CHAPTER 5 EARLY ATOMIC THEORY AND STRUCTURE SOLUTIONS TO REVIEW QUESTIONS 1. (a) (b) (c) (d) (e) Element copper nitrogen phosphorus radium zinc Atomic number 29 7 15 88 30 2. The neutron is about 1840 times heavier than an electron. 3. Particle Charge Mass proton neutron electron þ1 0 1 1 amu 1 amu 0 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. Isotopic notation A ZE Z represents the atomic number A represents the mass number 6. Isotopes contain the same number of protons and the same number of electrons. Isotopes have different numbers of neutrons and thus different atomic masses. - 31 - - Chapter 5 - SOLUTIONS TO EXERCISES 1. The formula for water is H2O. There is one atom of oxygen for every two atoms of hydrogen. The molar mass of oxygen is 16.00 g and the molar mass of hydrogen is 1.008 g. For H2O the mass of two hydrogen atoms is 2.016 g and the mass of one oxygen atom is 16.00 g. The ratio of hydrogen to oxygen is approximately 2:16 or 1:8. Therefore, there is 1 gram of hydrogen for every 8 grams of oxygen. 2. The formula for hydrogen peroxide is H2O2. There are two atoms of oxygen for every two atoms of hydrogen. The molar mass of oxygen is 16.00 g and the molar mass of hydrogen is 1.008 g. For hydrogen peroxide the total mass of hydrogen is 2.016 g and the total mass of oxygen is 32.00 g for a ratio of hydrogen to oxygen of approximately 2: 32 or 1:16. Therefore, there is 1 gram of hydrogen for every 16 grams of oxygen. 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 - 32 - - Chapter 5 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. 10. The isotope of 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) 17. (a) (b) (c) (d) Neutrons 34 36 37 38 40 65 29 Cu 45 20 Ca 84 36 Kr 109 47 Ag 18 8O 57 26 Fe 59 27 Co 31 15 P 184 74 W 235 92 U Nucleus contains 27 protons and 32 neutrons Nucleus contains 15 protons and 16 neutrons Nucleus contains 74 protons and 110 neutrons Nucleus contains 92 protons and 143 neutrons - 33 - - Chapter 5 18. (a) (b) (c) (d) 25 12 Mg 91 40 Zr 122 50 Sn 202 80 Hg Nucleus contains 12 protons and 13 neutrons Nucleus contains 40 protons and 51 neutrons Nucleus contains 50 protons and 72 neutrons Nucleus contains 80 protons and 122 neutrons 19. (a) (b) (c) The atomic number of the element is 24. The symbol of the element is Cr. The element contains 30 neutrons. 20. (a) (b) (c) The atomic number of the element is 35. The symbol of the element is Br. The element contains 45 neutrons. 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 amu ¼ x ¼ 50. ¼ mass of the fifth isotope of titanium 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 A 3 ¼ ¼ 3 ¼ ¼ 3 Vnucleus 4 3 1:0 rN 1:0 1013 prN 3 - 34 - The ratio of atomic volume to nuclear volume is 1:0 1015 : 1:0: - Chapter 5 26. 3:0 108 cm 1:5 105 ¼ 1:0 2:0 1013 cm 27. (a) (b) (c) The ratio of the diameter of an Al atom to its nucleus diameter is 1:5 105 : 1:0: 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 29. ð8:5 in:Þ ¼ 9:2 108 atoms Si 8 in: 2:34 10 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 60 Q ¼ 50% Q63 ¼ 50% 33. (a) 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) - 35 - - Chapter 5 453:6 g 1 atom Ag 34. ð0:52 lb AgÞ ¼ 1:3 1024 atoms Ag lb 1:79 1022 g 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 Element Chlorine 37. 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 Element Symbol Au Ni Atomic # Mass # Protons Neutrons Electrons Xe 54 134 54 80 54 Ag 47 107 47 60 47 9 19 9 10 9 U 92 235 92 143 92 K 19 41 19 22 19 Xenon 134 Silver 107 Fluorine 19 Uranium 235 Potassium 41 F - 36 - - Chapter 5 38. Exercise 38 should refer to Figure 5.5 (not 5.4). e– e– O2– O Na+ Na e– (a) (b) e– e– P3– P Ca2+ Ca e– e– e– (c) (d) 39. Exercise 39 should refer to Figure 5.8 (not 5.7). 2e– 3e– 2p 1n 2p 2n 3p 3n 3p 4n 3 He 2 4 He 2 6 Li 3 7 Li 3 (a) (b) 5e– 6e– 5p 5n 5p 6n 6p 7n 6p 8n 10 B 5 11 B 5 13 C 6 14 C 6 (c) (d) 40. 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 ð15Þð9:110 1028 g (b) Phosphorus has 15 electrons. ð100Þ ¼ 0:02657% electrons 5:143 1023 g ð36Þð9:110 1028 g (c) Krypton has 36 electrons. ð100Þ ¼ 0:02356% electrons 1:392 1022 g ð78Þð9:110 1028 g (d) Platinum has 78 electrons. ð100Þ ¼ 0:02193% electrons 3:240 1022 g - 37 - - Chapter 5 41. 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 (b) Xenon has 54 protons. ð100Þ ¼ 41:44% protons 2:180 1022 g ð17Þð1:673 1024 g (c) Chlorine has 17 protons. ð100Þ ¼ 48:31% protons 5:887 1023 g ð56Þð1:673 1024 g ð100Þ ¼ 41:09% protons (d) Barium has 56 protons. 2:280 1022 g 42. The electron region is the area around the nucleus where electrons are most likely to be located. Abundance 43. 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. - 38 -