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ISBN-13: 978-1118324578
ISBN-10: 1118324579

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CHAPTER 2
ATOMIC STRUCTURE AND INTERATOMIC BONDING
PROBLEM SOLUTIONS
Download Full
Solution Manual for Materials Science and Engineering An Introduction 9th Edition by Callister
: http://testbankair.com/download/solution-manual-for-materials-science-and-engineering-an-introduction-9th-edition-by-callister/
Fundamental Concepts Electrons in Atoms
2.1
Cite the difference between atomic mass and atomic weight.
Solution Atomic mass is the mass of an individual atom, whereas atomic weight is the average (weighted) of the atomic masses of an atom's naturally occurring isotopes. 2.2
Silicon has three naturally occurring isotopes: 92.23% of
28
Si, with an atomic weight of 27.9769 amu, 4.68% of
29
Si, with an atomic weight of 28.9765 amu, and 3.09% of
30
Si, with an atomic weight of 29.9738 amu. On the basis of these data, confirm that the average atomic weight of Si is 28.0854 amu.
Solution The average atomic weight of silicon
(
A
Si
)
is computed by adding fraction-of-occurrence/atomic weight products for the three isotopes
—
i.e., using Equation 2.2. (Remember: fraction of occurrence is equal to the percent of occurrence divided by 100.) Thus
A
Si
=
f
28
Si
A
28
Si
+
f
29
Si
A
29
Si
+
f
30
Si
A
30
Si
=
(0.9223)(27.9769) + (0.0468)(28.9765) + (0.0309)(29.9738) = 28.0854
2.3
Zinc has five naturally occurring isotopes: 48.63% of
64
Zn
with an atomic weight of 63.929 amu; 27.90% of
66
Zn with an atomic weight of 65.926 amu
;
4.10% of
67
Zn with an atomic weight of 66.927 amu; 18.75% of
68
Zn with an atomic weight of 67.925 amu; and 0.62% of
70
Zn with an atomic weight of 69.925 amu. Calculate the average atomic weight of Zn.
Solution The average atomic weight of zinc
A
Zn
is computed by adding fraction-of-occurrence
—
atomic weight products for the five isotopes
—
i.e., using Equation 2.2. (Remember: fraction of occurrence is equal to the percent of occurrence divided by 100.) Thus
A
Zn
=
f
64
Zn
A
64
Zn
+
f
66
Zn
A
66
Zn
+
f
67
Zn
A
67
Zn
+
f
68
Zn
A
68
Zn
+
f
70
Zn
A
70
Zn
Including data provided in the problem statement we solve for
A
Zn
as
A
Zn
=
(0.4863)(63.929 amu) + (0.2790)(65.926 amu) + (0.0410)(66.927 amu) + (0.1875)(67.925 amu) + (0.0062)(69.925) = 65.400 amu 2.4
Indium has two naturally occurring isotopes:
113
In with an atomic weight of 112.904 amu, and
115
In with an atomic weight of 114.904 amu. If the average atomic weight for In is 114.818 amu, calculate the fractionofoccurrences of these two isotopes.
Solution The average atomic weight of indium
(
A
In
)
is computed by adding fraction-of-occurrence
—
atomic weight products for the two isotopes
—
i.e., using Equation 2.2, or
A
In
=
f
113
In
A
113
In
+
f
115
In
A
115
In
Because there are just two isotopes, the sum of the fracture-of-occurrences will be 1.000; or
f
113
+
f
115
=
1.000
In In
which means that
f
113
=
1.000
−
f
115
In In
Substituting into this expression the one noted above for
f
113
, and incorporating the atomic weight values provided
In
in the problem statement yields
114.818 amu
=
f
113
A
113
+
f
115
A
115
In In In In
114.818 amu
=
(1.000
−
f
113
)
A
113
+
f
115
A
115
In In In In
114.818 amu
=
(1.000
−
f
115
)(112.904 amu)
+
f
115
(114.904 amu)
In In
114.818 amu
=
112.904 amu
−
f
115
(112.904 amu)
+
f
115
(114.904 amu)
In In
Solving this expression for
f
115
yields
f
115
=
0.957
. Furthermore, because
In In
f
113
=
1.000
−
f
115
In In
then
f
113
=
1.000
−
0.957
=
0.043
In
2.5
(a) How many grams are there in one amu of a material? (b) Mole, in the context of this book, is taken in units of gram-mole. On this basis, how many atoms are there in a pound-mole of a substance?
Solution (a)
In order to determine the number of grams in one amu of material, appropriate manipulation of the amu/atom, g/mol, and atom/mol relationships is all that is necessary, as
æ
1 mol
öæ
1 g/mol
ö
#g/amu =
ç è
6.022
´
10
23
atoms
÷øçè
1 amu/atom
÷ø
= 1.66 10
24
g/amu (b)
Since there are 453.6 g/lb
m
,
1 lb-mol = (453.6 g/lb
m
)(6.022
×
10
23
atoms/g-mol)
= 2.73 10
26
atoms/lb-mol 2.6
(a)
Cite two important quantum-mechanical concepts associated with the Bohr model of the atom. (b) Cite two important additional refinements that resulted from the wave-mechanical atomic model.
Solution (a)
Two important quantum-mechanical concepts associated with the Bohr model of the atom are (1) that electrons are particles moving in discrete orbitals, and (2) electron energy is quantized into shells. (b)
Two important refinements resulting from the wave-mechanical atomic model are (1) that electron position is described in terms of a probability distribution, and (2) electron energy is quantized into both shells and subshells- -each electron is characterized by four quantum numbers.

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