Descriptive Inorganic Chemistry, DIC, Fifth edition, 5 edition
Chapter 1 answers:
1
Chapter 1
THE ELECTRONIC STRUCTURE OF THE ATOM: A REVIEW
Exercises
1.2 (a) Region in space around a nucleus where the probability of finding an
electron is high.
(b) Orbital energy levels of the same energy.
(c) When occupying orbitals of equal energy, it is energetically preferable
for the electrons to adopt a parallel spin arrangement.
1.4 5.
1.6 6s.
1.8 The quantum number l relates to the orbital shape.
1.10 The pairing energy for the double occupancy of the 2s orbital is less than
the energy separation of the 2s and 2p orbitals.
1.12 (a) [Ar]4s2; (b) [Ar]4s13d5; (c) [Xe]6s24f145d106p2.
1.14 (a) [Ar]; (b) [Ar]3d7; (c) [Ar]3d3.
1.16 2+ and 4+. Tin has a noble gas core ground-state electron configuration of
[Kr]5s24d105p2. The two 5p electrons are lost first, giving an ion of 2+
charge; the two 5s electrons are lost next, giving an ion of 4+ charge.
1.18 4+. Zirconium has a noble gas core ground-state electron configuration of
[Ar]4s23d2. Thus loss of both the two 4s electrons and the two 3d
electrons will give a 4+ ion.
2 Chapter 1
1.20 (a) 3; (b) 2; (c) 4.
1.22 (a) and (d).
Beyond the Basics
1.24 The Dirac wave equation was developed by the English physicist P. A. M.
Dirac. He applied the ideas of Einstein’s special theory of relativity to
quantum mechanics. Dirac’s model requires four quantum numbers, not
the three of the Schrödinger model (where the spin quantum number is not
part of the solution to the equation). A fourth quantum number results
from the special theory of relativity where events are defined by the three
spatial coordinates plus a time coordinate.
In the Dirac model, like the Schrödinger model, the principal
quantum number, n, determines the size of an orbital. The other quantum
numbers have different meanings—the third and the fourth (instead of the
second) determine the shape of the orbitals. The shapes of the orbitals
themselves differ from those using the Schrödinger equation, and there are
no nodes. This removes the conceptual problem of how an electron moves
from one lobe of a p orbital to the other if there is a zero probability in
between. The answer is that the ―simplistic‖ Schrödinger equation is in
error. For high-atomic-number atoms, relativistic effects become of
increasing importance and the Schrödinger equation becomes inadequate;
the Dirac equation must be used.
For a good introduction to the Dirac equation, see R. E. Powell,
Relativistic Quantum Chemistry, J. Chem. Educ. 45 (1968): 558–563.
1.26 Curium. [Rn]7s
2
5f
7
6d
1
.
1.28 Of course, one can argue that orbitals are human constructs only! This
question is a good topic for debate, but these authors veers toward the
view that an orbital actually exists only when it is populated. Empty
orbitals only potentially exist.
1
Chapter 1
THE ELECTRONIC STRUCTURE OF THE ATOM: A REVIEW
Exercises
1.1 (a) Surface where the electron probability is zero.
(b) No two electrons in an atom can have exactly the same set of quantum
numbers.
(c) Paramagnetic—the attraction into a magnetic field by an unpaired
electron.
1.3
1.5 5p.
1.7 The quantum number n relates to the size of an orbital.
1.9 The two electrons paired and occupying the same orbital would be least
favorable, because the pairing energy would be necessary to overcome the
repulsive forces. Paired but in different orbitals also comes with an
energy cost because there is a finite probability that the electrons will
occupy the same volume of space, again resulting in a repulsive energy
factor. With parallel spins there is zero probability that the electrons will
occupy the same volume of space; hence this is the lowest energy
condition.
2 Chapter 1
1.11 (a) [Ne]3s1; (b) [Ar]4s23d8; (c) [Ar]4s13d10.
1.13 (a) [Ar]; (b) [Ar]; (c) [Ar]3d9.
1.15 1+ and 3+. Thallium has a noble gas core ground-state electron
configuration of [Xe]6s24f145d106p1. The 6p electron is lost first,
giving an ion of 1+ charge; the two 6s electrons are lost next, giving an
ion of 3+ charge and corresponding to the removal of all outer electrons:
[Xe]4f145d10.
1.17 1+. Silver has a noble gas core ground state electron configuration of
[Kr]5s14d10. The 5s electron is lost first, giving an ion of 1+ charge and
corresponding to the removal of all outer electrons: [Kr]4d10.
1.19 (a) 2; (b) 0; (c) 4.
1.21 Electron configuration of atom: [Rn]7s
2
5f
14
6d
10
7p
1
.
Electron configuration of +1 ion: [Rn]7s
2
5f
14
6d
10
.
Electron configuration of +3 ion: [Rn]5f
14
6d
10
.
Beyond the Basics
1.23 9, 5, 121.
1.25 There are seven f orbitals. There are (at least) two separate ways of
depicting them and designating them: the general set and the cubic set.
The seven solutions for the cubic set are: x
3
, y
3
, z
3
, xyz, z(x
2
-y
2
), y(z
2
-x
2
),
and x(z
2
-y
2
). The f x3 , f y3 , f z3 resemble the d z2 in that they have lobes along
the particular axis, but with double ―doughnut‖ rings around the middle
The Electronic Structure of the Atom 3
rather than single rings. The other f orbitals resemble the d x2-y2 , d xy , d xz ,
and d yz orbitals in that they consist of eight lobes (rather than four)
between the axes. Several texts, such as that by Huheey, discuss f orbitals.
See also E.A. Ogryzlo, On the Shapes of f Orbitals, J. Chem. Educ. 42
(1965): 150–151 (1965) and refs. therein.
1.27 Hydrogen heads the alkali metal group even though hydrogen is a non-
metal with unique properties. Helium heads the alkaline earth metal group
even though helium is better classified as a noble gas.
4 Chapter 1
1.1 Define the following terms: (a) nodal surface;
(b) Pauli exclusion principle; (c) paramagnetic.
1.2 Define the following terms: (a) orbital; (b) degenerate;
(c) Hund’s rule.
1.3 Construct a quantum number tree for the principal
quantum number n 5 4 similar to that depicted for n 5 3 in
Figure 1.3.
1.4 Determine the lowest value of n for which m l can
(theoretically) have a value of 14.
1.5 Identify the orbital that has n 5 5 and l 5 1.
1.6 Identify the orbital that has n 5 6 and l 5 0.
1.7 How does the quantum number n relate to the
properties of an orbital?
1.8 How does the quantum number l relate to the
properties of an orbital?
1.9 Explain concisely why carbon has two electrons in
different p orbitals with parallel spins rather than the other
possible arrangements.
1.10 Explain concisely why beryllium has a ground-state
electron confi guration of 1s
2
2s
2
rather than 1s
2
2s
1
2p
1
.
1.11 Write noble gas core ground-state electron confi g-
urations for atoms of (a) sodium; (b) nickel; (c) copper.
1.12 Write noble gas core ground-state electron confi g-
urations for atoms of (a) calcium; (b) chromium; (c) lead.
1.13 Write noble gas core ground-state electron confi gu-
rations for ions of (a) potassium; (b) scandium 31; (c) cop-
per 21.
1.14 Write noble gas core ground-state electron confi gu-
rations for ions of (a) chlorine; (b) cobalt 21; (c) manga-
nese 41.
1.15 Predict the common charges of the ions of thallium.
Explain your reasoning in terms of electron confi gurations.
1.16 Predict the common charges of the ions of tin. Explain
your reasoning in terms of electron confi gurations.
1.17 Predict the common charge of the silver ion. Explain
your reasoning in terms of electron confi gurations.
1.18 Predict the highest possible charge of a zirconium ion.
Explain your reasoning in terms of electron confi gurations.
1.19 Use diagrams similar to Figure 1.12 to determine
the number of unpaired electrons in atoms of (a) oxygen;
(b) magnesium; (c) chromium.CHAPTER 1 • The Electronic Structure of the Atom: A Review 18
BEYOND THE BASICS
1.23 The next set of orbitals after the f orbitals are the g
orbitals. How many g orbitals would there be? What would
be the lowest principal quantum number n that would pos-
sess g orbitals? Deduce the atomic number of the fi rst ele-
ment at which g orbitals would begin to be fi lled on the
basis of the patterns of the d and f orbitals.
1.24 An alternative to the Schrödinger wave equation is
the Dirac wave equation. Using online sources, research the
Dirac wave equation and contrast it with the Schrödinger
wave equation.
1.25 Use an advanced inorganic chemistry text as a
source of information on the f orbitals. What are their com-
mon features? How do they differ among themselves?
1.26 In Section 1.3, gadolinium is mentioned as having
an electron confi guration that deviates from the lanthanoid
pattern. Which element in the actinoids should show a simi-
lar deviation? What would be its electron confi guration?
1.27 In Figure 1.13, the elements are organized logically
according to the order of orbital fi lling. Identify two disad-
vantages of organizing the elements in this way.
1.28 A philosophical question: Does an orbital exist even
if it does not contain an electron? Discuss.
1.20 Use diagrams similar to Figure 1.12 to determine
the number of unpaired electrons in atoms of (a) nitrogen;
(b) silicon; (c) iron.
1.21 Write the electron confi guration expected for ele-
ment 113 and the confi gurations for the two cations that it
is most likely to form.
1.22 Which of the following species are hydrogen-like?
(a) He
1
; (b) He
–
; (c) Li
1
; (d) Li
21
.
