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 toether 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 formulatin his theory. 3. Dalton said that compounds could form only by combinin whole atoms, not parts of atoms. Thus chemical formulas will always show whole numbers of atoms combinin. 4. An atom is electrically neutral, containin equal numbers of protons and electrons. An ion has a chare resultin from an imbalance between the numbers of protons and electrons. 5. The force of attraction increases as the distance between the chared particles decreases. 6. Cations are ions with a positive chare and anions are ions with a neative chare. 7. The neutron is about 1840 times heavier than an electron. 8. Particle Chare Mass proton þ1 1 amu neutron 0 1 amu electron 1 0 9. Element Atomic number (a) copper 29 nitroen 7 phosphorus 15 (d) radium 88 (e) zinc 30 10. Isotopic notation A Z E 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-
SOLUTIONS TO EXERCISES 1. N 3,O 2, and Te 3 2. M 2+,Cr 3+,Ba 2+,Ca 2+, and Y 3+ 3. Gold nuclei are very massive (compared to an alpha particle) and have a lare positive chare. As the positive alpha particles approach the atom, some are deflected by this positive chare. Alpha particles approachin a old nucleus directly are deflected backwards by the massive positive nucleus. 4. (a) 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 fliht indicates the nucleus of the atom is also positively chared. Most alpha particles pass throuh the old foil undeflected leadin 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 remainin space within the atom outside the nucleus. 6. The nucleus of an atom contains nearly all of its mass. 7. (a) 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 chare 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 throuhout 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 throuhout 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. most elements exist in nature as a mixture of isotopes with different atomic masses due to different numbers of neutrons. The atomic mass iven in the periodic table is the averae mass of all these isotopes. -36-
10. The isotope of 12 6C with a mass of 12 is an exact number by definition. The mass of other isotopes, such as Cu, will not be an exact number for reasons iven in Exercise 9. 63 29 11. The isotopes of hydroen are protium, deuterium, and tritium. 12. All three isotopes of hydroen 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 Neutrons number 70 38 72 40 73 41 74 42 76 44 14. All five isotopes have nuclei that contain 30 protons. The numbers of neutrons are: 15. (a) 65 29 Cu 45 20 Ca 84 36 Kr 16. (a) 109 47 A 18 8 O 57 26 Fe Isotope mass Neutrons number 64 34 66 36 67 37 68 38 70 40 17. (a) 29 protons, 29 electrons, and 34 neutrons 16 protons, 16 electrons, and 16 neutrons 25 protons, 25 electrons, and 30 neutrons (d) 19 protons, 19 electrons, and 20 neutrons 18. (a) 26 protons, 26 electrons, and 28 neutrons 11 protons, 11 electrons, and 12 neutrons 35 protons, 35 electrons, and 44 neutrons (d) 15 protons, 15 electrons, and 16 neutrons 19. (a) 33 Arsenic, As -37-
43 (d) The chare is 3, this is an anion. (e) 76 33 As 20. (a) 56 Barium, Ba 79 (d) The chare is þ2, this is a cation. (e) 135 56 Ba 21. For each isotope: (%)(amu) ¼ that portion of the averae atomic mass for that isotope. Add toether to obtain the averae 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 averae atomic mass of Zr 22. For each isotope: (%)(amu) ¼ that portion of the averae atomic mass for that isotope. The sum of the portions ¼ the averae 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 averae 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 averae atomic mass The element is chlorine (see periodic table). 25. V sphere ¼ 4 3 pr3 r A ¼ radius of atom; r N ¼ radius of nucleus 4 V atom ¼ 3 pr3 3 A ¼ r3 A 1:0 10 8 V nucleus 4 r 3 ¼ 3 pr3 N 1:0 10 13 3 ¼ N 1:0 1015 1:0 The ratio of atomic volume to nuclear volume is 1:0 10 15 : 1:0: 26. 3:0 10 8 cm 1:5 105 2:0 10 13 ¼ cm 1:0 The ratio of the diameter of an Al atom to its nucleus diameter is 1:5 10 5 : 1:0: -38-
27. (a) In Rutherford s experiment the majority of alpha particles passed throuh the old 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 comin from both the anode and the cathode. In Rutherford s experiment an alpha particle was occasionally dramatically deflected by the nucleus of a old atom. The direction of deflection showed the nucleus to be positive. Positive chares repel each other. 28. Elements (a) and are isotopes of phosphorus. 29. 2:54 cm 1 atom Si ð8:5in: Þ in: 2:34 10 8 ¼ 9:2 10 8 atoms Si 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 thouh the nuclear composition of the atoms are different. 31. 156 Dy has 90 neutrons; 160 Gd has 96 neutrons; 162 Er has 94 neutrons; 165 Ho has 98 neutrons. In order of increasin number of neutrons: Dy<Er<Gd<Ho On the periodic table, the order is based on increasin 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: amuþþð1 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% 63 Q ¼ 50% 33. (a) Compare the mass of the unknown element to the mass of a carbon-12 atom. 3:27 10 19 1 12:0 amu m unknown element 1000 m 1:9927 10 23 ¼ 197 amu The atomic mass of the unknown element is 197 amu The unknown element is Au, old (see periodic table) 34. ð0:52 lb AÞ 453:6 lb 1 atom A 1:79 10 22 A ¼ 1:3 10 24 atoms A -39-
35. These are the elements that have the same number of protons, neutrons, and electrons. protons neutrons electrons He 2 2 2 C 6 6 6 N 7 7 7 O 8 8 8 Ne 10 10 10 M 12 12 12 Si 14 14 14 S 16 16 16 Ca 20 20 20 36. C + O + O 2+ 6 protons, 5 electrons 8 protons, 7 electrons 8 protons, 6 electrons 37. 38. Mineral Supplement Mineral use Ion provided Number protons Number electrons Calcium carbonate Bones and Teeth Ca 2+ 20 18 Iron(II) sulfate Hemolobin Fe 2+ 26 24 Chromium(III) nitrate Insulin Cr 3+ 24 21 Manesium sulfate Bones M 2+ 12 10 Zinc sulfate Cellular metabolism Zn 2+ 30 28 Potassium iodide Thyroid function I 53 54 Element Symbol Atomic # Mass # Protons Neutrons Electrons Chlorine Gold Barium Aron Nickel 36 Cl 17 36 17 19 17 197 Au 79 197 79 118 79 135 Ba 56 135 56 79 56 38 Ar 18 38 18 20 18 58 Ni 28 58 28 30 28-40-
39. Element Symbol Atomic # Mass # Protons Neutrons Electrons Xenon Silver Fluorine Uranium Potassium 134 Xe 54 134 54 80 54 107 A 47 107 47 60 47 19 F 9 19 9 10 9 235 U 92 235 92 143 92 41 K 19 41 19 22 19 40. O O 2 Na Na + (a) P P 3 Ca 2+ (d) Ca 41. 2 3 2p 1n 2p 2n 3p 3n 3p 4n 3 2 He 4 2 He (a) 5 6 3 Li 7 3 Li 6 5p 5n 5p 6n 6p 7n 6p 8n 10 5 B 11 5 B 13 6 C 14 6 C (d) 42. The mass of one electron is 9:110 10 28 rams. ð13þð9:110 10 28 (a) Aluminum has 13 electrons. 4:480 10 23 ð100þ ¼ 0:02644% electrons -41-
(d) ð15þð9:110 10 28 Phosphorus has 15 electrons. 5:143 10 23 ð100þ ¼ 0:02657% electrons ð36þð9:110 10 28 Krypton has 36 electrons. 1:392 10 22 ð100þ ¼ 0:02356% electrons ð78þð9:110 10 28 Platinum has 78 electrons. 3:240 10 22 ð100þ ¼ 0:02193% electrons 43. The mass of one proton is 1:673 10 24 rams. (a) ð34þð1:673 10 24 Selenium has 34 protons. 1:311 10 22 ð100þ ¼ 43:39% protons ð54þð1:673 10 24 Xenon has 54 protons. 2:180 10 22 ð100þ ¼ 41:44% protons ð17þð1:673 10 24 Chlorine has 17 protons. 5:887 10 23 ð100þ ¼ 48:31% protons (d) ð56þð1:673 10 24 Barium has 56 protons. 2:280 10 22 ð100þ ¼ 41:09% protons 44. The electron reion is the area around the nucleus where electrons are most likely to be located. 45. Abundance 265 266 267 268 269 270 271 272 Mass averae 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 reater than 107. -42-