5.1 MODELS OF THE ATOM Section Review Objectives Identify inadequacies in the Rutherford atomic model Identify the new assumption in the Bohr model of the atom Describe the energies and positions of electrons according to the quantum mechanical model Describe how the shapes of orbitals at different sublevels vary Vocabulary energy levels quantum Part A Completion quantum mechanical model atomic orbital Use this completion exercise to check your understanding of the concepts and terms that are introduced in this section. Each blank can be completed with a term, short phrase, or number. The chemical properties of atoms, ions, and molecules 1. are related to the arrangement of the 1 within them. 2. The first modern atomic theory, proposed by 2, 3. portrayed the atom as a solid, indivisible mass. After the discovery 4. of the electron by 3, the atomic model was revised to 5. include them. J.J. Thomson s model is referred to as the 4 6. model. Rutherford pictured the atom as a dense 5 7. surrounded by electrons. In the Bohr model, the electrons move 8. in 6 paths. The 7 model is the modern description of the electrons in atoms. This model estimates the 8 of finding an electron within a certain volume of space surrounding the nucleus. Part B True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 9. Electrons must have a certain minimum amount of energy called a quantum in order to move from one energy level to the next higher energy level. 10. The electron probability clouds for atomic orbitals are spherical in shape. Chapter 5 Electrons in Atoms 105
Name Class Date 11. The number of sublevels in an energy level is equal to the square of the principal quantum number of that energy level. 12. The maximum number of electrons that can occupy the fourth principal energy level of an atom is 32. 13. The higher the energy level occupied by an electron the more energetic it is. 14. The principal quantum number equals the number of sublevels within that principal energy level. Part C Matching Match each description in Column B to the correct term in Column A. Column A Column B 15. quantum 16. atomic orbitals 17. energy level 18. quantum mechanical model a. a region in space around the nucleus of an atom where an electron is likely to be moving b. the regions around the nucleus within which the electrons have the highest probability of being found c. the amount of energy required to move an electron from its present energy level to the next higher one d. the modern description of the behavior of electrons in atoms Part D Questions and Problems Answer the following in the space provided. 19. Summarize the development of atomic theory. 20. How many orbitals are in each of the following sublevels? a. 4p sublevel Prentice Hall, Inc. All rights reserved. b. 3d sublevel c. 4f sublevel d. 2s sublevel 106 Core Teaching Resources
5.2 ELECTRON ARRANGEMENT IN ATOMS Section Review Objectives Describe how to write the electron configuration for an atom Explain why the actual electron configurations for some elements differ from those predicted by the Aufbau principle Vocabulary electron configurations Aufbau principle Pauli exclusion principle Hund s rule Part A Completion Use this completion exercise to check your understanding of the concepts and terms that are introduced in this section. Each blank can be completed with a term, short phrase, or number. The ways in which electrons are arranged around the nuclei 1. of atoms are called 1. The 2 describes the sequence 2. in which orbitals are filled. The various orbitals within a sublevel 3. of a principle energy level are always of 3 energy. The 4. 4 principle states that a maximum of only 5 5. electrons can occupy each orbital. To occupy the same orbital, two 6. electrons must have 6 spins. Hund s rule states that the 7. electrons pair up only after each orbital in a sublevel is occupied 8. by 7. When using the shorthand method for showing the 9. electron configuration of an atom, 8 are used to indicate 10. the number of 9 occupying each sublevel. Correct electron configurations can be obtained by using the Aufbau diagram for the elements up to and including vanadium. 10 and copper are exceptions to the Aufbau principle. Chapter 5 Electrons in Atoms 107
Name Class Date Part B True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 11. The orbitals of a principal energy level are lower in energy than the orbitals in the next higher principal energy level. 12. The configuration 3d 4 4s 2 is more stable than the configuration 3d 5 4s 1. 13. As many as four electrons can occupy the same orbital. 14. The Pauli exclusion principle states that an atomic orbital may describe at most two electrons. 15. The electron configuration for potassium is 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1. 16. The electron configuration for copper is 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 9. Part C Matching Match each description in Column B to the correct term in Column A. Column A Column B 17. electron configuration 18. Aufbau principle 19. Pauli exclusion principle 20. Hund s rule 21. neon a. When electrons occupy orbitals of equal energy, one electron enters each orbital until all the orbitals contain one electron with parallel spins. b. An atomic orbital may describe at most two electrons. c. 1s 2 2s 2 2p 6 d. Electrons enter orbitals of lowest energy first. e. the most stable arrangement of electrons around the nucleus of an atom Part D Questions and Problems Answer the following in the space provided. 22. Write the electron configurations for the following atoms. a. C c. K b. S d. Ar 23. Identify the elements described below: a. Contains a full third energy level. Prentice Hall, Inc. All rights reserved. b. Contains the first p electron. 108 Core Teaching Resources
5.3 PHYSICS AND THE QUANTUM MECHANICAL MODEL Section Review Objectives Describe the relationship between the wavelength and frequency of light Explain how the frequencies of light are related to changes in electron energies Distinguish between quantum mechanics and classical mechanics Identify the cause of the atomic emission spectrum Vocabulary amplitude wavelength ( ) frequency ( ) hertz (Hz) electromagnetic radiation spectrum atomic emission spectrum ground state photons Heisenberg uncertainty principle Key Equations c E h h m Part A Completion Use this completion exercise to check your understanding of the concepts and terms that are introduced in this section. Each blank can be completed with a term, short phrase, or number. According to quantum mechanics, the motions of subatomic 1. particles may be described as 1. The frequency and 2. wavelength of all waves are 2 related. 3. Every element emits 3 if it is heated by passing an 4. electric discharge through its gas or vapor. Passing this emission 5. through a prism gives the 4 of the element. 6. 5 The quantum concept developed from Planck s studies of 7. and Einstein's explanation of the 6 effect. Planck showed that the amount of radiant energy absorbed or emitted by a body is proportional to the 7 of the radiation. Chapter 5 Electrons in Atoms 109
Name Class Date Part B True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 8. The speed of light is a constant that can be obtained by dividing the frequency of light by its wavelength. 9. The amplitude of a wave is the distance between the crests. 10. The energy of a body can change only in small discrete units. 11. The position and velocity of an electron in an atom can be determined with great certainty. 12. The photoelectric effect will occur no matter what frequency of light strikes a metal. Part C Matching Match each description in Column B to the correct term in Column A. Column A Column B 13. photons 14. de Broglie s equation 15. visible light 16. ground state 17. wavelength a. predicts that all matter exhibits wavelike motions b. the distance between two consecutive wave crests c. light quanta d. the lowest energy level for a given electron e. example of electromagnetic radiation Part D Questions and Problems Answer the following in the space provided. 18. What is the frequency of radiation whose wavelength is 2.40 10 5 cm? 19. Apply quantum theory to explain the photoelectric effect. Prentice Hall, Inc. All rights reserved. 110 Core Teaching Resources
5 ELECTRONS IN ATOMS Practice Problems In your notebook, solve the following problems. SECTION 5.1 MODELS OF THE ATOM 1. How many sublevels are in the following principal energy levels? a. n 1 c. n 3 e. n 5 b. n 2 d. n 4 f. n 6 2. How many orbitals are in the following sublevels? a. 1s sublevel d. 4f sublevel g. fifth principal energy level b. 5s sublevel e. 7s sublevel h. 6d sublevel c. 4d sublevel f. 3p sublevel 3. What are the types of sublevels and number of orbitals in the following energy levels? a. n 1 c. n 3 e. n 5 b. n 2 d. n 4 SECTION 5.2 ELECTRON ARRANGEMENT IN ATOMS 1. Write a complete electron configuration of each atom. a. hydrogen d. barium g. krypton b. vanadium e. bromine h. arsenic c. magnesium f. sulfur i. radon SECTION 5.3 PHYSICS AND THE QUANTUM MECHANICAL MODEL 1. What is the wavelength of the radiation whose frequency is 5.00 10 15 s 1? In what region of the electromagnetic spectrum is this radiation? 2. An inexpensive laser that is available to the public emits light that has a wavelength of 670 nm. What are the color and frequency of the radiation? 3. What is the energy of a photon whose frequency is 2.22 10 14 s 1? 4. What is the frequency of a photon whose energy is 6.00 10 15 J? 5. Arrange the following types of electromagnetic radiation in order of increasing frequency. a. infrared c. visible light e. microwaves b. cosmic rays d. radio waves f. ultraviolet 6. Suppose that your favorite AM radio station broadcasts at a frequency of 1600 khz. What is the wavelength in meters of the radiation from the station? Chapter 5 Electrons in Atoms 111
5 INTERPRETING GRAPHICS Use with Section 5.3 Lyman series Balmer series Paschen series Frequency (ultraviolet) (visible) (infrared) (hertz) 10 16 10 15 10 14 n = 7 6 5 4 3 2 1 Table 1 Figure 1 The emission spectrum and orbit-transition diagram for hydrogen. Transition E (J) (s 1 ) (m) Type of Radiation n 6 n 5 n 6 n 4 n 6 n 3 n 6 n 2 2.66 10 20 7.57 10 20 1.82 10 19 4.84 10 19 n 6 n 1 n 5 n 4 n 5 n 3 n 5 n 2 n 5 n 1 n 4 n 3 n 4 n 2 n 4 n 1 n 3 n 2 n 3 n 1 2.12 10 18 4.91 10 20 1.55 10 19 4.56 10 19 2.09 10 18 1.06 10 19 4.09 10 19 2.04 10 18 3.03 10 19 1.94 10 18 n 2 n 1 1.64 10 18 112 Core Teaching Resources
1. Figure 1 summarizes the quantum model of the hydrogen atom originally proposed by Neils Bohr to account for the interaction of hydrogen with electromagnetic radiation. The energy changes associated with each electron transition for the lowest six energy levels of hydrogen are listed in Table 1. Calculate the frequency of the emitted radiation for each transition. 2. Calculate the wavelength in meters for each energy level transition and fill in the column for wavelength. 3. Determine the type of radiation (ultraviolet, visible, or infrared) that corresponds to each wavelength. 4. Which transitions result in the emission of visible light? 5. If the wavelengths of blue, green, and red light are approximately 400 nm, 500 nm, and 650 nm, respectively, what colors in the visible spectrum correspond to the transitions stated in your answer to question 4? 6. What is the common feature among transitions where the resulting radiation lies within the visible light range of the electromagnetic spectrum? 7. The Bohr model, although historically important, was limited in its ability to explain the behavior of more complex elements and ions. To which of the following atoms or ions would you expect the Bohr model to apply? Be, He, K, Li 2 Chapter 5 Electrons in Atoms 113
5 ELECTRONS IN ATOMS Vocabulary Review Choose the term from the following list that best matches each description. quantum photons hertz Pauli exclusion principle wavelength Hund s rule atomic emission spectrum photoelectrons Aufbau principle quantum mechanical model 1. The lowest-energy arrangement of electrons in a subshell is obtained by putting electrons into separate orbitals of the subshell before pairing electrons. 2. packets/quanta of electromagnetic energy 3. the SI unit of frequency 4. An atomic orbital can hold no more than two electrons. 5. the amount of energy required to move an electron from its present energy level to the next higher one 6. the modern description of the location and energy of electrons in an atom 7. This principle states that electrons enter orbitals of lowest energy first. 8. the distance between two adjacent crests of an electromagnetic wave 9. This is produced by passing the light emitted by an element through a prism. 10. These are sometimes produced when light shines on metals. 114 Core Teaching Resources
5 ELECTRONS IN ATOMS Chapter Quiz Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 1. The orbitals of a principal energy level are lower in energy than the 5.1 orbitals in the next higher principal energy level. 2. The configuration 3d 4 4s 2 is more stable than the configuration 3d 5 4s 1. 5.2 3. In the quantum mechanical model of the atom, the probability of 5.3 finding an electron within a certain volume of space surrounding the nucleus can be portrayed as a fuzzy cloud. 4. The fourth principal energy level of an atom contains 32 electrons. 5.1 5. There are five orbitals in the 4d energy level. 5.1 6. The amplitude of a wave is the distance between the crests. 5.3 Fill in the word(s) that will make each statement true. 7. In the equation E h, h is called 7. 7. 5.3 8. The electron in a hydrogen atom has the least energy in the 8. 8. 9. Einstein proposed that light is composed of particle-like quanta 9. of energy; light quanta are known as 9. 10. The 10 effect occurs when light above the threshold 10. frequency strikes a metal. 11. De Broglie developed the idea that matter in motion exhibits 11. 11 properties. 5.3 5.3 5.3 5.3 Chapter 5 Electrons in Atoms 115
5 ELECTRONS IN ATOMS Chapter Test A A. Matching Match each description in Column B with the correct term in Column A. Write the letter of the correct description on the line. Column A Column B 1. 2. 3. 4. 5. 6. hertz atomic orbital spectrum atomic emission spectrum quantum of energy amplitude a. the number of wave cycles that pass a given point per unit of time b. the SI unit of frequency c. lines of colored light obtained by passing the light emitted by an element through a prism d. the region around an atomic nucleus where an electron is likely to be moving e. a range of colors seen when light passes through a prism f. Electrons enter orbitals of lowest energy first. 7. 8. 9. wavelength energy level Aufbau principle 10. frequency B. Multiple Choice Choose the best answer and write its letter on the line. g. a region outside the nucleus where there is high probability of finding an electron 11. The fourth principal energy level has a. 4 orbitals. c. 32 orbitals. b. 16 orbitals. d. 9 orbitals. h. the amount of energy required to move an electron from one energy level to the next higher one i. the distance between crests of waves j. the height of a wave from the origin to the crest 12. If the electron configuration of an element is 1s 2 2s 2 2p 6 3s 2 3p 5, the element is a. iron. c. chlorine. b. bromine. d. phosphorus. 116 Core Teaching Resources
13. The quantum mechanical model of the atom a. is concerned with the probability of finding an electron in a certain position. b. was proposed by Neils Bohr. c. defines the exact path of an electron around the nucleus. d. has many analogies in the visible world. 14. The electron configuration of calcium is a. 1s 2 2s 2 2p 2 3s 2 3p 3 4s 2. c. 1s 2 2s 2 3s 2 3p 6 3d 8. b. 1s 2 2s 2 2p 10 3s 2 3p 4. d. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2. 15. The maximum number of electrons that can occupy the third principal energy level is a. 18. c. 2. b. 32. d. 8. 16. As the frequency of light increases, the wavelength a. increases. c. decreases. b. remains the same. d. approaches the speed of light. 17. The formula 2n 2 represents a. the number of sublevels in any energy level. b. the maximum number of electrons that can occupy an energy level. c. the number of orbitals in a sublevel. d. none of the above 18. In order to occupy the same orbital, two electrons must have a. the same direction of spin. c. opposite charge. b. low energy. d. opposite spin. 19. Stable electron configurations are likely to contain a. high-energy electrons. b. unfilled s orbitals. c. fewer electrons than unstable configurations. d. filled energy sublevels. 20. According to Hund s rule, when electrons occupy orbitals of equal energy, one electron enters each orbit until a. all the orbitals contain one electron, with spins parallel. b. all the orbitals contain one electron, with opposite spins. c. there are two electrons in each orbital. d. electron velocities become constant. C. Problems Solve the following problems in the space provided. Show your work. 21. Write electron configurations for these atoms, using arrows to represent electrons. Then, use the shorthand method to write the configurations. a. S b. Na Chapter 5 Electrons in Atoms 117
22. What is the frequency of radiation whose wavelength is 2.40 10 5 cm? 23. Identify the elements that have the following electron configurations. a. 1s 2 2s 2 2p 6 3s 2 3p 1 a. b. 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 b. c. 1s 2 2s 2 2p 6 3s 2 3p 6 3d 7 4s 2 c. 24. Consider the elements neon, bromine, and phosphorus. Which has a. three electrons in its 3p sublevel? a. b. its highest energy level completely filled? b. c. the highest occupied energy level? c. 25. What is the maximum number of electrons that can occupy each of the first five principal energy levels? D. Essay Write a short essay for the following. 26. Explain why the 5s sublevel fills before any electrons are added to the 4d sublevel. 118 Core Teaching Resources
E. Additional Matching Match each description in Column B with the correct term in Column A. Write the letter of the correct description on the line. Column A Column B 27. 28. 29. 30. 31. 32. ground state photoelectric effect photons Heisenberg uncertainty principle de Broglie s equation Planck s constant a. a process in which electrons are ejected by metals when certain wavelengths of light shine on them b. the lowest energy level for a given electron c. predicts that all matter exhibits wavelike motions d. 6.6262 10 34 Js e. It is impossible to know both the velocity and the position of a particle at the same time. f. quanta of light F. True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 33. The energy of a body can change only in small discrete units. 34. The position and velocity of an electron in an atom can be determined with great certainty. 35. Above the threshold frequency, increasing the intensity of the light striking a metal increases the number of electrons ejected. 36. Electrons moving from one energy level to another emit photons. 37. The photoelectric effect will occur no matter what frequency of light strikes a metal. 38. In the Bohr model of the hydrogen atom, when the electron is in the ground state, n 1. 39. The lines in the emission spectrum of hydrogen can be correlated to transitions of electrons from higher energy levels to lower energy levels. 40. The outermost s orbital of an atom contains two electrons. 41. According to quantum mechanics, the motions of subatomic particles may be described as wavelike. Chapter 5 Electrons in Atoms 119
5 ELECTRONS IN ATOMS Chapter Test B A. Matching Match each term in Column B with the correct description in Column A. Write the letter of the correct term on the line. Column A Column B 1. 2. 3. 4. 5. the ways in which electrons are arranged around the nuclei of atoms the ejection of electrons by metals when light shines on them the region around the nucleus of an atom where an electron is likely to be moving An atomic orbital may describe at most two electrons. the regions within which electrons have the highest probability of being found a. Aufbau principle b. quantum c. photoelectric effect d. atomic orbitals e. Pauli exclusion principle 6. 7. 8. 9. When electrons occupy orbitals of equal energy, one electron enters each orbital until all the orbitals contain one electron. the amount of energy required to move an electron from its present energy level to the next higher one light quanta B. Multiple Choice Electrons enter orbitals of lowest energy first. 10. the modern description of the electrons in atoms Choose the best answer and write its letter on the line. f. energy level g. Hund s rule 11. Bohr s contribution to the development of atomic structure a. was referred to as the plum pudding model. b. was the discovery that electrons surround a dense nucleus. c. was proposed that electrons travel in circular orbits around the nucleus. d. is the quantum mechanical model. h. electron configurations i. quantum mechanical model j. photons 12. What is the total number of orbitals in the third principal energy level? a. 1 c. 9 b. 4 d. 16 120 Core Teaching Resources
13. What is the maximum number of electrons allowed in the third energy level? a. 2 c. 18 b. 8 d. 32 14. What is the maximum number of electrons that can occupy one orbital? a. 1 c. 8 b. 2 d. 18 15. The electron configuration for fluorine is a. 1s 2 2s 2 2p 3. c. 1s 2 2s 2 2p 6. b. 1s 2 2s 2 2p 5. d. 1s 2 2s 2 2p 6 3s 2. 16. The first three electrons that enter into p orbitals must have a. parallel spins. c. low energy levels. b. opposite spins. d. opposite charges. 17. The atom whose electron configuration is 1s 2 2s 2 2p 6 3s 2 3p 1 is a. B. c. Al. b. Na. d. Ga. 18. The configuration for the outermost energy level in Ca is a. 3s 2. c. 2s 1. b. 4s 2. d. 4s 1. 19. The element having the same s and p configurations for principal energy level 3 as the element F has for its principal energy level 2 is a. Na. c. P. b. Al. d. Cl. 20. The frequency and wavelength of all waves are a. directly related. c. unrelated. b. inversely related. d. equal. 21. The SI unit of cycles per second is called a a. photon. c. hertz. b. quantum. d. hund. 22. Among the following groups of atoms, which have the same outer energy level configurations? a. H, He c. Mg, Al, Ca, Ga b. Li, Be, N, Ne d. N, P, As, Bi 23. The wavelength of light with a frequency of 2.50 10 13 s 1 is a. 1.20 10 5 m. c. 1.20 10 5 m. b. 8.33 10 5 m. d. 8.33 10 5 m. 24. Once the electron in a hydrogen atom absorbs a quantum of energy, it a. is now in its ground state. c. has released a photon. b. is now in its excited state. d. none of the above Chapter 5 Electrons in Atoms 121
C. Problems Solve the following problems in the space provided. Show your work. 25. Write the electron configurations for the following atoms. a. Mg b. P c. Br d. Xe 26. Identify the elements described below. a. Configuration 1s 2 2s 2 2p 6 3s 2 3p 4 b. Contains a full second energy level c. Contains the first d electron d. Contains seven electrons in its fourth energy level e. Contains only two electrons in its fifth energy level f. Contains three unpaired electrons in its third energy level g. Contains five electrons in its 3d orbitals h. Has its outermost electron in 7s 1 27. What is the frequency of radiation whose wavelength is 6.25 10 5 cm? 122 Core Teaching Resources
28. What is the energy of a photon whose frequency is 5.2 10 15 s 1? h 6.6262 10 34 Js D. Essay Write a short essay for the following. 29. Distinguish between the Bohr model and the quantum mechanical model of an atom in terms of the positions of the electrons in an atom. E. Additional Matching Match each term in Column B with the correct description in Column A. Write the letter of the correct term on the line. 30. 31. 32. 33. 34. 35. Column A the lowest energy level within which an electron can be found the height of an electromagnetic wave from the origin to the crest It is impossible to know exactly both the velocity and the position of a particle at the same time. the number of electromagnetic wave cycles to pass a given point per unit of time All matter exhibits wavelike motion. the distance between the crests of an electromagnetic wave Column B a. Heisenberg uncertainty principle b. wavelength c. ground state d. amplitude e. de Broglie s equation f. frequency Chapter 5 Electrons in Atoms 123
F. True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 36. The energy levels in an atom can be viewed like the rungs on a ladder. 37. The electrons in an atom are arranged in concentric orbits around the nucleus. 38. The principal quantum number equals the number of sublevels within that principal energy level. 39. As many as eight electrons may occupy the same orbital. 40. In all natural phenomena, change proceeds toward the lowest possible energy state. 41. The photoelectric effect will occur only if the frequency of light striking an electron in a metal is above a certain threshold frequency. 42. The behavior of light can be explained in terms of waves. 43. According to the Heisenberg uncertainty principle, as the velocity of a moving particle is known with increasing accuracy, the position of that particle becomes less accurately known. 44. Quantum mechanics describes the motions of subatomic particles and atoms as waves that gain or lose energy in packages called quanta. 124 Core Teaching Resources