5 3 Atomic Emission Spectra and the Quantum

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 1 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Objectives 1. Explain light and atomic emission spectra 2. Calculate wavelength or frequency 3. Describe Einstein’s explanation of the photoelectric effect 4. Explain how the frequencies of light emitted by an atom are related to changes of electron energies 5. Distinguish between quantum mechanics and classical mechanics 2 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > CHEMISTRY & YOU 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. 3 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra What causes atomic emission spectra? spectrum: wavelengths of visible light that are separated when a beam of light passes through a prism; range of wavelengths of electromagnetic radiation. 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. 4 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 (a disturbance or variation that transfers energy progressively from point to point, Merriam-Webster’s dictionary). • The amplitude of a wave is the wave’s height from zero to the crest. • The wavelength, represented by (the Greek letter lambda), is the distance between the crests. 5 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra The Nature of Light • The frequency, represented by (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). 6 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra The Nature of Light The product of frequency and wavelength equals a constant (c), the speed of light. c = 7 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra The frequency ( ) and wavelength ( ) of light are inversely proportional to each other. As the wavelength increases, the frequency decreases. 8 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra The Nature of Light 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. 9 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra The Nature of Light The sun and incandescent light bulbs emit white light, which consists of light with a continuous range of wavelengths and frequencies. • 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. 10 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra The electromagnetic spectrum consists of radiation over a broad range of wavelengths. Low energy ( = 700 nm) Frequency (s-1) 3 x 106 102 Wavelength (m) 11 High energy ( = 380 nm) 3 x 1012 3 x 1022 10 -8 10 -14 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 12 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra A prism separates light into the colors it contains. White light produces a rainbow of colors. Screen Light bulb 13 Slit Prism Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Light and Atomic Emission Spectra Light from a helium lamp produces discrete lines. Screen Helium lamp 14 Slit Prism Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 _______to identical 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. same emission • No two elements have the _______ spectrum. 15 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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). 16 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 2 1 Analyze List the knowns and the unknown. l to solve for the Use the equation c = ____ unknown wavelength. KNOWNS frequency ( ) = 5. 09 × 1014 /s c = 2. 998 × 108 m/s UNKNOWN wavelength ( ) = ? m 17 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 2 2 Calculate Solve for the unknown. Rearrange the equation to solve for . c = 18 Solve for by dividing both sides by : c = Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 2 2 Calculate Solve for the unknown. Substitute the known values for and c into the equation and solve. c 2. 998 108 m/s – 7 m = = = 5. 89 10 5. 09 1014 /s 19 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 2 3 Evaluate Does the answer make sense? 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. 20 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > What is the frequency of a red laser that has a wavelength of 676 nm? 21 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > What is the frequency of a red laser that has a wavelength of 676 nm? c = c 2. 998 108 m/s = = 6. 76 10– 7 /s = 4. 43 1014 m 22 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons How did Einstein explain the photoelectric effect? 23 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Quantization of Energy 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 ( ). E 24 or E = h Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Quantization of Energy 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. E 25 or E = h Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Photoelectric Effect Albert Einstein used Planck’s quantum theory to explain the photoelectric effect. In the photoelectric effect, electrons are ejected when light shines on a metal. 26 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Photoelectric Effect Not just any frequency of light will cause 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. 27 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Photoelectric Effect • 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. 28 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Photoelectric Effect To explain the photoelectric effect, Einstein proposed that light could be described as quanta of energy that behave as if they were particles. 29 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Photoelectric Effect 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. • Light behaves as waves in other situations; we must consider that light possesses both wave-like and particle-like properties. 30 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Quantum Concept and Photons The Photoelectric Effect No electrons are ejected because the frequency of the light is below the threshold frequency. 31 If the light is at or above threshold frequency, electrons are ejected. If the frequency is increased, the ejected electrons will travel faster. Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 3 Calculating the Energy of a Photon What is the energy of a photon of microwave radiation with a frequency of 3. 20 × 1011/s? 32 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 3 1 Analyze List the knowns and the unknown. Use the equation E = _____ to calculate h× the energy of the photon. KNOWNS frequency ( ) = 3. 20 × 1011/s h = 6. 626 × 10– 34 J·s UNKNOWN energy (E) = ? J 33 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 3 2 Calculate Solve for the unknown. Substitute the known values for and h into the equation and solve. E = h = (6. 626 10– 34 J·s) (3. 20 1011/s) = 2. 12 10– 22 J 34 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Sample Problem 5. 3 3 Evaluate Does the result make sense? Individual photons have very small energies, so the answer seems reasonable. 35 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > What is the frequency of a photon whose energy is 1. 166 10– 17 J? E = ________________ 36 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > What is the frequency of a photon whose energy is 1. 166 10– 17 J? E = h E 6. 626 10– 34 J = h = 1. 166 10– 17 J·s = 1. 760 1016 Hz 37 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > An Explanation of Atomic Spectra How are the frequencies of light emitted by an atom related to changes of electron energies? 38 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 39 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 40 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 41 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > CHEMISTRY & YOU 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. 42 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 43 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Quantum Mechanics How does quantum mechanics differ from classical mechanics? 44 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Quantum Mechanics Given that light behaves as waves and particles, can particles of matter behave as waves? • 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. 45 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Quantum Mechanics The Wavelike Nature of Matter Today, the wavelike properties of beams of electrons are useful in viewing objects that cannot be viewed with an optical microscope. • 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. 46 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 47 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 48 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 49 After collision: The impact changes the electron’s velocity, making it uncertain. Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > The Heisenberg uncertainty principle states that it is impossible to simultaneously know which two attributes of a particle? velocity and position _____________ 50 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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. 51 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 = E=h 52 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 53 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > Glossary Terms • electromagnetic radiation: energy waves that travel in a vacuum at a speed of 2. 998 108 m/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 54 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 ( ) • photoelectric effect: the phenomenon in which electrons are ejected when light shines on a metal 55 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > 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 56 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > BIG IDEA Electrons and the Structure of Atoms • 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. 57 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

5. 3 Atomic Emission Spectra and the Quantum Mechanical Model > END OF 5. 3 58 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.