Unit 3 Atomic Structure Part 2 Electrons In Atoms Revising the Atomic Model Electron Arrangement in Atoms Atomic Emission Spectra and the Quantum Mechanical Model Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Limitations of Rutherford’s Atomic Model Energy Levels in Atoms Limitations of Rutherford’s Atomic Model It explained only a few simple properties of atoms. It could not explain the chemical properties of elements. For example, Rutherford’s model could not explain why an object such as the iron scroll shown here first glows dull red, then yellow, and then white when heated to higher and higher temperatures. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Energy Levels in Atoms The Bohr Model In 1913, Niels Bohr (1885–1962), a young Danish physicist and a student of Rutherford, developed a new atomic model. He changed Rutherford’s model to incorporate newer discoveries about how the energy of an atom changes when the atom absorbs or emits light. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Energy Levels in Atoms The Bohr Model Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Each possible electron orbit in Bohr’s model has a fixed energy. Energy Levels in Atoms The Bohr Model Each possible electron orbit in Bohr’s model has a fixed energy. The fixed energies an electron can have are called energy levels. A quantum of energy is the amount of energy required to move an electron from one energy level to another energy level. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Energy Levels in Atoms The Bohr Model The rungs on this ladder are somewhat like the energy levels in Bohr’s model of the atom. A person on a ladder cannot stand between the rungs. Similarly, the electrons in an atom cannot exist between energy levels. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Energy Levels in Atoms The Bohr Model The rungs on this ladder are somewhat like the energy levels in Bohr’s model of the atom. The energy levels in atoms are unequally spaced, like the rungs in this unusual ladder. The higher energy levels are closer together. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

How does the Bohr model improve upon the Rutherford model? The Rutherford model could not explain why elements that have been heated to higher and higher temperatures give off different colors of light. The Bohr model explains how the energy levels of electrons in an atom change when the atom emits light. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Quantum Mechanical Model Austrian physicist Erwin Schrödinger (1887–1961) used new theoretical calculations and experimental results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom. The modern description of the electrons in atoms, the quantum mechanical model, came from the mathematical solutions to the Schrödinger equation. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Quantum Mechanical Model Like the Bohr model, the quantum mechanical model of the atom restricts the energy of electrons to certain values. Unlike the Bohr model, however, the quantum mechanical model does not specify an exact path the electron takes around the nucleus. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Quantum Mechanical Model The quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus of an atom. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Quantum Mechanical Model Probability describes how likely it is to find an electron in a particular location around the nucleus of an atom. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Quantum Mechanical Model In the quantum mechanical model, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloudlike region. The cloud is more dense where the probability of finding the electron is high. Electron cloud Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

How are the quantum mechanical model and the Bohr model alike How are the quantum mechanical model and the Bohr model alike? How are they different? Like the Bohr model, the quantum mechanical model restricts the energy of electrons to certain values. Unlike the Bohr model, the quantum mechanical model does not specify an exact path the electron takes around the nucleus. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Orbitals Solutions to the Schrödinger equation give the energies, or energy levels, an electron can have. For each energy level, the Schrödinger equation also leads to a mathematical expression, called an atomic orbital. An atomic orbital is represented pictorially as a region of space in which there is a high probability of finding an electron. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

These numbers are assigned the values n = 1, 2, 3, 4, and so forth. Atomic Orbitals The energy levels of electrons in the quantum mechanical model are labeled by principal quantum numbers (n). These numbers are assigned the values n = 1, 2, 3, 4, and so forth. For each principal energy level greater than 1, there are several orbitals with different shapes and at different energy levels. These energy levels within a principal energy level constitute energy sublevels. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Orbitals Each energy sublevel corresponds to one or more orbitals of different shapes. The orbitals describe where an electron is likely to be found. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Different atomic orbitals are denoted by letters. The s orbitals are spherical. The p orbitals are dumbbell-shaped. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Orbitals For a given principal energy level greater than 1, there is one s orbital… Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Orbitals For a given principal energy level greater than 1, there is one s orbital, 3 p orbitals... Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Orbitals For a given principal energy level greater than 1, there is one s orbital, 3 p orbitals, and 5 d orbitals. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Orbitals Four of the five d orbitals have the same shape but different orientations in space. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Orbitals The numbers and types of atomic orbitals depend on the principal energy level. Summary of Principal Energy Levels and Sublevels Principal energy level Number of sublevels Type of sublevel Maximum number of electrons n = 1 1 1s (1 orbital) 2 n = 2 2s (1 orbital), 2p (3 orbitals) 8 n = 3 3 3s (1 orbital), 3p (3 orbitals), 3d (5 orbitals) 18 n = 4 4 4s (1 orbital), 4p (3 orbitals), 4d (5 orbitals), 4f (7 orbitals) 32 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The number of orbitals in a principal energy level is equal to n2. Atomic Orbitals The principal quantum number, n, always equals the number of sublevels within that principal energy level. The number of orbitals in a principal energy level is equal to n2. A maximum of two electrons can occupy an orbital. Therefore, the maximum number of electrons that can occupy a principal energy level is given by the formula 2n2. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate the maximum number of electrons in the 5th principal energy level (n = 5). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate the maximum number of electrons in the 5th principal energy level (n = 5). The maximum number of electrons that can occupy a principal energy level is given by the formula 2n2. If n = 5, 2n2 = 50. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU Why do scientists no longer use physical models to describe the motion of electrons? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU Why do scientists no longer use physical models to describe the motion of electrons? Previous models of the atom were physical models based on the motion of large objects. Theoretical calculations and experimental results showed that these models did not always correctly describe electron motion. Schrödinger devised a mathematical equation describing the behavior of the electron in a hydrogen atom. The quantum mechanical model came from the solutions to the Schrödinger equation. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Arrangement in Atoms Revising the Atomic Model Atomic Emission Spectra and the Quantum Mechanical Model Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations The ways in which electrons are arranged in various orbitals around the nuclei of atoms are called electron configurations. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Three rules—the aufbau principle, the Pauli exclusion principle, and Hund’s rule—tell you how to find the electron configurations of atoms. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Aufbau Principle According to the aufbau principle, electrons occupy the orbitals of lowest energy first. In the aufbau diagram, each box represents an atomic orbital. Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Aufbau Principle Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p The aufbau diagram shows the relative energy levels of the various atomic orbitals. Orbitals of greater energy are higher on the diagram. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Aufbau Principle Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p The range of energy levels within a principal energy level can overlap the energy levels of another principal level. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Pauli Exclusion Principle According to the Pauli exclusion principle, an atomic orbital may describe at most two electrons. To occupy the same orbital, two electrons must have opposite spins; that is, the electron spins must be paired. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Pauli Exclusion Principle Spin is a quantum mechanical property of electrons and may be thought of as clockwise or counterclockwise. A vertical arrow indicates an electron and its direction of spin ( or ). An orbital containing paired electrons is written as . Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Hund’s Rule According to Hund’s rule, electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Hund’s Rule Three electrons would occupy three orbitals of equal energy as follows. Electrons then occupy each orbital so that their spins are paired with the first electron in the orbital. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Look at the orbital filling diagram of the oxygen atom. An oxygen atom contains eight electrons. Electron Configurations of Selected Elements Element 1s 2s 2px 2py 2pz 3s Electron configuration H 1s1 He 1s2 Li 1s22s1 C 1s22s22p2 N 1s22s22p3 O 1s22s22p4 F 1s22s22p5 Ne 1s22s22p6 Na 1s22s22p63s1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Look at the orbital filling diagram of the oxygen atom. Electron Configurations of Selected Elements Element 1s 2s 2px 2py 2pz 3s Electron configuration H 1s1 He 1s2 Li 1s22s1 C 1s22s22p2 N 1s22s22p3 O 1s22s22p4 F 1s22s22p5 Ne 1s22s22p6 Na 1s22s22p63s1 The 1s orbital has two electrons of opposite spin. The 2s orbital also has two electrons of opposite spin. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Look at the orbital filling diagram of the oxygen atom. Electron Configurations of Selected Elements Element 1s 2s 2px 2py 2pz 3s Electron configuration H 1s1 He 1s2 Li 1s22s1 C 1s22s22p2 N 1s22s22p3 O 1s22s22p4 F 1s22s22p5 Ne 1s22s22p6 Na 1s22s22p63s1 Each of the three 2p orbitals has one electron. The remaining electron now pairs with an electron occupying one of the 2p orbitals. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations A convenient shorthand method for showing the electron configuration of an atom involves writing the energy level and the symbol for every sublevel occupied by an electron. You indicate the number of electrons occupying that sublevel with a superscript. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations For hydrogen, with one electron in a 1s orbital, the electron configuration is written 1s1. For oxygen, with two electrons in a 1s orbital, two electrons in a 2s orbital, and four electrons in 2p orbitals, the electron configuration is 1s22s22p4. Note that the sum of the superscripts equals the number of electrons in the atom. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU Explain why the correct electron configuration of oxygen is 1s22s22p4 and not 1s22s22p33s1. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU Explain why the correct electron configuration of oxygen is 1s22s22p4 and not 1s22s22p33s1. The 2p orbitals are lower in energy than the 3s orbital, so they will be completely filled before any electrons will be found in the 3s orbital. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Writing Electron Configurations Sample Problem 5.1 Writing Electron Configurations The atomic number of phosphorus is 15. Write the electron configuration of a phosphorus atom. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Apply the concepts to this problem. Sample Problem 5.1 Apply the concepts to this problem. Use the aufbau diagram to place electrons in the orbital with the lowest energy (1s) first. Continue placing electrons in each orbital with the next higher energy level. 1s 2s 2p 3p 3s 4s The electron configuration of phosphorus is 1s22s22p63s23p3. The superscripts add up to the number of electrons. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Solve Apply the concepts to this problem. Sample Problem 5.1 Solve Apply the concepts to this problem. 2 Write the electron configuration. The electron configuration of phosphorus is 1s22s22p63s23p3. The superscripts add up to the number of electrons. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Exceptional Electron Configurations You can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the aufbau diagram for orbital filling. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Exceptional Electron Configurations You can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the aufbau diagram for orbital filling. If you were to continue in that fashion, however, you would assign chromium and copper the following incorrect configurations. Cr 1s22s22p63s23p63d44s2 Cu 1s22s22p63s23p63d94s2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Exceptional Electron Configurations The correct electron configurations are as follows: Cr 1s22s22p63s23p63d54s1 Cu 1s22s22p63s23p63d104s1 These arrangements give chromium a half-filled d sublevel and copper a filled d sublevel. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Configurations Exceptional Electron Configurations Some actual electron configurations differ from those assigned using the aufbau principle because although half-filled sublevels are not as stable as filled sublevels, they are more stable than other configurations. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the correct electron configuration of a sulfur atom? A. 1s22s22p43s23p6 B. 1s22s22p63s23p3 C. 1s22s22p63s23p4 D. 1s22s22p63s63p2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the correct electron configuration of a sulfur atom? A. 1s22s22p43s23p6 B. 1s22s22p63s23p3 C. 1s22s22p63s23p4 D. 1s22s22p63s63p2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Emission Spectra and the Quantum Mechanical Model Revising the Atomic Model Electron Arrangement in Atoms Atomic Emission Spectra and the Quantum Mechanical Model Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What gives gas-filled lights their colors? 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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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  (the Greek letter lambda), is the distance between the crests. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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

Light and Atomic Emission Spectra The frequency () and wavelength () of light are inversely proportional to each other. As the wavelength increases, the frequency decreases. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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

Light and Atomic Emission Spectra Light from a helium lamp produces discrete lines. Screen Slit Prism Helium lamp Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating the Wavelength of Light 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). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 5.2 1 Analyze List the knowns and the unknown. Use the equation c = ln to solve for the unknown wavelength. KNOWNS frequency (n) = 5.09 × 1014 /s c = 2.998 × 108 m/s UNKNOWN wavelength (l) = ? m Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 5.2 2 Calculate Solve for the unknown. Write the expression that relates the frequency and wavelength of light. c =  Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 5.2 Calculate Solve for the unknown. 2 Rearrange the equation to solve for l. Solve for l by dividing both sides by n: = n c ln c = ln l = n c Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 5.2 Calculate Solve for the unknown. 2 Substitute the known values for n and c into the equation and solve.  = = = 5.89  10–7 m c 2.998  108 m/s  5.09  1014 /s Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Evaluate Does the answer make sense? 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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the frequency of a red laser that has a wavelength of 676 nm? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the frequency of a red laser that has a wavelength of 676 nm? c = ln c   =  = = = 4.43  1014 /s c 2.998  108 m/s  6.76  10–7 m Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 (n). E n or E = hn Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 n or E = hn Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 wavelike and particle-like properties. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Quantum Concept and Photons The Photoelectric Effect 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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating the Energy of a Photon 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? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 5.3 1 Analyze List the knowns and the unknown. Use the equation E = h × n to calculate the energy of the photon. KNOWNS frequency (n) = 3.20 × 1011/s h = 6.626 × 10–34 J·s UNKNOWN energy (E) = ? J Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 5.3 2 Calculate Solve for the unknown. Write the expression that relates the energy of a photon of radiation and the frequency of the radiation. E = h n Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 5.3 2 Calculate Solve for the unknown. Substitute the known values for n and h into the equation and solve. E = h  = (6.626  10–34 J·s)  (3.20  1011/s) = 2.12  10–22 J Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Evaluate Does the result make sense? Sample Problem 5.3 3 Evaluate Does the result make sense? Individual photons have very small energies, so the answer seems reasonable. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the frequency of a photon whose energy is 1.166  10–17 J? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the frequency of a photon whose energy is 1.166  10–17 J? E = h n n = h E  = = = 1.760  1016 Hz E 1.166  10–17 J·s h 6.626  10–34 J Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Wavelike Nature of Matter 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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Heisenberg Uncertainty Principle 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. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

To locate an electron, you might strike it with a photon. 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. After collision: The impact changes the electron’s velocity, making it uncertain. Before collision: A photon strikes an electron during an attempt to observe the electron’s position. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Heisenberg uncertainty principle states that it is impossible to simultaneously know which two attributes of a particle? velocity and position Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.