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.

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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

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- 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

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- 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

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 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