AP Chem Problem Set # 5
1. (a) What is the frequency of radiation that has a wavelength of 0.589 pm? (b) What is the wavelength of radiation that has a frequency of 5.11 X 1011 s-1? (c) Would the radiations in part (a) or part (b) be visible to the human eye? (d) What distance does electromagnetic radiation travel in 6.54 s?
2. Excited mercury atoms emit light strongly at a wavelength of 436 nm. What is the frequency of this radiation? Using Figure 6.4, predict the color associated with this wavelength.
Quantized Energy and Photons
3. (a) Calculate the smallest increment of energy (a quantum) that can be emitted or absorbed at a wavelength of 812 nm. (b) Calculate the energy of a photon of frequency 5.72 X 1013 s-1. (c) What wavelength of radiation has photons of energy 5.44 X 10-18 J? In what portion of the electromagnetic spectrum would this radiation be found?
4. A diode laser emits at a wavelength of 987 nm. All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 sec. How many photons per second are being emitted by the laser?
5. Molybdenum metal must absorb radiation with a minimum frequency of 1.09 X 1015 s-1 before it can emit an electron from its surface via the photoelectric effect. (a) What is the minimum energy required to produce this effect? (b) What wavelength radiation will provide a photon of this energy? (c) If molybdenum is irradiated with light of wavelength of 120 nm, what is the maximum possible kinetic energy of the emitted electrons?
Bohrs Model; Matter Waves
6. Explain how the existence of line spectra is consistent with Bohrs theory of quantized energies for the electron in the hydrogen atom.
7. Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at 60 km/hr; (b) a 50-g golf ball traveling at 400 m/s; (c) a lithium atom moving at 6.5 X 105 m/s.
8. In what ways does de Broglies hypothesis require revision of our picture of the hydrogen atom based on Bohrs model?
Quantum Mechanics and Atomic Orbitals
9. (a) For n = 4, what are the possible values of l? (b) For l = 2, what are the possible values of ml?
10. Give the values for n, I, and ml for (a) each orbital in the 2p subshell; (b) each orbital in the 5d subshell.
11. Which of the following are permissible sets of quantum numbers for an electron in a hydrogen atom: (a) n = 2, l = 1, ml = 1; (b) n = 1, l = 0, ml = -1; (c) n = 4, l = 2, ml = 2, (d) n = 3, l = 3, ml = 0? For those combinations that are permissible, write the appropriate designation for the subshell to which the orbital belongs (that is, 1s, and so on).
12. (a) What are the similarities and differences between the hydrogen atom 1s and 2s orbitals? (b) In what sense does a 2p orbital have directional character? Compare the "directional" characteristics of the px and dx2-y2 orbitals (that is, in what direction or region of space is the electron density concentrated?). (c) What can you say about the average distance from the nucleus of an electron in a 2s orbital as compared with a 3s orbital? (d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): 4f, 6s, 3d, 1s, 2p.
Many-Electron Atoms; Electron Spin
13. Which quantum numbers must be the same in order for orbitals to be degenerate (have the same energy) (a) in a hydrogen atom and (b) in a many-electron atom?
14. Explain why the effective nuclear charge experienced by a 2s electron in boron is greater than that for the 2p electron.
15. Which should experience the greater effective nuclear charge, a 2p electron in oxygen or a 2p electron in neon?
16. (a) What are the possible values of the electron spin quantum number? (b) What piece of experimental equipment can be used to distinguish electrons that have different values of the electron spin quantum number? (c) Two electrons in an atom both occupy the 1s orbital. What quantity must be different for the two electrons? What principle governs the answer to this question?
17. What is the maximum number of electrons that can occupy each of the following subshells: (a) 3d; (b) 4s; (c) 2p; (d) 5f?
18. List the possible values for the four quantum numbers for a 2p electron in beryllium.
19. Write the electron configurations for the following atoms, using the appropriate noble-gas inner-core abbreviation: (a) Rb; (b) Se; (c) Zn; (d) V; (e) Pb; (f) Yb.
20. Draw the orbital diagrams for the valence electrons of each of the following elements: (a) As; (b) Te; (c) Sb; (d) Ag; (e) Hf. (f) How many unpaired electrons would you expect in each of these atoms?
21. Identify the group of elements that corresponds to each of the following electron configurations: (a) 1s22s22p63s2; (b) [Ne]3s23p1; (c) [Ar]4s13d5; (d) [Kr]5s24d105p4.
22. A photocell, such as that illustrated in Figure 7.6(b), is a device used to measure the intensity of light. In a certain experiment, when light of wavelength 550 nm is directed on the photocell, electrons are emitted at the rate of 8.6 X 10-13 C/s. Assume that each photon that impinges on the photocell emits one electron. How many photons per second are striking the photocell? How much energy per second is the photocell absorbing?
Periodic Table; Electron Shells; Atomic Radii
23. Which will be closer to the nucleus, the n = 3 electron shell in Ar or the n = 3 shell in Kr?
24. Why does the quantum mechanical description of many-electron atoms make it difficult to define a precise atomic radius?
25. How does the size of atoms change as we move (a) from left to right in a row in the periodic table; (b) from top to bottom in a group in the periodic table? (c) Arrange the following atoms in order of increasing atomic radius: F, P, S, As.
26. (a) Why does the He atom have a smaller radius than the H atom? (b) Why is the He atom smaller than the Ne atom?
Ionization Energies; Electron Affinities
27. Write equations that show the processes that describe the first, second, and third ionization energies of a tellurium atom.
28. Why is the second ionization energy of lithium much greater than that of beryllium?
29. What is the trend in first ionization energies as one proceeds down the group 8A elements? Explain how this trend relates to the variation of atomic radii.
30. Based on their positions in the periodic table, predict which atom of the following pairs will have the largest first ionization energy: (a) O, Ne; (b) Mg, Sr; (c) K, Cr; (d) Br, Sb; (e) Ga, Ge.
31. The atoms and ions Na, Mg+, Al2+, and Si3- all have the same number of electrons they are an isoelectronic series. (a) For which of these will the effective nuclear charge acting on the outermost electron be the smallest? (b) For which will it be the greatest? (c) How do the data in Table 7.2 provide support for your answer?
32. The electron affinity of lithium is a negative value, whereas the electron affinity of beryllium is a positive value. Account for this observation by using electron configurations.
Properties of Metals and Nonmetals
33. For each of the following pairs, which element will have the greater metallic character: (a) Li or Be; (b) Li or Na; (c) Sn or P; (d) Al or B?
34. Predict whether each of the following oxides is ionic or molecular: SO2, MgO, Li2O, P2O5, Y2O3, N2O, XeO3. Explain the reasons for your choices.
35. What is meant by the terms acidic oxide and basic oxide? Give an example of each.
36. Write balanced equations for the following reactions: (a) calcium oxide with water; (b) copper(II) oxide with nitric acid; (c) sulfur trioxide with water; (d) carbon dioxide with aqueous sodium hydroxide.
Group Trends in Metals and Nonmetals
37. Write a balanced equation for the reaction that occurs in each of the following cases: (a) Potassium is added to water; (b) Barium is added to water; (c) Lithium is heated in nitrogen, forming lithium nitride; (d) Magnesium burns in oxygen.
38. Compare the elements fluorine and chlorine with respect to the following properties: (a) electron configuration; (b) most common ionic charge; (c) first ionization energy; (d) reactivity toward water; (e) electron affinity; (f) atomic radius. Account for the differences between the two elements.