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Chapter 5

Electrons In Atoms

5.1 Revising the Atomic Model

5.2 Electron Arrangement in Atoms

5.3 Atomic Emission Spectra

and the Quantum

Mechanical Model

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What gives gas-filled lights their colors?

An electric current passing through the gas in each glass tube makes the gas glow with its own characteristic color.

CHEMISTRY & YOU

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Light and Atomic�Emission Spectra

Light and Atomic Emission Spectra

What causes atomic emission spectra?

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Light and Atomic Emission Spectra

The Nature of Light

By the year 1900, there was enough experimental evidence to convince scientists that light consisted of waves.
The amplitude of a wave is the wave’s height from zero to the crest.
The wavelength, represented by λ (the Greek letter lambda), is the distance between the crests.

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Light and Atomic Emission Spectra

The frequency, represented by ν (the Greek letter nu), is the number of wave cycles to pass a given point per unit of time.

The SI unit of cycles per second is called the hertz (Hz).

The Nature of Light

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Light and Atomic Emission Spectra

The product of frequency and wavelength equals a constant (c), the speed of light.

c = λν

The Nature of Light

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Light and Atomic Emission Spectra

The frequency (ν) and wavelength (λ) of light are inversely proportional to each other. As the wavelength increases, the frequency decreases.

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Light and Atomic Emission Spectra

According to the wave model, light consists of electromagnetic waves.

Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays.
All electromagnetic waves travel in a vacuum at a speed of 2.998 × 10⁸ m/s.

The Nature of Light

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Light and Atomic Emission Spectra

The sun and incandescent light bulbs emit white light, which consists of light with a continuous range of wavelengths and frequencies.

The Nature of Light

When sunlight passes through a prism, the different wavelengths separate into a spectrum of colors.
In the visible spectrum, red light has the longest wavelength and the lowest frequency.

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Light and Atomic Emission Spectra

The electromagnetic spectrum consists of radiation over a broad range of wavelengths.

Wavelength λ (m)

Low energy

(λ = 700 nm)

High energy

(λ = 380 nm)

Frequency ν (s^-1)

3 x 10⁶

3 x 10¹²

3 x 10²²

10²

10^-8

10^-14

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Light and Atomic Emission Spectra

When atoms absorb energy, their electrons move to higher energy levels. These electrons lose energy by emitting light when they return to lower energy levels.

Atomic Emission Spectra

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Light and Atomic Emission Spectra

A prism separates light into the colors it contains. White light produces a rainbow of colors.

Light

bulb

Slit

Prism

Screen

Atomic Emission Spectra

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Light and Atomic Emission Spectra

Light from a helium lamp produces discrete lines.

Slit

Prism

Screen

Helium

lamp

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Light and Atomic Emission Spectra

The energy absorbed by an electron for it to move from its current energy level to a higher energy level is identical to the energy of the light emitted by the electron as it drops back to its original energy level.
The wavelengths of the spectral lines are characteristic of the element, and they make up the atomic emission spectrum of the element.
No two elements have the same emission spectrum.

Atomic Emission Spectra

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Sample Problem 5.2

Calculating the Wavelength of Light

Calculate the wavelength of the yellow light emitted by a sodium lamp if the frequency of the radiation is 5.09 × 10¹⁴ Hz (5.09 × 10¹⁴/s).

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Sample Problem 5.2

Use the equation c = λν to solve for the unknown wavelength.

KNOWNS

frequency (ν) = 5.09 × 10¹⁴/s

c = 2.998 × 10⁸ m/s

UNKNOWN

wavelength (λ) = ? m

Analyze List the knowns and the unknown.

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Sample Problem 5.2

Write the expression that relates the frequency and wavelength of light.

c = λν

Calculate Solve for the unknown.

2

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Sample Problem 5.2

Rearrange the equation to solve for λ.

λ =

ν

c

Solve for λ by dividing both sides by ν:

=

ν

c

ν

λν

Calculate Solve for the unknown.

2

c = λν

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Sample Problem 5.2

Substitute the known values for ν and c into the equation and solve.

λ = = = 5.89 × 10^–7 m

c 2.998 × 10⁸ m/s

ν 5.09 × 10¹⁴ /s

Calculate Solve for the unknown.

2

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Sample Problem 5.2

The magnitude of the frequency is much larger than the numerical value of the speed of light, so the answer should be much less than 1. The answer should have 3 significant figures.

Evaluate Does the answer make sense?

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What is the frequency of a red laser that has a wavelength of 676 nm?

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What is the frequency of a red laser that has a wavelength of 676 nm?

c = λν

ν = = = 4.43 × 10¹⁴ m

c 2.998 × 10⁸ m/s

λ 6.76 × 10^–7 /s

c

λ

ν =

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The Quantum Concept and Photons

How did Einstein explain the photoelectric effect?

The Quantum Concept and Photons

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The Quantum Concept and Photons

German physicist Max Planck (1858–1947) showed mathematically that the amount of radiant energy (E) of a single quantum absorbed or emitted by a body is proportional to the frequency of radiation (ν).

The Quantization of Energy

E ν or E = hν

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The Quantum Concept and Photons

The constant (h), which has a value of 6.626 × 10^–34 J·s (J is the joule, the SI unit of energy), is called Planck’s constant.

The Quantization of Energy

E ν or E = hν

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The Quantum Concept and Photons

Albert Einstein used Planck’s quantum theory to explain the photoelectric effect.

The Photoelectric Effect

In the photoelectric effect, electrons are ejected when light shines on a metal.

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The Quantum Concept and Photons

Not just any frequency of light will cause the photoelectric effect.

The Photoelectric Effect

Red light will not cause potassium to eject electrons, no matter how intense the light.
Yet a very weak yellow light shining on potassium begins the effect.

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The Quantum Concept and Photons

The photoelectric effect could not be explained by classical physics.
Classical physics correctly described light as a form of energy.
But, it assumed that under weak light of any wavelength, an electron in a metal should eventually collect enough energy to be ejected.

The Photoelectric Effect

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The Quantum Concept and Photons

To explain the photoelectric effect, Einstein proposed that light could be described as quanta of energy that behave as if they were particles.

The Photoelectric Effect

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The Quantum Concept and Photons

These light quanta are called photons.

Einstein’s theory that light behaves as a stream of particles explains the photoelectric effect and many other observations.

The Photoelectric Effect

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The Quantum Concept and Photons

These light quanta are called photons.

The Photoelectric Effect

Einstein’s theory that light behaves as a stream of particles explains the photoelectric effect and many other observations.
Light behaves as waves in other situations; we must consider that light possesses both wavelike and particle-like properties.

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The Quantum Concept and Photons

No electrons are ejected because the frequency of the light is below the threshold frequency.

If the light is at or above the threshold frequency, electrons are ejected.

If the frequency is increased, the ejected electrons will travel faster.

The Photoelectric Effect

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Calculating the Energy of a Photon

What is the energy of a photon of microwave radiation with a frequency of 3.20 × 10¹¹/s?

Sample Problem 5.3

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Sample Problem 5.3

Use the equation E = h × ν to calculate the energy of the photon.

KNOWNS

frequency (ν) = 3.20 × 10¹¹/s

h = 6.626 × 10^–34 J·s

UNKNOWN

energy (E) = ? J

Analyze List the knowns and the unknown.

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Sample Problem 5.3

Write the expression that relates the energy of a photon of radiation and the frequency of the radiation.

E = h ν

Calculate Solve for the unknown.

2

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Substitute the known values for ν and h into the equation and solve.

E = h ν = (6.626 × 10^–34 J·s) × (3.20 × 10¹¹/s)

= 2.12 × 10^–22 J

Sample Problem 5.3

Calculate Solve for the unknown.

2

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Sample Problem 5.3

Individual photons have very small energies, so the answer seems reasonable.

Evaluate Does the result make sense?

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What is the frequency of a photon whose energy is 1.166 × 10^–17 J?

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What is the frequency of a photon whose energy is 1.166 × 10^–17 J?

E = h ν

ν =

h

E

ν = = = 1.760 × 10¹⁶ Hz

E 6.626 × 10^–34 J

h 1.166 × 10^–17 J·s

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An Explanation of Atomic Spectra

How are the frequencies of light emitted by an atom related to changes of electron energies?

An Explanation of Atomic Spectra

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An Explanation of Atomic Spectra

When an electron has its lowest possible energy, the atom is in its ground state.

In the ground state, the principal quantum number (n) is 1.

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An Explanation of Atomic Spectra

When an electron has its lowest possible energy, the atom is in its ground state.

In the ground state, the principal quantum number (n) is 1.
Excitation of the electron by absorbing energy raises the atom to an excited state with n = 2, 3, 4, 5, or 6, and so forth.
A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level.

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An Explanation of Atomic Spectra

The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron.

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An Explanation of Atomic Spectra

The three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels.

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The glass tubes in lighted signs contain helium, neon, argon, krypton, or xenon gas, or a mixture of these gases. Why do the colors of the light depend on the gases that are used?

CHEMISTRY & YOU

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The glass tubes in lighted signs contain helium, neon, argon, krypton, or xenon gas, or a mixture of these gases. Why do the colors of the light depend on the gases that are used?

Each different gas has its own characteristic emission spectrum, creating different colors of light when excited electrons return to the ground state.

CHEMISTRY & YOU

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In the hydrogen spectrum, which of the following transitions produces a spectral line of the greatest energy?

A. n = 2 to n = 1

B. n = 3 to n = 2

C. n = 4 to n = 3

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In the hydrogen spectrum, which of the following transitions produces a spectral line of the greatest energy?

A. n = 2 to n = 1

B. n = 3 to n = 2

C. n = 4 to n = 3

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Quantum Mechanics

How does quantum mechanics differ from classical mechanics?

Quantum Mechanics

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Quantum Mechanics

Given that light behaves as waves and particles, can particles of matter behave as waves?

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Quantum Mechanics

Louis de Broglie referred to the wavelike behavior of particles as matter waves.
His reasoning led him to a mathematical expression for the wavelength of a moving particle.

Given that light behaves as waves and particles, can particles of matter behave as waves?

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Quantum Mechanics

Today, the wavelike properties of beams of electrons are useful in viewing objects that cannot be viewed with an optical microscope.

The Wavelike Nature of Matter

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Quantum Mechanics

Today, the wavelike properties of beams of electrons are useful in viewing objects that cannot be viewed with an optical microscope.

The Wavelike Nature of Matter

The electrons in an electron microscope have much smaller wavelengths than visible light.
These smaller wavelengths allow a much clearer enlarged image of a very small object, such as this pollen grain, than is possible with an ordinary microscope.

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Quantum Mechanics

Classical mechanics adequately describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves.

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Quantum Mechanics

The Heisenberg Uncertainty Principle

The Heisenberg uncertainty principle states that it is impossible to know both the velocity and the position of a particle at the same time.

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Quantum Mechanics

The Heisenberg Uncertainty Principle

The Heisenberg uncertainty principle states that it is impossible to know both the velocity and the position of a particle at the same time.

This limitation is critical when dealing with small particles such as electrons.
But it does not matter for ordinary-sized objects such as cars or airplanes.

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Quantum Mechanics

To locate an electron, you might strike it with a photon.
The electron has such a small mass that striking it with a photon affects its motion in a way that cannot be predicted accurately.
The very act of measuring the position of the electron changes its velocity, making its velocity uncertain.

Before collision: A photon strikes an electron during an attempt to observe the electron’s position.

After collision: The impact changes the electron’s velocity, making it uncertain.

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The Heisenberg uncertainty principle states that it is impossible to simultaneously know which two attributes of a particle?

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The Heisenberg uncertainty principle states that it is impossible to simultaneously know which two attributes of a particle?

velocity and position

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Key Concepts and Key Equations

When atoms absorb energy, their electrons move to higher energy levels. These electrons lose energy by emitting light when they return to lower energy levels.

To explain the photoelectric effect, Einstein proposed that light could be described as quanta of energy that behave as if they were particles.

The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron.

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Key Concepts and Key Equations

Classical mechanics adequately describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves.

C = λν

E = h × ν

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Glossary Terms

amplitude: the height of a wave’s crest
wavelength: the distance between adjacent crests of a wave
frequency: the number of wave cycles that pass a given point per unit of time; frequency and wavelength are inversely proportional to each other
hertz: the unit of frequency, equal to one cycle per second

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Glossary Terms

electromagnetic radiation: energy waves that travel in a vacuum at a speed of 2.998 × 10⁸m/s; includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays
spectrum: wavelengths of visible light that are separated when a beam of light passes through a prism; range of wavelengths of electromagnetic radiation

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Glossary Terms

atomic emission spectrum: the pattern formed when light passes through a prism or diffraction grating to separate it into the different frequencies of light it contains
Planck’s constant: the constant (h) by which the amount of radiant energy (E) is proportional to the frequency of the radiation (ν)
photoelectric effect: the phenomenon in which electrons are ejected when light shines on a metal

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Glossary Terms

photon: a quantum of light; a discrete bundle of electromagnetic energy that interacts with matter similarly to particles
ground state: the lowest possible energy of an atom described by quantum mechanics
Heisenberg uncertainty principle: it is impossible to know both the velocity and the position of a particle at the same time

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Electrons and the Structure of Atoms

BIG IDEA

Electrons can absorb energy to move from one energy level to a higher energy level.
When an electron moves from a higher energy level back down to a lower energy level, light is emitted.

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