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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- 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
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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<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
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- 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.
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