Unit 4 Electrons in Atoms and Periodic Trends Accelerated Chemistry I

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1 Name: Date: Unit 4 Electrons in Atoms and Periodic Trends Accelerated Chemistry I Modern Atomic Theory The behavior of visible objects moving at ordinary speeds is described by Newtonian mechanics. Another system of mechanics is needed to describe the behavior of tiny particles traveling at very high speeds. Several scientists, including Bohr, de Broglie, Schrödinger, and Heisenberg, made major contributions to this new system of mechanics. 1. How did Bohr envision the relationship between the electron and the nucleus of the hydrogen atom? 2. How did Bohr s model explain the emission of only discrete wavelengths of light by excited hydrogen atoms? 3. Why did Bohr s model not stand up as more experiments were performed using elements other than hydrogen? 4. What is the name of the scientist who treated the electron mathematically as a wave? 5. Mechanics is a word used to describe a system of mathematical equations. Which system of mathematical equations is used to describe the behavior of extremely small particles traveling at velocities near the speed of light? 6. Define or explain the following. a. wave-particle duality of nature b. What is the relationship between the wavelength and frequency of radiant energy? 8. What is the energy of light with a frequency of 4.31 X Hz? Answ: 2.86x10-19 J Unit 4 Student Handout 1

2 9. A certain violet light has a wavelength of 413 nm. What is the frequency and the energy of the light? Answ: ν= 7.26x10 14 Hz 4.81x10-19 J h 10. Complete the table using de Broglie s equation, λ =, for the wavelength λ of a particle of mass mv m and velocity v [h = J s = kg m 2 /s]. m (kg) µ (m/s) λ (m) Excited mercury atoms emit light strongly at a wavelength of 436 nm. What is the frequency of this radiation? Predict the color associated with this wavelength. Answ: ν= 6.88x10 14 Hz (Blue/Violet) 12. What is the energy of a photon light emitted by excited mercury atoms? Answ: E= 4.56x10-19 J Quantum Mechanics and Quantum Numbers The solution to Schrödinger's equations yields four quantum numbers that describe the various states and energy levels available to electrons. A set of four quantum numbers can describe the electron configuration of any atom. 1. What is the name of the scientist who pointed out that it is impossible to know both the exact position and the exact momentum of an electron at the same time? Unit 4 Student Handout 2

3 2. What is the formula for calculating the maximum number of electrons that can occupy any energy level in an atom? 3. Complete the following table. Energy level Number of sublevels Number of orbitals Maximum number of electrons Complete the following table. Sublevel s p d f Number of orbitals Maximum number of electrons 5. State the Pauli Exclusion Principle. 6. Which quantum number signifies the size of the electron cloud? 7. The sublevel or shape of the electron cloud is designated by which quantum number? 8. How do wave mechanical orbitals differ from Bohr s orbits? What does it mean to say that an orbital represented a probability map for an electron? Unit 4 Student Handout 3

4 Orbitals per energy level Shell n Orbitals 1 n = 1 1s 2 n = 2 2s 2p x, 2p y, 2p z 3 n = 3 3s 3p x, 3p y, 3p z 3d, 3d, 3d, 3d, 3d 4 n = 4 4s 4p x, 4p y, 4p z 4d, 4d, 4d, 4d, 4d 4f, 4f, 4f, 4f, 4f, 4f, 4 Orbitals Being Filled for Elements in the Periodic Table Electron Configurations 1. Write the electron configurations, using the spdf notation for: a. Phosphorus b. Chlorine c. Vanadium Unit 4 Student Handout 4

5 d. Iridium e. Silver f. Mercury g. Cerium h. Curium 2. Using the noble gas notation, depict the electron configurations of: a. P and P 3- b. Cr and Cr 3+ c. Mn 2+ and Mn 4+ Complete the orbital box diagrams for the following atoms by drawing in the arrows indicating the electrons with appropriate spins for each orbital. d. beryllium (Z = 4) 1s 2s 2p 3s 3p e. carbon (Z = 6) f. fluorine (Z = 9) Unit 4 Student Handout 5

6 Write T for true or F for false. If a statement is false, replace the underlined word with one that will make the statement true. 3. If two electrons occupy the same orbital, they must have opposite spins. 4. The principal quantum number describes the energy level of an electron in an atom. 5. The Schrödinger wave equation is solvable for any multi-electron system. 6. Four quantum numbers are required to describe completely an electron in an atom. 7. The ground state is the least stable energy state of the atom. 8. Identify the following elements. a. An excited state of this element has the electron configuration 1s 2 2s 2 2p 5 3s 1. b. The ground-state electron configuration is [Ne]3s 2 3p 4. c. An excited state of this element has the electron configuration [Kr]5s 2 4d 6 5p 2 6s 1. d. The ground-state electron configuration contains three unpaired 6p electrons. Periodic Trends Grouping Elements Identify each of the following elements as a metal (M), nonmetal (NM), or a metalloid/semimetal (SM): 1. Sodium 2. Silicon 3. Neon 4. Calcium 5. Nitrogen 6. Tungsten What is the name of the following families? 7. Group 1 8. Group 2 9. Group Group What properties distinguish metals from nonmetals? 12. What does an electron configuration tell you about an element? Unit 4 Student Handout 6

7 Periodic Trends Atomic Radius, Ionization Energy, Electronegativity 1. What is meant by effective nuclear charge (Z eff )? 2. How does the effective nuclear charge vary going from left to right across a period of the Periodic Table? How does this affect the size of atomic radii going across a period? 3. Write equations that show the processes that describe the first, second, and third ionization energies of a tellurium atom. 4. Why does Li have a larger first ionization energy than Na? 5. Which pair of atoms or ions has the larger atomic radius? Circle the correct answer. a. Be or Ba b. Si or S c. Fe or Fe 2+ d. K + or O 2 e. Ba 2+ or I 6. In each of the following sets of elements, which element would be expected to have the highest ionization energy? Circle that element. a. Cs, K, Li b. I, Br, Cl c. Mg, Si, S d. Cu, Cr e. Ca, Ra f. K, K+ g. I, I- 7

8 More questions about electronegativity and ionization energy comparisons!!! 7. Contrast ionization energy with electronegativity. 8. In general, what can you say about ionization energy and electron affinities when comparing the values for metals and non-metals? Vocabulary Review degenerate electron cloud Heisenberg uncertainty principle Lewis electron dot diagram momentum Newtonian mechanics orbital Pauli exclusion principle principal quantum number probability quantum mechanics quantum numbers sublevel wave-particle duality of nature 1. Classical mechanics, or, describes the behavior of visible objects traveling at ordinary velocities. 2. Four are used in Schrödinger's description of electron behavior. 3. Orbitals that are alike in size and shape and differ only in direction have the same energy and are said to be. 4. The product of the mass and velocity of an object is a vector quantity known as. 5. The volume in which an electron is likely to be found is called a(n). 6. The states that there is always some uncertainty about the position and momentum of an electron. 7. The idea of the two-sided nature of waves and particles is called the. 8. A(n) is one of many energy states grouped closely together to form an energy level. 9. The behavior of extremely small particles traveling at velocities near that of light is described by. 10. The letter n represents the, which is used to describe energy levels. 11. The states that no two electrons in an atom have the same set of four quantum numbers. 12. A(n) is the space occupied by a pair of electrons. 8

9 Challenge Problems 1. In a photoelectric effect experiment a student shines a light of greater than the threshold frequency upon the surface of the metal. She observes that after a long time the number of ejected electrons begins to decline. Can you explain why? 2. Look up the electron configuration of molybdenum. Why is it exceptional? Explain. 3. Look up the electron configuration of europium. Why is it exceptional? Explain. 4. Draw the orbital diagram for copper. 5. There is a large jump between the second and third ionization energies of magnesium. There is also a large jump between the third and fourth ionization energies of aluminum. Explain these observations. 9