48 • Chapter 2 /
Atomic Structure and Interatomic Bonding
QUESTIONS AND PROBLEMS
Problem available (at instructor’s discretion) in WileyPLUS
Fundamental Concepts
Electrons in Atoms
The Periodic Table
2.1 Cite the difference between atomic mass and
atomic weight.
2.11 With regard to electron configuration, what do
all the elements in Group IIA of the periodic table have in common?
2.2 Silicon has three naturally occurring isotopes:
92.23% of 28Si, with an atomic weight of 27.9769
amu; 4.68% of 29Si, with an atomic weight of
28.9765 amu; and 3.09% of 30Si, 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.
2.13 Without consulting Figure 2.8 or Table 2.2, determine whether each of the following electron
configurations is an inert gas, a halogen, an alkali
metal, an alkaline earth metal, or a transition
metal. Justify your choices.
2.3 Zinc has five naturally occurring isotopes: 48.63%
of 64Zn, with an atomic weight of 63.929 amu;
27.90% of 66Zn, with an atomic weight of 65.926
amu; 4.10% of 67Zn, with an atomic weight of
66.927 amu; 18.75% of 68Zn, with an atomic
weight of 67.925 amu; and 0.62% of 70Zn, with an
atomic weight of 69.925 amu. Calculate the average atomic weight of Zn.
2.4 Indium has two naturally occurring isotopes: 113In,
with an atomic weight of 112.904 amu; and 115In,
with an atomic weight of 114.904 amu. If the average atomic weight for In is 114.818 amu, calculate
the fraction-of-occurrences of these two isotopes.
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?
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.
2.7 Relative to electrons and electron states, what
does each of the four quantum numbers specify?
2.8 For the K shell, the four quantum numbers for
each of the two electrons in the 1s state, in the
order of nlmlms, are 10012 and 100( - 12). Write the
four quantum numbers for all of the electrons in
the L and M shells, and note which correspond to
the s, p, and d subshells.
2.12 To what group in the periodic table would an element with atomic number 112 belong?
(a) 1s22s22p63s23p5
(b) 1s22s22p63s23p63d74s2
(c) 1s22s22p63s23p63d104s24p6
(d) 1s22s22p63s23p64s1
(e) 1s22s22p63s23p63d104s24p64d55s2
(f) 1s22s22p63s2
2.14 (a) What electron subshell is being filled for the
rare earth series of elements on the periodic table?
(b) What electron subshell is being filled for the
actinide series?
Bonding Forces and Energies
2.15 Calculate the force of attraction between a Ca2
and an O2 ion whose centers are separated by a
distance of 1.25 nm.
2.16 The atomic radii of Mg2 and F ions are 0.072
and 0.133 nm, respectively.
(a) Calculate the force of attraction between
these two ions at their equilibrium interionic separation (i.e., when the ions just touch one another).
(b) What is the force of repulsion at this same
separation distance?
2.17 The force of attraction between a divalent cation
and a divalent anion is 1.67 10 8 N. If the ionic
radius of the cation is 0.080 nm, what is the anion
radius?
2.18 The net potential energy between two adjacent
ions, EN, may be represented by the sum of
Equations 2.9 and 2.11; that is,
2.9 Give the electron configurations for the following
ions: P5 , P3 , Sn4 , Se 2 , I , and Ni2 .
2.10 Potassium iodide (KI) exhibits predominantly ionic
bonding. The K and I ions have electron structures that are identical to which two inert gases?
EN = -
A
B
+ n
r
r
(2.17)
Calculate the bonding energy E0 in terms of the parameters A, B, and n using the following procedure:
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Questions and Problems • 49
1. Differentiate EN with respect to r, and then set
the resulting expression equal to zero, because the
curve of EN versus r is a minimum at E0.
(ii) Solve for C in terms of D, r, and r0.
2. Solve for r in terms of A, B, and n, which yields
r0, the equilibrium interionic spacing.
(b) Derive another expression for E0 in terms of
r0, C, and r using a procedure analogous to the
one outlined in part (a).
3. Determine the expression for E0 by substituting r0 into Equation 2.17.
2.19 For an Na —Cl ion pair, attractive and repulsive energies EA and ER, respectively, depend on
the distance between the ions r, according to
EA = ER =
-6
For these expressions, energies are expressed
in electron volts per Na —Cl pair, and r is the
distance in nanometers. The net energy EN is just
the sum of the preceding two expressions.
(a) Superimpose on a single plot EN, ER, and EA
versus r up to 1.0 nm.
(b) On the basis of this plot, determine (i) the
equilibrium spacing r0 between the Na and Cl
ions, and (ii) the magnitude of the bonding energy
E0 between the two ions.
(c) Mathematically determine the r0 and E0 values using the solutions to Problem 2.18, and compare these with the graphical results from part (b).
2.20 Consider a hypothetical X —Y ion pair for which
the equilibrium interionic spacing and bonding energy values are 0.38 nm and 5.37 eV, respectively.
If it is known that n in Equation 2.17 has a value of 8,
using the results of Problem 2.18, determine explicit
expressions for attractive and repulsive energies EA
and ER of Equations 2.9 and 2.11.
2.21 The net potential energy EN between two adjacent
ions is sometimes represented by the expression
EN = -
Primary Interatomic Bonds
2.22 (a) Briefly cite the main differences among
ionic, covalent, and metallic bonding.
(b) State the Pauli exclusion principle.
1.436
r
7.32 * 10
r8
(iii) Determine the expression for E0 by substitution for C in Equation 2.18.
C
r
+ D expa - b
r
r
(2.18)
2.23 Make a plot of bonding energy versus melting
temperature for the metals listed in Table 2.3.
Using this plot, approximate the bonding energy
for molybdenum, which has a melting temperature of 2617 C.
Secondary Bonding or van der Waals Bonding
2.24 Explain why hydrogen fluoride (HF) has a
higher boiling temperature than hydrogen chloride (HCl) (19.4 C vs. 85 C), even though HF
has a lower molecular weight.
Mixed Bonding
2.25 Compute %IC of the interatomic bond for each
of the following compounds: MgO, GaP, CsF,
CdS, and FeO.
2.26 (a) Calculate %IC of the interatomic bonds for
the intermetallic compound Al6Mn.
(b) On the basis of this result, what type of interatomic bonding would you expect to be found
in Al6Mn?
Bonding Type–Material Classification Correlations
2.27 What type(s) of bonding would be expected for
each of the following materials: solid xenon, calcium fluoride (CaF2), bronze, cadmium telluride
(CdTe), rubber, and tungsten?
Spreadsheet Problems
in which r is the interionic separation and C, D,
and r are constants whose values depend on the
specific material.
2.1SS Generate a spreadsheet that allows the user to
input values of A, B, and n (Equation 2.17) and
then does the following:
(a) Derive an expression for the bonding energy
E0 in terms of the equilibrium interionic separation r0 and the constants D and r using the following procedure:
(a) Plots on a graph of potential energy versus
interatomic separation for two atoms/ions, curves
for attractive (EA), repulsive (ER), and net (EN)
energies.
(i) Differentiate EN with respect to r, and set the
resulting expression equal to zero.
(b) Determines the equilibrium spacing (r0) and
the bonding energy (E0).
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50 • Chapter 2 /
Atomic Structure and Interatomic Bonding
2.2SS Generate a spreadsheet that computes %IC of
a bond between atoms of two elements, once the
user has input values for the elements’ electronegativities.
FUNDAMENTALS OF ENGINEERING
QUESTIONS AND PROBLEMS
(C) 14.2%
(B) 4.3%
(D) 63.7%
2.3FE What type(s) of bonding would be expected for
brass (a copper–zinc alloy)?
(B) Metallic bonding
(C) Covalent bonding with some van der Waals
bonding
(D) van der Waals bonding
2.4FE What type(s) of bonding would be expected
for rubber?
(A) Ionic bonding
(B) Metallic bonding
2.2FE Which of the following electron configurations
is for an inert gas?
(A) 1s22s22p63s23p6
(D) 1s22s22p63s23p63d24s2
(A) Ionic bonding
2.1FE The chemical composition of the repeat unit
for nylon 6,6 is given by the formula C12H22N2O2.
Atomic weights for the constituent elements are
AC 12, AH 1, AN 14, and AO 16. According
to this chemical formula (for nylon 6,6), the percentage (by weight) of carbon in nylon 6,6 is most
nearly
(A) 31.6%
(C) 1s22s22p63s23p64s1
(C) Covalent bonding with some van der Waals
bonding
(D) van der Waals bonding
(B) 1s22s22p63s2
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