EARLY ATOMIC THEORY AND STRUCTURE

C H A P T E R 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 Charge Mass

proton þ1 1 amu

neutron 0 1 amu

electron 1 0

9. Element Atomic number

(a) copper 29

(b) nitrogen 7

(c) phosphorus 15

(d) radium 88

(e) zinc 30

10. Isotopic notation ^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.

SOLUTIONS TO EXERCISES

1. N^3, O^2, and Te^3

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) 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.

(b) The deflection of the positive alpha particles from their initial flight indicates the nucleus of the atom is also positively charged.

(c) 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) Dalton contributed the concept that each element is composed of atoms which are unique, and can combine in ratios of small whole numbers.

(b) 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.

(c) 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 differ- ent numbers of neutrons. The atomic mass given in the periodic table is the average mass of all these isotopes.

10. The isotope of¹²₆C with a mass of 12 is an exact number by definition. The mass of other isotopes, such as

63

29Cu, 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

Neutrons

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:

Isotope mass number

Neutrons

64 34

66 36

67 37

68 38

70 40

15. (a) ⁶⁵₂₉Cu (b) ⁴⁵₂₀Ca (c) ⁸⁴₃₆Kr 16. (a) ¹⁰⁹₄₇Ag

(b) ¹⁸₈O (c) ⁵⁷₂₆Fe

17. (a) 29 protons, 29 electrons, and 34 neutrons (b) 16 protons, 16 electrons, and 16 neutrons (c) 25 protons, 25 electrons, and 30 neutrons (d) 19 protons, 19 electrons, and 20 neutrons 18. (a) 26 protons, 26 electrons, and 28 neutrons (b) 11 protons, 11 electrons, and 12 neutrons (c) 35 protons, 35 electrons, and 44 neutrons (d) 15 protons, 15 electrons, and 16 neutrons 19. (a) 33

(b) Arsenic, As

(c) 43

(d) The charge is3, this is an anion.

(e) ⁷⁶₃₃As 20. (a) 56

(b) Barium, Ba (c) 79

(d) The charge isþ2, this is a cation.

(e) ¹³⁵₅₆Ba 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 amuþ 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 portions¼ 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 x amu ¼2:7 amu

0:054 x ¼ 50. ¼ mass of the fifth isotope of titanium 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. Vsphere¼4

3pr³ rA ¼ radius of atom; rN¼ radius of nucleus Vatom

Vnucleus¼ 4 3pr³A

4 3pr³N

¼r³_A

r³_N ¼ 1:0  10^8
3

1:0  10^13
3¼1:0  10¹⁵

1:0 The ratio of atomic volume to nuclear volume is 1:0  10¹⁵: 1:0:

26. 3:0  10^8cm

2:0  10^13cm¼1:5  10⁵

1:0 The ratio of the diameter of an Al atom to its nucleus diameter is 1:5  10⁵: 1:0:

27. (a) 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.

(b) In Thomson’s experiments with the cathode ray tube, rays were observed coming from both the anode and the cathode.

(c) 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.

29. ð8:5 in:Þ 2:54 cm in:

 

1 atom Si 2:34  10^8cm

 

¼ 9:2  10⁸atoms Si

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. ¹⁵⁶Dy 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 sample⁶⁰Q¼ x percent of sample⁶³Q¼ 1  x

x

ð Þ 60: amuð Þ þ 1  xð Þ 63 amuð Þ 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

60Q¼ 50%

63Q¼ 50%

33. (a) Compare the mass of the unknown element to the mass of a carbon-12 atom.

3:27  10^19mg unknown element
1 g 1000 mg

 

12:0 amu 1:9927  10^23g

 

¼ 197 amu

The atomic mass of the unknown element is 197 amu (b) The unknown element is Au, gold (see periodic table)

34. ð0:52 lb AgÞ 453:6 g lb

 

1 atom Ag 1:79  10^22g Ag

 

¼ 1:3  10²⁴atoms Ag

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

Mg 12 12 12

Si 14 14 14

S 16 16 16

Ca 20 20 20

36. C⁺ 6 protons, 5 electrons O⁺ 8 protons, 7 electrons O²⁺ 8 protons, 6 electrons 37.

Mineral Supplement Mineral use Ion provided

Number protons

Number electrons

Calcium carbonate 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

38. Element Symbol Atomic # Mass # Protons Neutrons Electrons

Chlorine ³⁶Cl 17 36 17 19 17

Gold ¹⁹⁷Au 79 197 79 118 79

Barium ¹³⁵Ba 56 135 56 79 56

Argon ³⁸Ar 18 38 18 20 18

Nickel ⁵⁸Ni 28 58 28 30 28

39. Element Symbol Atomic # Mass # Protons Neutrons Electrons

Xenon ¹³⁴Xe 54 134 54 80 54

Silver ¹⁰⁷Ag 47 107 47 60 47

Fluorine ¹⁹F 9 19 9 10 9

Uranium ²³⁵U 92 235 92 143 92

Potassium ⁴¹K 19 41 19 22 19

40.

O O^2–

e^–

e^– Na Na⁺

e^–

P P^3–

e^–

e^– e^–

e^–

e^–

Ca²⁺ Ca

41.

2p 1n

3

2He ⁴₂He

2p 2n 2e^–

3p 3n

6

3Li ⁷₃Li

3p 4n 3e^–

5p 5n

10

5B ¹¹₅B

5p 6n 5e^–

13

6C ¹⁴₆C

6p 7n

6p 8n 6e^–

42. The mass of one electron is 9:110  10^28 grams.

(a) Aluminum has 13 electrons. ð13Þð9:110  10^28g 4:480  10^23g

 

ð100Þ ¼ 0:02644% electrons

(a) (b)

(c) (d)

(a) (b)

(c) (d)

(b) Phosphorus has 15 electrons. ð15Þð9:110  10^28g 5:143  10^23g

 

ð100Þ ¼ 0:02657% electrons

(c) Krypton has 36 electrons. ð36Þð9:110  10^28g 1:392  10^22g

 

ð100Þ ¼ 0:02356% electrons

(d) Platinum has 78 electrons. ð78Þð9:110  10^28g 3:240  10^22g

 

ð100Þ ¼ 0:02193% electrons

43. The mass of one proton is 1:673  10^24 grams.

(a) Selenium has 34 protons. ð Þð1:673  1034 ^24g 1:311  10^22g

 

ð100Þ ¼ 43:39% protons

(b) Xenon has 54 protons. ð Þð1:673  1054 ^24g 2:180  10^22g

 

ð100Þ ¼ 41:44% protons

(c) Chlorine has 17 protons. ð Þð1:673  1017 ^24g 5:887  10^23g

 

ð100Þ ¼ 48:31% protons

(d) Barium has 56 protons. ð56Þð1:673  10^24g 2:280  10^22g

 

ð100Þ ¼ 41:09% protons

44. The electron region is the area around the nucleus where electrons are most likely to be located.

45.

265 266 267 268 Mass

Abundance

269 270 271 272

average atomic mass: 0:1081ð Þ 269:14 amuð Þ ¼ 29:09 amu 0:3407

ð Þ 270:51 amuð Þ ¼ 92:16 amu 0:5512

ð Þ 271:23 amuð Þ ¼ 149:50 amu Total ¼ 270:75 amu

An atomic mass of 270.75 amu would come somewhere after Bohrium (mass¼ 264 amu). So, the atomic number of this new element would be greater than 107.