a second electron.

The negative charge of the second electron diminishes the effect of the positive nucleus.


38.7


This added electron makes the atom electrically neutral.

The two electrons assume an orbit characteristic of helium.

In a lithium atom, an additional proton pulls the electrons into an even closer orbit and holds a third electron in a second orbit.


38.7


As the nuclear charge increases, the inner orbits shrink because of the stronger electrical attraction to the nucleus.

This means that the heavier elements are not much larger in diameter than the lighter elements.

The diameter of the uranium atom, for example, is only about three hydrogen diameters, even though it is 238 times more massive.


38.7


Each element has a unique arrangement of electron orbits.

The radii of orbits for the sodium atom are the same for all sodium atoms, but different from the radii of orbits for other kinds of atoms.

Each element has its own distinct orbits.


38.7


The Bohr model solved the mystery of the atomic spectra of the elements.

It accounted for X-rays that were emitted when electrons made transitions from outer orbits to innermost orbits.

Bohr was able to predict X-ray frequencies that were later experimentally confirmed.


38.7


Bohr calculated the ionization energy of the hydrogen atom —the energy needed to knock the electron out of the atom completely.

This also was verified by experiment.

The model accounted for the chemical properties of the elements and predicted properties of hafnium, which led to its discovery.


38.7


Bohr was quick to point out that his model was to be interpreted as a crude beginning.

The picture of electrons whirling like planets about the sun was not to be taken literally.

His discrete orbits were conceptual representations of an atom whose later description involved a wave description.


38.7

Relative Sizes of Atoms a. In the Bohr model, the electrons orbit the nucleus like planets going around the sun.


38.7

Relative Sizes of Atoms a. In the Bohr model, the electrons orbit the nucleus like planets going around the sun. b.

According to de Broglie’s idea, a wave follows along an orbit.


38.7

Relative Sizes of Atoms a. In the Bohr model, the electrons orbit the nucleus like planets going around the sun. b.

According to de Broglie’s idea, a wave follows along an orbit.

c.

The wave model —electrons are distributed in a

“cloud” throughout the volume of the atom.


38.7

Relative Sizes of Atoms think!

What fundamental force dictates the size of an atom?


38.7

Relative Sizes of Atoms think!

What fundamental force dictates the size of an atom?

Answer:

The electrical force.


38.7


What determines the radii of the electron orbits in the Bohr model of the atom?


38.8

Quantum Physics

The subatomic interactions described by quantum mechanics are governed by laws of probability, not laws of certainty.


38.8

Quantum Physics

Physicists became convinced that the Newtonian laws that work so well for large objects do not apply to the microworld of the atom.

In the macroworld, the study of motion is called mechanics, or sometimes classical mechanics.

The study of the motion of particles in the microworld of atoms and nuclei is called quantum mechanics.

The branch of physics that is the general study of the microworld of photons, atoms, and nuclei is simply called quantum physics.


38.8

Quantum Physics

There are fundamental uncertainties in the measurements of the atomic domain.

For the measurement of macroscopic quantities, such as the temperature of materials or the speeds of light and sound, there is no limit to the accuracy with which the experimenter can measure.


38.8

Quantum Physics

Subatomic measurements, such as the momentum and position of an electron or the mass of an extremely short-lived particle, are entirely different.

In this domain, the uncertainties in many measurements are comparable to the magnitudes of the quantities themselves.

The subatomic interactions described by quantum mechanics are governed by laws of probability, not laws of certainty.


38.8

Quantum Physics

What laws govern the interactions described by quantum mechanics?


38.9

Predictability and Chaos

Predictability in orderly systems, both

Newtonian and quantum, depends on knowledge of initial conditions.


38.9


When we know the initial conditions of an orderly system we can make predictions about it.

Knowing the initial conditions lets us state where a planet will be after a certain time or where a launched rocket will land.

In the quantum microworld, we give odds where an electron is likely to be. We calculate the probability that a radioactive particle will decay in a given time interval.


38.9


Some systems, however, whether Newtonian or quantum, are not orderly —they are inherently unpredictable.

These are called “chaotic systems.”

A feature of chaotic systems is that slight differences in initial conditions result in wildly different outcomes later.


38.9


Weather is chaotic. Small changes in one day’s weather can produce big (and largely unpredictable) changes a week later.

This barrier to good prediction first led the scientist

Edward Lorenz to ask, “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”

Now we talk about the butterfly effect when dealing with situations where very small effects can amplify into very big effects.


38.9


What determines predictability in orderly systems?


Assessment Questions

1.

A model of an atom is useful when it a.

shows exactly what an atom looks like.

b.

magnifies what the eye can’t see.

c.

helps to visualize processes that cannot be seen with our eyes.

d.

is shown only as the planetary model.



1.

A model of an atom is useful when it a.

shows exactly what an atom looks like.

b.

magnifies what the eye can’t see.

c.

helps to visualize processes that cannot be seen with our eyes.

d.

is shown only as the planetary model.

Answer: C



2.

In the equation E = hf, f stands for the a.

frequency of a photon with energy E .

b.

wavelength of a photon with energy E .

c.

Planck’s constant with energy h .

d.

quantum of energy.



2.

In the equation E = hf, f stands for the a.

frequency of a photon with energy E .

b.

wavelength of a photon with energy E .

c.

Planck’s constant with energy h .

d.

quantum of energy.

Answer: A



3.

Which of these photons is more likely to initiate the photoelectric effect? a.

red b.

green c.

blue d.

violet



3.

Which of these photons is more likely to initiate the photoelectric effect? a.

red b.

green c.

blue d.

violet

Answer: D



4.

Which of these best illustrates the dual nature of light? a.

Light travels as a wave and interacts with solid matter like a particle.

b.

Light travels as a particle and interacts with solid matter like a wave.

c.

Light can interact in empty spaces as do particles, and travel around solid matter as do waves.

d.

Light does not have a dual nature.



4.

Which of these best illustrates the dual nature of light? a.

Light travels as a wave and interacts with solid matter like a particle.

b.

Light travels as a particle and interacts with solid matter like a wave.

c.

Light can interact in empty spaces as do particles, and travel around solid matter as do waves.

d.

Light does not have a dual nature.

Answer: A



5.

The wavelength of a matter wave is a.

directly proportional to its momentum.

b.

inversely proportional to its momentum.

c.

equal to its momentum.

d.

theoretical only.



5.

The wavelength of a matter wave is a.

directly proportional to its momentum.

b.

inversely proportional to its momentum.

c.

equal to its momentum.

d.

theoretical only.

Answer: B



6.

The view of radii of electrons about the atomic nucleus is nicely understood by thinking of the electrons as a.

standing waves.

b.

discrete particles.

c.

resonating vibrations.

d.

reflections.



6.

The view of radii of electrons about the atomic nucleus is nicely understood by thinking of the electrons as a.

standing waves.

b.

discrete particles.

c.

resonating vibrations.

d.

reflections.

Answer: A



7.

The greater the number of protons in a nucleus, the a.

larger the orbits of the outermost electron.

b.

tighter the orbits of all electrons.

c.

looser inner orbits become.

d.

more electrically neutral the atom becomes.



7.

The greater the number of protons in a nucleus, the a.

larger the orbits of the outermost electron.

b.

tighter the orbits of all electrons.

c.

looser inner orbits become.

d.

more electrically neutral the atom becomes.

Answer: B



8.

Subatomic interactions described by quantum mechanics are governed by a.

the same laws of classical physics.

b.

laws of certainty.

c.

laws of probability.

d.

exact measurements.



8.

Subatomic interactions described by quantum mechanics are governed by a.

the same laws of classical physics.

b.

laws of certainty.

c.

laws of probability.

d.

exact measurements.

Answer: C



9.

A feature of chaotic systems is that small changes in initial conditions a.

lead to small differences later.

b.

lead to big differences later.

c.

may lead to big differences later.

d.

have little or no relation to small or big differences later.



9.

A feature of chaotic systems is that small changes in initial conditions a.

lead to small differences later.

b.

lead to big differences later.

c.

may lead to big differences later.

d.

have little or no relation to small or big differences later.

Answer: C

38 The Atom and the Quantum

Material particles and light have both wave properties and particle properties.

Explanation of the Photoelectric Effect

Support for the Particle Model of Light

Bohr Model Explanation of Atomic Spectra

De Broglie’s Theory

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38 The Atom and the Quantum

Material particles and light have both wave properties and particle properties.

Explanation of the Photoelectric Effect

Support for the Particle Model of Light

Bohr Model Explanation of Atomic Spectra

De Broglie’s Theory

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