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Materials Science and Engineering: An Introduction

William D. Callister Jr., David G. Rethwisch

Chapter 2

Atomic Structure and Interatomic Bonding - all with Video Answers

Educators


Chapter Questions

01:03

Problem 1

Cite the difference between atomic mass and atomic weight.

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
03:16

Problem 2

Chromium has four naturally occurring isotopes: $4.34 \%$ of ${ }^{50} \mathrm{Cr}$, with an atomic weight of $49.9460$ amu; $83.79 \%$ of ${ }^{52} \mathrm{Cr}$, with an atomic weight of $51.9405 \mathrm{amu} ; 9.50 \%$ of ${ }^{53} \mathrm{Cr}$, with an atomic weight of $52.9407 \mathrm{amu} ;$ and $2.37 \%$ of ${ }^{54} \mathrm{Cr}$, with an atomic weight of $53.9389$ amu. On the basis of these data, confirm that the average atomic weight of $\mathrm{Cr}$ is $51.9963 \mathrm{amu}$

Susan Hallstrom
Susan Hallstrom
Numerade Educator
02:52

Problem 3

(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?

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
03:51

Problem 4

(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.

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:43

Problem 5

Relative to electrons and electron states, what does each of the four quantum numbers specify?

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
03:38

Problem 6

6 Allowed values for the quantum numbers of electrons are as follows:
$$
\begin{aligned}
n &=1,2,3, \ldots \\
l &=0,1,2,3, \ldots, n-1 \\
m_{l} &=0, \pm 1, \pm 2, \pm 3, \ldots, \pm l \\
m_{s} &=\pm \frac{1}{2}
\end{aligned}
$$
The relationships between $n$ and the shell designations are noted in Table 2.1. Relative to the subshells,
$l=0$ corresponds to an $s$ subshell $l=1$ corresponds to a $p$ subshell $l=2$ corresponds to a $d$ subshell $l=3$ corresponds to an $f$ subshell For the $K$ shell, the four quantum numbers for each of the two electrons in the $1 s$ state, in the order of $n l m_{i} m_{s}$, are $100 \frac{1}{2}$ and $100\left(-\frac{1}{2}\right)$ 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.

Abhinav Roy
Abhinav Roy
Numerade Educator
04:31

Problem 7

Give the electron configurations for the following ions: $\mathrm{Fe}^{2+}, \mathrm{Al}^{3+}, \mathrm{Cu}^{+}, \mathrm{Ba}^{2+}, \mathrm{Br}^{-}$, and $\mathrm{O}^{2-}$

Cameron Oden
Cameron Oden
Numerade Educator
01:18

Problem 8

Sodium chloride $(\mathrm{NaCl})$ exhibits predominantly ionic bonding. The $\mathrm{Na}^{+}$and $\mathrm{Cl}^{-}$ions have electron structures that are identical to which two inert gases?

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:19

Problem 9

With regard to electron configuration, what do all the elements in Group VIIA of the periodic table have in common?

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
00:43

Problem 10

To what group in the periodic table would an element with atomic number 114 belong?

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:40

Problem 11

Without consulting Figure $2.6$ 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.
(a) $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} 4 s^{2}$
(b) $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}$
(c) $1 s^{2} 2 s^{2} 2 p^{5}$
(d) $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}$
(e) $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{2} 4 s^{2}$
(f) $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}$

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:23

Problem 12

(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?

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:31

Problem 13

Calculate the force of attraction between a $\mathrm{K}^{+}$ and an $\mathrm{O}^{2-}$ ion whose centers are separated by a distance of $1.5 \mathrm{~nm}$.

Mir  Afzal
Mir Afzal
Numerade Educator
05:04

Problem 14

The net potential energy between two adjacent ions, $E_{N}$, may be represented by the sum of Equations $2.8$ and $2.9$; that is,
$$
E_{N}=-\frac{A}{r}+\frac{B}{r^{n}}
$$
Calculate the bonding energy $E_{0}$ in terms of the parameters $A, B$, and $n$ using the following procedure:
1. Differentiate $E_{N}$ with respect to $r$, and then set the resulting expression equal to zero, because the curve of $E_{N}$ versus $r$ is a minimum at $E_{0 \text { - }}$
2. Solve for $r$ in terms of $A, B$, and $n$, which yields $r_{0}$, the equilibrium interionic spacing.
3. Determine the expression for $E_{0}$ by substituting $r_{0}$ into Equation $2.11$.

Brandy Heflin
Brandy Heflin
Numerade Educator
12:43

Problem 15

For $\mathrm{a} \mathrm{K}^{+}-\mathrm{Cl}^{-}$ion pair, attractive and repulsive energies $E_{A}$ and $E_{R}$, respectively, depend on the distance between the ions $r$, according to
$$
\begin{aligned}
E_{A} &=-\frac{1.436}{r} \\
E_{R} &=\frac{5.86 \times 10^{-6}}{r^{9}}
\end{aligned}
$$
For these expressions, energies are expressed in electron volts per $\mathrm{K}^{+}-\mathrm{Cl}^{-}$pair, and $r$ is the distance in nanometers. The net energy $E_{N}$ is just the sum of the preceding two expressions.
(a) Superimpose on a single plot $E_{N}, E_{R}$, and $E_{A}$ versus $r$ up to $1.0 \mathrm{~nm}$.
(b) On the basis of this plot, determine (i) the equilibrium spacing $r_{0}$ between the $\mathrm{K}^{+}$and $\mathrm{Cl}^{-}$ions, and (ii) the magnitude of the bonding energy $E_{0}$ between the two ions.
(c) Mathematically determine the $r_{0}$ and $E_{0}$ values using the solutions to Problem $2.14$ and compare these with the graphical results from part (b).

Brandy Heflin
Brandy Heflin
Numerade Educator
07:03

Problem 16

Consider a hypothetical $\mathrm{X}^{+}-\mathrm{Y}^{-}$ion pair for which the equilibrium interionic spacing and bonding energy values are $0.35 \mathrm{~nm}$ and $-6.13$ $\mathrm{eV}$, respectively. If it is known that $n$ in Equation $2.11$ has a value of 10 , using the results of Problem 2.14, determine explicit expressions for attractive and repulsive energies $E_{A}$ and $E_{R}$ of Equations $2.8$ and $2.9$.

Abhinav Roy
Abhinav Roy
Numerade Educator
04:14

Problem 17

The net potential energy $E_{N}$ between two adjacent ions is sometimes represented by the expression $$
E_{N}=-\frac{C}{r}+D \exp \left(-\frac{r}{\rho}\right)
$$
in which $r$ is the interionic separation and $C$, $D$, and $\rho$ are constants whose values depend on the specific material.
(a) Derive an expression for the bonding energy $E_{0}$ in terms of the equilibrium interionic separation $r_{0}$ and the constants $D$ and $\rho$ using the following procedure:
1. Differentiate $E_{N}$ with respect to $r$ and set the resulting expression equal to zero.
2. Solve for $C$ in terms of $D, \rho$, and $r_{0}$ -
3. Determine the expression for $E_{0}$ by substitution for $C$ in Equation $2.12$.
(b) Derive another expression for $E_{0}$ in terms of $r_{0}, C$, and $\rho$ using a procedure analogous to the one outlined in part (a).

Abhinav Roy
Abhinav Roy
Numerade Educator
05:30

Problem 18

(a) Briefly cite the main differences between ionic, covalent, and metallic bonding.
(b) State the Pauli exclusion principle.

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:30

Problem 19

Compute the percent ionic character of the interatomic bonds for the following compounds: $\mathrm{TiO}_{2}, \mathrm{ZnTe}, \mathrm{CsCl}, \mathrm{InSb}$, and $\mathrm{MgCl}_{2}$.

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:05

Problem 20

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 copper, which has a melting temperature of $1084^{\circ} \mathrm{C}$.

Brandy Heflin
Brandy Heflin
Numerade Educator
03:15

Problem 21

Using Table $2.2$, determine the number of covalent bonds that are possible for atoms of the following elements: germanium, phosphorus, selenium, and chlorine.

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:15

Problem 22

What type(s) of bonding would be expected for each of the following materials: brass (a copper-zinc alloy), rubber, barium sulfide (BaS), solid xenon, bronze, nylon, and aluminum phosphide (AIP)?

Abhinav Roy
Abhinav Roy
Numerade Educator
01:53

Problem 23

Explain why hydrogen fluoride (HF) has a higher boiling temperature than hydrogen chloride (HCl) $\left(19.4^{\circ} \mathrm{C}\right.$ vs. $\left.-85^{\circ} \mathrm{C}\right)$, even though HF has a lower molecular weight.

Mirza  Aslam Beig
Mirza Aslam Beig
Numerade Educator