# Materiales chapter 2

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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 fournaturally-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 [pic] is computedby adding fraction-of-occurrence/atomic weight products for the three isotopes. Thus

[pic]

[pic]
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

[pic]

= 1.66 ( 10-24 g/amu

(b) Since there are 453.6 g/lbm,

[pic]

= 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 thewave-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 probabilitydistribution, and (2) electron energy is quantized into both shells and subshells--each electron is characterized by four quantum numbers.
2.5 Relative to electrons and electron states, what does each of the four quantum numbers specify?

Solution
The n quantum number designates the electron shell.
The l quantum number designates the electron subshell.
The ml quantum number designates thenumber of electron states in each electron subshell.
The ms quantum number designates the spin moment on each electron.
2.6 Allowed values for the quantum numbers of electrons are as follows:
n = 1, 2, 3, . . .
l = 0, 1, 2, 3, . . . , n –1
ml = 0, ±1, ±2, ±3, . . . , ±l
[pic]
The relationships between n and the shell designations are noted in Table 2.1. Relative to the subshells,
l = 0corresponds 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 1s state, in the order of nlmlms, are 100([pic]) and 100([pic]). 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.

Solution
For the L state, n = 2, and eight electron states are possible. Possible l values are 0 and 1, while possible ml values are 0 and ±1; and possible ms values are [pic] Therefore, for the s states, the quantum numbers are [pic] and [pic]. For the p states, the quantum numbers are [pic], [pic], [pic], [pic], [pic], and [pic].
For the M state, n = 3, and 18states are possible. Possible l values are 0, 1, and 2; possible ml values are 0, ±1, and ±2; and possible ms values are [pic] Therefore, for the s states, the quantum numbers are [pic], [pic], for the p states they are [pic], [pic], [pic], [pic], [pic], and [pic]; for the d states they are [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], and [pic].
2.7 Give the electron...