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C05 06/13/2012 17:38:26 Page 35 CHAPTER 5 EARLY ATOMIC THEORY AND STRUCTURE SOLUTIONS TO REVIEW QUESTIONS 1. Elements are composed of indivisable particles called atoms. Atoms of the same element have the same properties; atoms of different elements have different properties. Compounds are composed of atoms joined together to form compounds. Atoms combine in whole number ratios to form compounds. Atoms may combine in different ratios to form more than one compound. 2. Dalton used Democritus’ idea that all matter was composed of tiny indivisible particles or atomos when formulating his theory. 3. Dalton said that compounds could form only by combining whole atoms, not parts of atoms. Thus chemical formulas will always show whole numbers of atoms combining. 4. An atom is electrically neutral, containing equal numbers of protons and electrons. An ion has a charge resulting from an imbalance between the numbers of protons and electrons. 5. The force of attraction increases as the distance between the charged particles decreases. 6. Cations are ions with a positive charge and anions are ions with a negative charge. 7. The neutron is about 1840 times heavier than an electron. 8. Particle proton neutron electron 9. (a) (b) (c) (d) (e) Charge Mass þ1 0 1 1 amu 1 amu 0 Element copper nitrogen phosphorus radium zinc 10. Isotopic notation Atomic number 29 7 15 88 30 A ZE Z represents the atomic number A represents the mass number 11. Isotopes contain the same number of protons and the same number of electrons. Isotopes have different numbers of neutrons and thus different atomic masses. 12. The mass number is equal to the sum of the number of protons and the number of neutrons in an atom. It is not possible to have a partial proton or neutron in an atom, thus the total number of nuclear particles will always be a whole number. - 35 - C05 06/13/2012 17:38:26 Page 36 - Chapter 5 - SOLUTIONS TO EXERCISES 1. N3, O2, and Te3 2. Mg2+, Cr3+, Ba2+, Ca2+, and Y3+ 3. Gold nuclei are very massive (compared to an alpha particle) and have a large positive charge. As the positive alpha particles approach the atom, some are deflected by this positive charge. Alpha particles approaching a gold nucleus directly are deflected backwards by the massive positive nucleus. 4. (a) (b) (c) The nucleus of the atom contains most of the mass since only a collision with a very dense, massive object would cause an alpha particle to be deflected back towards the source. The deflection of the positive alpha particles from their initial flight indicates the nucleus of the atom is also positively charged. Most alpha particles pass through the gold foil undeflected leading to the conclusion that the atom is mostly empty space. 5. In the atom, protons and neutrons are found within the nucleus. Electrons occupy the remaining space within the atom outside the nucleus. 6. The nucleus of an atom contains nearly all of its mass. 7. (a) (b) (c) Dalton contributed the concept that each element is composed of atoms which are unique, and can combine in ratios of small whole numbers. Thomson discovered the electron, determined its properties, and found that the mass of a proton is 1840 times the mass of the electron. He developed the Thomson model of the atom. Rutherford devised the model of a nuclear atom with the positive charge and mass concentrated in the nucleus. Most of the atom is empty space. 8. Electrons: Dalton – electrons are not part of his model Thomson – electrons are scattered throughout the positive mass of matter in the atom Rutherford – electrons are located out in space away from the central positive nucleus Positive matter: Dalton – no positive matter in his model Thomson – positive matter is distributed throughout the atom Rutherford – positive matter is concentrated in a small central nucleus 9. Atomic masses are not whole numbers because: (a) the neutron and proton do not have identical masses and neither is exactly 1 amu. (b) most elements exist in nature as a mixture of isotopes with different atomic masses due to different numbers of neutrons. The atomic mass given in the periodic table is the average mass of all these isotopes. - 36 - C05 06/13/2012 17:38:26 Page 37 - Chapter 5 10. The isotope of 126 C with a mass of 12 is an exact number by definition. The mass of other isotopes, such as 63 29 Cu, will not be an exact number for reasons given in Exercise 9. 11. The isotopes of hydrogen are protium, deuterium, and tritium. 12. All three isotopes of hydrogen have the same number of protons (1) and electrons (1). They differ in the number of neutrons (0, 1, and 2). 13. All five isotopes have nuclei that contain 32 protons. The numbers of neutrons are: Isotope mass number 70 72 73 74 76 Neutrons 38 40 41 42 44 14. All five isotopes have nuclei that contain 30 protons. The numbers of neutrons are: Isotope mass number 64 66 67 68 70 15. (a) (b) (c) 16. (a) (b) (c) Neutrons 34 36 37 38 40 65 29 Cu 45 20 Ca 84 36 Kr 109 47 Ag 18 8O 57 26 Fe 17. (a) (b) (c) (d) 29 protons, 29 electrons, and 34 neutrons 16 protons, 16 electrons, and 16 neutrons 25 protons, 25 electrons, and 30 neutrons 19 protons, 19 electrons, and 20 neutrons 18. (a) (b) (c) (d) 26 protons, 26 electrons, and 28 neutrons 11 protons, 11 electrons, and 12 neutrons 35 protons, 35 electrons, and 44 neutrons 15 protons, 15 electrons, and 16 neutrons 19. (a) (b) 33 Arsenic, As - 37 - C05 06/13/2012 17:38:27 Page 38 - Chapter 5 (c) (d) (e) 43 The charge is 3, this is an anion. 76 33 As 20. (a) (b) (c) (d) (e) 56 Barium, Ba 79 The charge is þ2, this is a cation. 135 56 Ba 21. For each isotope: (%)(amu) ¼ that portion of the average atomic mass for that isotope. Add together to obtain the average atomic mass. (0.5145)(89.905 amu) þ (0.1122)(90.906 amu) þ (0.1715)(91.905 amu) þ (0.1738)(93.906 amu) þ (0.0280)(95.908 amu) 46.26 amu þ 10.20 amu þ 15.76 amu þ 16.32 amu þ 2.69 amu ¼ 91.23 amu ¼ average atomic mass of Zr 22. For each isotope: (%)(amu) ¼ that portion of the average atomic mass for that isotope. The sum of the portions ¼ the average atomic mass. (0.080)(45.953) þ (0.073)(46.952) þ (0.738)(47.948) þ (0.055)(48.948) þ (1.000 0.946)x amu ¼ 47.9 amu ¼ 3.7 amu þ 3.4 amu þ 35.4 amu þ 2.7 amu þ 0.054x amu ¼ 47.9 amu ¼ 45.2 amu þ 0.054x ¼ 47.9 amu 0.054x ¼ 47.9 amu 45.2 amu 2:7 amu x ¼ 50. ¼ mass of the fifth isotope of titanium x amu ¼ 0:054 23. (0.6917)(62.9296 amu) þ (1.0000 0.6917)(64.9278 amu) ¼ 43.53 amu þ 20.02 amu ¼ 63.55 amu ¼ average atomic mass The element is copper (see periodic table). 24. (0.7577)(34.9689 amu) þ (1.0000 0.7577)(36.9659 amu) ¼ 26.50 amu þ 8.96 amu ¼ 35.46 amu ¼ average atomic mass The element is chlorine (see periodic table). 25. 4 Vsphere ¼ pr3 3 rA ¼ radius of atom; rN ¼ radius of nucleus 4 3 3 prA r3 1:0 108 Vatom 1:0 1015 3 A ¼ ¼ 3 ¼ ¼ 3 Vnucleus 4 3 1:0 rN 1:0 1013 prN 3 26. 3:0 108 cm 1:5 105 ¼ 1:0 2:0 1013 cm The ratio of atomic volume to nuclear volume is 1:0 1015 : 1:0: The ratio of the diameter of an Al atom to its nucleus diameter is 1:5 105 : 1:0: - 38 - C05 06/13/2012 17:38:27 Page 39 - Chapter 5 27. (a) (b) (c) In Rutherford’s experiment the majority of alpha particles passed through the gold foil without deflection. This shows that the atom is mostly empty space and the nucleus is very small. In Thomson’s experiments with the cathode ray tube, rays were observed coming from both the anode and the cathode. In Rutherford’s experiment an alpha particle was occasionally dramatically deflected by the nucleus of a gold atom. The direction of deflection showed the nucleus to be positive. Positive charges repel each other. 28. Elements (a) and (c) are isotopes of phosphorus. 2:54 cm 1 atom Si ¼ 9:2 108 atoms Si 29. ð8:5 in:Þ in: 2:34 108 cm 30. The properties of an element are related to the number of protons and electrons. If the number of neutrons differs, isotopes result. Isotopes of an element are still the same element even though the nuclear composition of the atoms are different. 31. 156 Dy has 90 neutrons; 160Gd has 96 neutrons; 162Er has 94 neutrons; 165Ho has 98 neutrons. In order of increasing number of neutrons: Dy<Er<Gd<Ho On the periodic table, the order is based on increasing number of protons, so the order is Gd<Dy<Ho<Er. 32. percent of sample 60 Q ¼ x percent of sample 63 Q ¼ 1 x ðxÞð60: amuÞ þ ð1 xÞð63 amuÞ ¼ 61:5 amu 60:x amu þ 63 amu 63x amu ¼ 61:5 amu 63 amu 61:5 amu ¼ 63x amu 60x amu 1:5 ¼ 3x 0:50 ¼ x 33. (a) 60 Q ¼ 50% 63 Q ¼ 50% Compare the mass of the unknown element to the mass of a carbon-12 atom. 1g 12:0 amu 19 3:27 10 mg unknown element ¼ 197 amu 1000 mg 1:9927 1023 g The atomic mass of the unknown element is 197 amu (b) The unknown element is Au, gold (see periodic table) 453:6 g 1 atom Ag 34. ð0:52 lb AgÞ ¼ 1:3 1024 atoms Ag lb 1:79 1022 g Ag - 39 - C05 06/13/2012 17:38:27 Page 40 - Chapter 5 35. These are the elements that have the same number of protons, neutrons, and electrons. 36. protons neutrons electrons He 2 2 2 C 6 6 6 N 7 7 7 O 8 8 8 Ne 10 10 10 Mg 12 12 12 Si 14 14 14 S 16 16 16 Ca 20 20 20 C+ 6 protons, 5 electrons O+ 8 protons, 7 electrons O2+ 8 protons, 6 electrons 37. 38. Ion provided Number protons Number electrons Bones and Teeth Ca2+ 20 18 Iron(II) sulfate Hemoglobin Fe2+ 26 24 Chromium(III) nitrate Insulin Cr3+ 24 21 Magnesium sulfate Bones Mg2+ 12 10 Zinc sulfate Cellular metabolism Zn2+ 30 28 Potassium iodide Thyroid function I 53 54 Mineral Supplement Mineral use Calcium carbonate Element Chlorine Symbol 36 Cl Atomic # Mass # Protons Neutrons Electrons 17 36 17 19 17 79 197 79 118 79 Gold 197 Barium 135 Ba 56 135 56 79 56 Argon 38 Ar 18 38 18 20 18 Nickel 58 28 58 28 30 28 Au Ni - 40 - C05 06/13/2012 17:38:27 Page 41 - Chapter 5 39. Element Symbol Atomic # Mass # Protons Neutrons Electrons Xenon 134 Xe 54 134 54 80 54 Silver 107 Ag 47 107 47 60 47 9 19 9 10 9 Fluorine 19 Uranium 235 U 92 235 92 143 92 Potassium 41 K 19 41 19 22 19 F 40. e– e– O2– O Na+ Na e– (a) (b) e– e– P3– P Ca2+ Ca e– e– e– (c) (d) 41. 2e– 3e– 2p 1n 2p 2n 3p 3n 3p 4n 3 He 2 4 He 2 6 Li 3 7 Li 3 (a) 5e– (b) 6e– 5p 5n 5p 6n 6p 7n 6p 8n 10 B 5 11 B 5 13 C 6 14 C 6 (c) (d) 42. The mass of one electron is 9:110 1028 grams. ð13Þð9:110 1028 g (a) Aluminum has 13 electrons. ð100Þ ¼ 0:02644% electrons 4:480 1023 g - 41 - 06/13/2012 17:38:28 Page 42 - Chapter 5 (b) (c) (d) ð15Þð9:110 1028 g Phosphorus has 15 electrons. ð100Þ ¼ 0:02657% electrons 5:143 1023 g ð36Þð9:110 1028 g ð100Þ ¼ 0:02356% electrons Krypton has 36 electrons. 1:392 1022 g ð78Þð9:110 1028 g ð100Þ ¼ 0:02193% electrons Platinum has 78 electrons. 3:240 1022 g 43. The mass of one proton is 1:673 1024 grams. ð34Þð1:673 1024 g (a) Selenium has 34 protons. ð100Þ ¼ 43:39% protons 1:311 1022 g ð54Þð1:673 1024 g ð100Þ ¼ 41:44% protons (b) Xenon has 54 protons. 2:180 1022 g ð17Þð1:673 1024 g ð100Þ ¼ 48:31% protons (c) Chlorine has 17 protons. 5:887 1023 g ð56Þð1:673 1024 g ð100Þ ¼ 41:09% protons (d) Barium has 56 protons. 2:280 1022 g 44. The electron region is the area around the nucleus where electrons are most likely to be located. 45. Abundance C05 265 266 267 268 269 Mass 270 271 272 average atomic mass : ð0:1081Þð269:14 amuÞ ¼ 29:09 amu ð0:3407Þð270:51 amuÞ ¼ 92:16 amu ð0:5512Þð271:23 amuÞ ¼ 149:50 amu Total ¼ 270:75 amu An atomic mass of 270.75 amu would come somewhere after Bohrium (mass ¼ 264 amu). So, the atomic number of this new element would be greater than 107. - 42 -