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, William d callister jr david solutios manual for materials science and engineering an introduction
CHAPTER 2
ATOMIC STRUCTURE AND INTERATOMIC BONDING
PROBLEM SOLUTIONS
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 Chromium has four naturally-occurring isotopes: 4.34% of 50Cr, with an atomic weight of 49.9460 amu,
83.79% of 52Cr, with an atomic weight of 51.9405 amu, 9.50% of 53Cr, with an atomic weight of 52.9407 amu, and
2.37% of 54Cr, with an atomic weight of 53.9389 amu. On the basis of these data, confirm that the average atomic
weight of Cr is 51.9963 amu.
Solution
The average atomic weight of silicon (ACr) is computed by adding fraction-of-occurrence/atomic weight
products for the three isotopes. Thus
ACr = f50 A50 + f52 A52 f53 A53 f54 A54
Cr Cr Cr Cr Cr Cr Cr Cr
(0.0434)(49.9460 amu) + (0.8379)(51.9405 amu) + (0.0950)(52.9407 amu) + (0.0237)(53.9389 amu) = 51.9963 amu
, 2.3 (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?
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
1 mol 1 g / mol
# g/amu = 23
, 6.022 10 atoms 1 amu / atom
= 1.66 10-24 g/amu
(b) Since there are 453.6 g/lbm,
1 lb - mol = (453.6 g/lbm) (6.022 10 23 atoms/g - mol)
= 2.73 1026 atoms/lb-mol
2.4 (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.
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.
Downloaded by: ScholarNova | Want to earn $1.236
Distribution of this document is illegal extra per year?
, William d callister jr david solutios manual for materials science and engineering an introduction
CHAPTER 2
ATOMIC STRUCTURE AND INTERATOMIC BONDING
PROBLEM SOLUTIONS
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 Chromium has four naturally-occurring isotopes: 4.34% of 50Cr, with an atomic weight of 49.9460 amu,
83.79% of 52Cr, with an atomic weight of 51.9405 amu, 9.50% of 53Cr, with an atomic weight of 52.9407 amu, and
2.37% of 54Cr, with an atomic weight of 53.9389 amu. On the basis of these data, confirm that the average atomic
weight of Cr is 51.9963 amu.
Solution
The average atomic weight of silicon (ACr) is computed by adding fraction-of-occurrence/atomic weight
products for the three isotopes. Thus
ACr = f50 A50 + f52 A52 f53 A53 f54 A54
Cr Cr Cr Cr Cr Cr Cr Cr
(0.0434)(49.9460 amu) + (0.8379)(51.9405 amu) + (0.0950)(52.9407 amu) + (0.0237)(53.9389 amu) = 51.9963 amu
, 2.3 (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?
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
1 mol 1 g / mol
# g/amu = 23
, 6.022 10 atoms 1 amu / atom
= 1.66 10-24 g/amu
(b) Since there are 453.6 g/lbm,
1 lb - mol = (453.6 g/lbm) (6.022 10 23 atoms/g - mol)
= 2.73 1026 atoms/lb-mol
2.4 (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.
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.
