E J The electron s energy difference between the second and third levels is J. = J

Transcription

1 The wavelength of light emitted is 654 nm. = c f c m/s f c m 1s m f z 1 s The frequency of the light emitted is z. E hf h J/z E J z 14 z E J The electron s energy difference between the second and third levels is J. (e) ---- n = n = n = 2 1 e n = 1 1 p + hydrogen atom E 4 2 = J E 3 2 = J ( J) ( J) = J The energy difference between hydrogen atom electron energy levels n = 4 and n = 3 will be J. 14. The most likely assumption would seem to be that theories would be advanced that would try to describe electron arrangements and energies for atoms more complex than hydrogen. 3.5 QUANTUM NUMBERS PRACTICE (Page 182) 1. Bohr and Sommerfeld both used observations of line spectra. 2. Bohr proposed circular electron orbits for hydrogen, while Sommerfeld proposed several elliptical orbits. 92 Chapter 3 Copyright 2003 Nelson

2 3. Table 3 Sommerfeld s Electron Energy Sublevels Primary energy Principal quantum Possible secondary Number of sublevels level number, n quantum numbers, l per primary level , ,1, ,1,2, For any principal quantum number, n, the highest possible value of l is n For any principal quantum number, n, the possible values of l include all of the integers from 0 to n 1. SECTION 3.5 QUESTIONS (Page 184) 1. The main kind of evidence used comes from atomic line spectra, particularly the splitting of lines. 2. The first quantum number describes the main energy level; the second quantum number describes small energy level steps within the main energy level corresponding to different shapes of orbits ; the third quantum number describes the orientation in space of the electron orbits ; and the fourth quantum number describes the spin of electrons. 3. (a) For l = 0, 1, 2, and 3, there are 0, 3, 5, and 7 possible values of m l, respectively. (b) Each number is the next greater odd integer (or 2l + 1 for all ls except l = 0). (c) From the answer to (b), the number of possible values for m l for l = 4 must be 9 (the next odd integer). 4. The fourth quantum number is m s, and it is necessary to explain magnetic properties of atoms. 5. Table 4 Summary of Quantum Numbers (n) (0 to n 1) ( l to +l) (+1/2 or 1/2) /2, 1/2 1-1, 0, +1 +1/2, 1/2 2-2, -1, 0, +1, +2 +1/2, 1/2 3-3, -2, -1, 0, +1, +2, +3 +1/2, 1/2 6. It takes four quantum numbers to describe fully an electron in an atom. An example listing labels and values of each quantum number might be n = 2, l = 1, m l = 1, and m s = +1/2. This might describe an electron in a hydrogen atom in an excited state. 7. For each principal quantum number from n = 1 to n = 3 (see Table 4), there can be 2, 8, and 18 different electron descriptions. 8. In the development of scientific knowledge, empirical knowledge usually comes first. Examples from this section are the investigation of bright line spectra and of magnetic effects upon these spectra both of which preceded the theory that attempts to explain them in terms of atomic structure. 3.6 ATOMIC STRUCTURE AND TE PERIODIC TABLE PRACTICE (Page 191) 1. The aufbau principle states that electrons occupy lowest energy orbitals first. The Pauli exclusion principle states that no more than two electrons (of opposite spin) may occupy the same orbital, and und s rule states that electrons are not paired within sublevel orbitals until each sublevel orbital has at least one electron. Copyright 2003 Nelson Atomic Theories 93

3 2. A periodic table can be used to help complete energy level diagrams because it is arranged according to electron energy levels, sublevels, and orbitals. 3. (a) 3p phosphorus atom, P (b) 4s potassium atom, K (c) 3d 4s manganese atom, Mn (d) nitride ion, N 3 (e) 4p 3d 4s bromide ion, Br 94 Chapter 3 Copyright 2003 Nelson

4 (f) 5s 4s 4d 4p 3d cadmium ion, Cd (a) potassium ion, K + chloride ion, Cl (b) An atom of the noble gas argon, Ar, has the same electron orbital energy level diagram as do these two ions. Extension 5. 1s would be n = 1, l = 0 2s would be n = 2, l = 0 2p would be n = 2, l = 1 3d would be n = 3, l = 2 PRACTICE (Page 194) 6. (a) beryllium (b) fluorine (c) sodium (d) sulfur 7. sodium 1s 2 2s 2 2p 6 3s 1 magnesium 1s 2 2s 2 2p 6 3s 2 aluminum 1s 2 2s 2 2p 6 3s 2 3p 1 silicon 1s 2 2s 2 2p 6 3s 2 3p 2 phosphorus 1s 2 2s 2 2p 6 3s 2 3p 3 sulfur 1s 2 2s 2 2p 6 3s 2 3p 4 chlorine 1s 2 2s 2 2p 6 3s 2 3p 5 argon 1s 2 2s 2 2p 6 3s 2 3p 6 8. fluorine [e] 2s 2 2p 5 chlorine [Ne] 3s 2 3p 5 bromine [Ar] 4s 2 4p 5 iodine [Kr] 5s 2 5p 5 astatine [Xe] 6s 6p 5 Each halogen configuration ends with two s and three p orbitals. Other chemical families, such as the alkali metals, also have similar valence orbital configurations. Copyright 2003 Nelson Atomic Theories 95

5 9. fluoride ion 1s 2 2s 2 2p 6 sodium ion 1s 2 2s 2 2p Isoelectronic means having the same number of electrons. 11. zinc ion [Ar] 3d 10 cadmium ion [Kr] 4d 10 mercury(ii) ion [Xe] 4f 14 5d 8 SECTION 3.6 QUESTIONS (Page 197) 1. Maximum number of electrons: (a) 2e (b) 8e (c) 18e (d) 32e 2. Orbitals and Electrons in s, p, d, and f Sublevels Sublevel Symbol Value of l Number of orbitals Max # of electrons (a) s (b) p (c) d (d) f The aufbau principle states that electrons occupy lower energy orbitals first. Either a diagonal orbital diagram or the periodic table can be used to determine this order of occupancy. 4. If four electrons are to be placed into a p subshell, the aufbau principle states that all lower energy levels must already be full, and und s rule states that each of the three p orbitals must already have one occupying electron before the fourth is placed in any one of the orbitals. 5. (a) 4s beryllium atom, Be magnesium atom, Mg calcium atom, Ca (b) These diagrams all show two s electrons in the highest energy orbital. 6. (a) s (b) d (c) p (d) f 7. (a) The halide ions have a charge of negative one, 1. (b) The electron configuration of each halogen shows one less electron than a full p orbital energy level; for example, fluorine is 1s 2 2s 2 2p 5, chlorine is 1s 2 2s 2 2p 6 3s 2 3p 5, bromine is 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5, and so on. We explain the ion charge by assuming that halogens strongly attract one extra electron to occupy the unfilled p orbital in the highest orbital energy level. 8. (a) A sodium ion, Na +, has a configuration of 1s 2 2s 2 2p 6, the same as that of a neon atom, Ne. (b) These two chemical entities are both chemically very stable, and have the same electron configuration; but sodium ions are positively charged and strongly attract negative ions to form ionic solid compounds, while neutral neon atoms have extremely weak attractive forces, and form a noble gas at room conditions. 9. The electron configuration for Sb 3+ is [Kr] 5s 2 4d 10. The electron configuration for Sb 5+ is [Kr]4d The electron configuration for a gallium atom, Ga, is [Ar] 4s 2 3d 10 4p 1. The Ga 3+ ion has most probably lost three electrons from the fourth shell, and so should have a configuration of [Ar] 3d Copper has an electron configuration of [Ar] 4s 1 3d 10 and therefore has an unpaired electron (4s 1 ). Zinc has an electron configuration of [Ar] 4s 2 3d 10 and has no unpaired electrons. 96 Chapter 3 Copyright 2003 Nelson

6 CAPTER 3 SELF-QUIZ (Page 219) 1. False: The region in space where an electron is most likely to be found is called an orbital. 2. False: Electron configurations are often condensed by writing them using the previous noble-gas core as a starting point. In this system, [Ar] 3d 3 4s 2 would represent vanadium. 3. False: The f sublevel is thought to have seven orbitals. 4. True 5. True 6. False: Rutherford knew the nucleus had to be very small because very few alpha particles were deflected when fired through a layer of gold atoms. 7. False: Electrons shifting to lower levels, according to Bohr, would account for emission spectra. 8. True 9. True 10. True 11. False: The Pauli exclusion principle states that no more than two electrons may occupy the same orbital, and that they must have opposite spins. 12. (b) 13. (d) 14. (a) 15. (c) 16. (c) 17. (b) 18. (b) 19. (d) CAPTER 3 REVIEW (Page 220) 1. (a) Rutherford interpreted the deflection of alpha particles travelling through a thin foil to mean that atoms had tiny, massive nuclei. (b) Bohr interpreted the bright-line spectrum of hydrogen to mean that electrons exist only at specific energy levels. 2. The Rutherford model explained nothing about the nature of electrons. The Bohr model did not make acceptable predictions for atoms larger than hydrogen. 3. Orbit and orbital are terms that both refer to electrons within atoms. An orbit is a simplistic representation of a small particle in a circular path, used in the Bohr Rutherford model. An orbital is a probability density for a wave function that occupies a volume of space, used in the visualizing of the quantum mechanical model. 4. The main kind of experimental work used to develop the concepts of quantum mechanics was spectroscopy, specifically the analysis of bright-line spectra. 5. (a) Quantum is a term referring to a smallest unit or part of something. (b) Orbital is a term describing a volume of space that is occupied by an electron. (c) Electron probability density describes the calculated likelihood of locating an electron at any point within a given volume of space. (d) Photon is a quantum of electromagnetic energy a smallest piece or package of light. 6. 2p (a) the main/principal energy level is the first number: 1,2,... (b) the energy sublevel (subshell) is the letter following: s, p,... (c) the orbital orientation (x, y, or z axis) is the respective line (d) the spin of the electron (up or down) is the arrow: or oxygen atom, O 7. The idea of electron spin comes from observations of line spectra influenced by a magnetic field as well as evidence from different kinds of magnetism. Copyright 2003 Nelson Atomic Theories 107

7 8. 1s 2s 3s 4s 5s 6s 7s 3d 4d 5d 6d 2p 3p 4p 5p 6p 1s 4f 5f 9. According to quantum mechanics, an element s properties relate to its position in the periodic table because its position is directly related to the orbital configuration of its atoms. 10. potassium ion, K + sulfide ion, S 2 An atom of the noble-gas argon, Ar, has the same electron orbital energy-level diagram as do these two ions. 11. (a) All of the alkali metals are soft, metallic solids with low melting and boiling points. They have high chemical reactivity, readily forming +1 ions. (b) We explain properties, using their electron configurations. All have a single s electron in the highest energy orbital, which is easily removed by the attraction of other atoms. The nearly empty valence shell creates the metallic properties conductivity, shininess, and so on. 12. (a) 1s 2 2s 2 2p 6 3s 2 (b) 1s 2 2s 2 2p 6 3s 2 3p 6 (c) 1s 2 2s 2 2p 6 3s 2 3p 6 (d) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 1 (e) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 1 4f 14 5d (a) [Kr] 5s 2 4d 1 (b) [Kr] 5s 2 4d 10 5p 3 (c) [Xe] Ba Aluminum and titanium should be paramagnetic because these two atoms have unpaired electrons. Beryllium and mercury have atoms with filled orbitals. 15. (a) arsenic atom, As (b) rubidium ion, Rb + (c) iodide ion, I (d) holmium atom, o 16. (a) 2e (b) 8e (c) 18e (d) 32e 17. A 2p x orbital is identical to the 2p y and 2p z orbitals, except for orientation. It lies at 90 to the other two. 18. (a) Max Planck explained that electromagnetic energy could be released only in smallest given amounts, which he called quanta, with the amount determined by the frequency of the radiation. (b) Louis de Broglie suggested that particles could have properties and characteristics of waves, and that this effect would be significant for tiny, fast-moving particles like electrons. 108 Chapter 3 Copyright 2003 Nelson

8 (e) Dishwashing liquid molecules must attract water molecules better than they attract each other because water dissolves the substance and washes it away. Gear oil molecules must attract each other better than they attract water molecules because water doesn t dissolve the oil or wash it away. (f) We observe that the dishwashing liquid will mix with (dissolve) the oil, and the mixture (solution) of the two will dissolve in water, and be washed away. It seems that dishwashing liquid molecules are somehow able to attract both water molecules and oil molecules. (g) Dishwasher detergent is thick and viscous, so its molecules are quite cohesive, and seem to be adhesive to glass and water and oil. Gear oil molecules are less cohesive, and not very adhesive to glass or water only to the dishwashing liquid. This seems logical, since dishwashing liquids are designed to attract and dissolve all kinds of food materials; and gear oil is designed to make metal surfaces slide against each other without wearing down. 4.1 LEWIS TEORY OF BONDING PRACTICE (Page 227) 1. (a) Mg - 2, Cl - 1 (b) C - 4, - 1 (c) -1, O - 2 (d) - 2, S - 2 (e) N - 3, In the order that they were created by chemists, we have the (c) Dalton atom, (b) empirical formulas, (d) Kekulé structures, (a) Lewis structures, and (e) Schrödinger quantum mechanics. 3. (a) 1s 2 2s 2 2p 6 3s 2 3p 1 Al (b) 1s 2 2s 2 2p 6 3s 2 3p 5 (c) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 (d) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 2 Cl Ca Ge 4. (a) O (b) P (c) Br (d) Rb 5. (a) C C (b) O O Copyright 2003 Nelson Chemical Bonding 111