Download Atomic Structure and the Periodic Table

Atomic Structure
and the Periodic Table
In the few years following the announcement of the Bohr theory, a series of revisions to
this model occurred. Bohr’s single quantum number (n) was expanded to a total of four
quantum numbers (n, l, ml , ms). These quantum numbers were necessary to explain a
variety of evidence associated with spectral lines and magnetism. In addition, these same
quantum numbers also greatly improved the understanding of the periodic table and
chemical bonding. You will recall that the atomic theory you used previously allowed only
a limited description of electrons in atoms up to atomic number 20, calcium. In this
section, you will see that the four quantum numbers improve the theoretical description
to include all atoms on the periodic table and they improve the explanation of chemical
properties.
Section 3.5 provided the empirical and theoretical background to quantum numbers.
The main thing that you need to understand is that there are four quantized values that
describe an electron in an atom. Quantized means that the values are restricted to certain discrete values — the values are not on a continuum like distance during a trip.
There are quantum leaps between the values. Table 4 in Section 3.5 illustrates the values
to which the quantum numbers are restricted.
The advantage of quantized values is that they add some order to our description of the
electrons in an atom. In this section, the picture of the atom is based upon the evidence
and concepts from Section 3.5, but the picture is presented much more qualitatively. For
example, as you shall see, the secondary quantum number values of 0, 1, 2, and 3 are presented as s, p, d, and f designations to represent the shape of the orbitals (Table 1). What
is truly amazing about the picture of the atom that is coming in this section is that the
energy description in Section 3.5 fits perfectly with both the arrangement of electrons
and the structure of the periodic table. The unity of these concepts is a triumph of scientific
achievement that is unparalleled in the past or present.
3.6
Figure 1
Orbitals are like “electron clouds.”
This computer-generated image
shows a 3d orbital of the hydrogen
atom, which has four symmetrical
lobes (in this image, two blue and
two red-orange), with the nucleus
at the centre. The bands in the
lobes show different probability
levels: the probability of finding an
electron decreases while moving
away from the nucleus. This is quite
a different image from the Bohr
electron orbits.
orbital a region of space around the
nucleus where an electron is likely
to be found
Table 1 Values and Letters for the Secondary Quantum Number
value of l
0
1
2
3
letter designation*
s
p
d
f
name designation
sharp
principal
diffuse
fundamental
Table 2 Orbits and Orbitals
* This is the primary method of communicating values of l later in this section.
Electron Orbitals
Although the Bohr theory and subsequent revisions were based on the idea of an electron travelling in some kind of orbit or path, a more modern view is that of an electron
orbital. A simple description of an electron orbital is that it defines a region (volume)
of space where an electron may be found. Figure 1 and Table 2 present some of the differences between the concepts of orbit and orbital.
At this stage in your chemistry education, the four quantum numbers apply equally
well to electron orbits (paths) or electron orbitals (clouds). A summary of what is coming
is presented in Table 3.
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Orbits
Orbitals
2-D path
3-D region in
space
fixed distance
from nucleus
variable
distance
from nucleus
circular or
elliptical path
no path;
varied shape
of region
2n 2 electrons
per orbit
2 electrons
per orbital
Atomic Theories 185
Table 3 Energy Levels, Orbitals, and Shells
Principal energy
level
n
shell
shell main energy level; the shell
number is given by the principal
quantum number, n; for the representative elements the shell number
also corresponds to the period
number on the periodic table for the
s and p subshells
subshell orbitals of different shapes
and energies, as given by the
secondary quantum number, l; the
subshells are most often referred to
as s, p, d, and f
Energy
sublevel
l
orbital shape
subshell
Energy in
magnetic field
ml
orbital orientation
Additional energy
differences
ms
electron spin
The first two quantum numbers (n and l) describe electrons that have different energies under normal circumstances in multi-electron atoms. The last two quantum numbers (ml , ms) describe electrons that have different energies only under special conditions,
such as the presence of a strong magnetic field. In this text, we will consider only the
first two quantum numbers, which deal with energy differences for normal circumstances. As we move from focusing on the energy of the electrons to focusing on their
position in space, the language will change from using main (principal) energy level to
shell, and from energy sublevel to subshell. The terms can be taken as being equivalent, although the contexts of energy and space can be used to decide when they are primarily used.
Rather than a complete mathematical description of energy levels using quantum numbers, it is common for chemists to use the number for the main energy level and a letter
designation for the energy sublevel (Table 4). For example, a 1s orbital, a 2p orbital, a 3d,
or a 4f orbital in that energy sub-level can be specified. This 1s symbol is simpler than
communicating n 51, l 5 0, and 2p is simpler than n 5 2, l 5 1. Notice that this orbital
description includes both the principal quantum number and the secondary quantum
number; e.g., 5s, 2p, 3d, or 4f. Including the third quantum number, ml, requires another
designation, for example 2px, 2py, and 2pz.
Table 4 Classification of Energy Sublevels (Subshells)
Value of l
Sublevel symbol
Number of orbitals
0
s
1
1
p
3
2
d
5
3
f
7
Although the s-p-d-f designation for orbitals is introduced here, the shape of these orbitals
is not presented until Section 3.7. The emphasis in this section is on more precise energy-level
diagrams and their relationship to the periodic table and the properties of the elements.
Creating Energy-Level Diagrams
Our interpretation of atomic spectra is that electrons in an atom have different energies.
The fine structure of the atomic spectra indicates energy sublevels. The designation of
these energy levels has been by quantum number. Now we are going to use energy-level
diagrams to indicate which orbital energy levels are occupied by electrons for a particular atom or ion.
These energy-level diagrams show the relative energies of electrons in various orbitals
under normal conditions. Note that the previous energy-level diagrams that you have
drawn included only the principal quantum number, n. Now you are going to extend these
diagrams to include all four quantum numbers.
186 Chapter 3
NEL
Section 3.6
6p
5d
32e2 6s
4f
5p
4d
18e2 5s
4p
3d
18e2 4s
3p
8e2 3s
2p
8e2 2s
1s
2e2
In Figure 2, you see that as the atoms become larger and the main energy levels become
closer together, some sublevels start to overlap in energy. This figure summarizes the
experimental information from many sources to produce the correct order of energies.
A circle is used to represent an electron orbital within an energy sublevel. Notice that the
energy of an electron increases with an increasing value of the principal quantum
number, n. For a given value of n, the sublevels increase in energy, in order, s<p<d<f. Note
also that the restrictions on the quantum numbers (Table 4) require that there can be only
one s orbital, three p orbitals, five d orbitals, and seven f orbitals. Completing this diagram for a particular atom provides important clues about chemical properties and patterns in the periodic table. We will now look at some rules for completing an orbital
energy-level diagram and then later use these diagrams to explain some properties of the
elements and the arrangement of the periodic table.
NEL
Figure 2
Diagram of relative energies of electrons in various orbitals. Each orbital
(circle) can potentially contain up to
two electrons.
Atomic Theories 187
1s
H
(a)
He
(b)
Figure 3
Energy-level diagrams for
(a) hydrogen and (b) helium atoms
Figure 4
Energy-level diagrams for lithium,
carbon, and fluorine atoms. Notice
that all of the 2p orbitals at the same
energy are shown, even though
some are empty.
Pauli exclusion principle no two
electrons in an atom can have the
same four quantum numbers; no
two electrons in the same atomic
orbital can have the same spin; only
two electrons with opposite spins
can occupy any one orbital
aufbau principle “aufbau” is
German for building up; each electron is added to the lowest energy
orbital available in an atom or ion
Hund’s rule one electron occupies
each of several orbitals at the same
energy before a second electron
can occupy the same orbital
In order to show the energy distribution of electrons in an atom, the procedure will be
restricted to atoms in their lowest or ground state, assuming an isolated gaseous atom. You
show an electron in an orbital by drawing an arrow, pointed up or down to represent the
electron spin (Figure 3a). It does not matter if you point the arrow up or down in any particular circle, but two arrows in a circle must be in opposite directions (Figure 3b). This is really
a statement of the Pauli exclusion principle, which requires that no two electrons in an
atom have the same four quantum numbers. Electrons (arrows) are placed into the orbitals
(circles) by filling the lowest energy orbitals first. An energy sublevel must be filled before
moving onto the next higher sublevel. This is called the aufbau principle. If you have several
orbitals at the same energy (e.g., p, d, or f orbitals), one electron is placed into each of the orbitals
before a second electron is added. In other words, spread out the electrons as much as possible horizontally before doubling up any pair of electrons. This rule is called Hund’s rule.You
follow this procedure until the number of electrons placed in the energy-level diagram for
the atom is equal to the atomic number for the element (Figure 4).
According to these rules, when electrons
are added to the second (n 5 2)
2p
energy level, there are s and p sublevels
2s
to fill with electrons (Figure 2). The
lower energy s sublevel is filled before
1s
the p sublevel is filled. According to
Li
C
F
Hund’s rule, one electron must go into
(a)
(b)
(c)
each of the p orbitals before a second
electron is used for pairing (Figure 4).
There are several ways of memorizing and understanding the order in which the
energy levels are filled without having the complete chart shown in Figure 2. One method
is to use a pattern like the one shown in Figure 5. In this aufbau diagram, all of the
orbitals with the same principal quantum number are listed horizontally. You can follow
the diagonal arrows starting with the ls orbital to add the required number of electrons.
An alternate procedure for determining the order in which energy levels are filled
comes from the arrangement of elements in the periodic table. As you move across the
periodic table, each atom has one more electron (and proton) than the previous atom.
Because the electrons are added sequentially to the lowest energy orbital available (aufbau
principle), the elements can be classified by the sublevel currently being filled (Figure 6).
To obtain the correct order of orbitals for any atom, start at hydrogen and move from
left to right across the periodic table, filling the orbitals as shown in Figure 6. Check to
see that this gives exactly the same order as shown in Figure 5.
1s
7s
7p
7d
7f
6s
6p
6d
6f
5s
Figure 5
In this aufbau diagram, start at
the bottom (1s) and add electrons in the order shown by the
diagonal arrows. You work your
way from the bottom left corner
to the top right corner.
188 Chapter 3
5p
5d
4s
4p
4d
3s
3p
3d
2s
2p
5f
4f
1s
2s
2p
3s
3p
4s
3d
4p
5s
4d
5p
6s
5d
6p
7s
6d
4f
1s
5f
Figure 6
Classification of elements by the sublevels
that are being filled
NEL
Section 3.6
SAMPLE problem
Drawing Energy-Level Diagrams for Atoms
Draw the electron energy-level diagram for an oxygen atom.
Since oxygen (O) has an atomic number of 8, there are 8 electrons to be placed in energy
levels. As the element is in period 2, there are electrons in the first two main energy levels.
• Using either the aufbau diagram (Figure 5) or the periodic table (Figure 6), we can
see that the first two electrons will occupy the 1s orbital.
1s
O
• The next two electrons will occupy the 2s orbital.
2s
1s
O
• The next three electrons are placed singly in each of the 2p orbitals.
2p
2p
• The last (eighth) electron must be paired with one of the electrons in the 2p orbitals. It
does not matter into which of the three p orbitals this last electron is placed. The final
diagram is drawn as shown.
Note that this energy-level diagram is not drawn to scale. The “actual” gap in energy is
much larger between the 1s and 2s levels than between the 2s and 2p levels.
2s
1s
O
Example
Draw the energy-level diagram for an iron atom.
Solution
3d
4s
3p
3s
2p
2s
1s
Fe
Creating Energy-Level Diagrams for Anions
The energy-level diagrams for anions, or negatively charged ions, are done using the
same method as for atoms. The only difference is that you need to add the extra electrons corresponding to the ion charge to the total number of electrons before proceeding to
distribute the electrons into orbitals. This is shown in the following sample problem.
NEL
Atomic Theories 189
SAMPLE problem
Drawing Energy-Level Diagrams for Anions
Draw the energy-level diagram for the sulfide ion.
Sulfur has an atomic number of 16 and is in period 3. A sulfide
ion has a charge of 2–, which means that it has two more electrons than a neutral atom. Therefore, we have 18 electrons to
distribute in three principal energy levels.
• Using either the aufbau diagram (Figure 5) or the periodic
table (Figure 6), we can see that the first two electrons will
occupy the 1s orbital.
• The next two electrons will occupy the 2s orbital, and six
more electrons will complete the 2p orbitals.
• The next two electrons fill the 3s orbital, which leaves the
final six electrons to completely fill the 3p orbitals.
Notice that all orbitals are now completely filled with the
18 electrons.
3p
3s
2p
2s
1s
S22
Creating Energy-Level Diagrams for Cations
For cations, positively charged ions, the procedure for constructing energy-level diagrams is slightly different than for anions. You must draw the energy-level diagram for
the corresponding neutral atom first, and then remove the number of electrons (corresponding to the ion charge) from the orbitals with the highest principal quantum number, n.
The electrons removed might not be the highest-energy electrons. However, in general,
this produces the correct arrangement of energy levels based on experimental evidence.
SAMPLE problem
Drawing Energy-Level Diagrams for Cations
Draw the energy-level diagram for the zinc ion.
First, we need to draw the diagram for the zinc atom
(atomic number 30). Using either the aufbau diagram
(Figure 5) or the periodic table (Figure 6), we can see
that the 30 electrons are distributed as follows:
• The first two electrons will occupy the 1s orbital.
• The next two electrons will occupy the 2s orbital, and
six more electrons complete the 2p orbitals.
• The next two electrons fill the 3s orbital, and six more
electrons complete the 3p orbitals.
• The next two electrons fill the 4s orbital and the final
10 electrons fill the 3d orbitals.
• The zinc ion, Zn21, has a two positive charge, and
therefore has two fewer electrons than the zinc atom.
Remove the two electrons from the orbital with the
highest n — the 4s orbital in this example.
3d
4s
3p
3s
2p
2s
1s
Zn21
190 Chapter 3
NEL
Section 3.6
SUMMARY
Electron Energy-Level Diagrams
Electrons are added into energy levels and sublevels for an atom or ion by the following
set of rules. Remembering the names for the rules is not nearly as important as being able
to apply the rules. These rules were created to explain the spectral and periodic-table
evidence for the elements.
• Start adding electrons into the lowest energy level (1s) and build up from the
bottom until the limit on the number of electrons for the particle is reached —
the aufbau principle.
• For anions, add extra electrons to the number for the atom. For cations, do the
neutral atom first, then subtract the required number of electrons from the
orbitals with the highest principal quantum number, n.
DID YOU KNOW
?
Gerhard Herzberg
Spectroscopy was an essential tool
in developing quantum numbers
and electron energy levels. A key
figure in the development of
modern spectroscopy was Gerhard
Herzberg (1904–1999). His
research in spectroscopy at the
University of Saskatchewan and
the National Research Council in
Ottawa earned him an international reputation and the Nobel
Prize in chemistry (1971).
• No two electrons can have the same four quantum numbers; if an electron is in
the same orbital with another electron, it must have opposite spin — the Pauli
exclusion principle.
• No two electrons can be put into the same orbital of equal energy until one electron has been put into each of the equal-energy orbitals — Hund’s rule.
This process is made simpler by labelling the sections of the periodic table and then
creating the energy levels and electron configurations in the order dictated by the periodic table.
Practice
Understanding Concepts
1. State the names of the three main rules/principles used to construct an energy-level
diagram. Briefly describe each of these in your own words.
2. How can the periodic table be used to help complete energy-level diagrams?
3. Complete electron energy-level diagrams for the
(a) phosphorus atom
(b) potassium atom
(c) manganese atom
(d) nitride ion
(e) bromide ion
(f) cadmium ion
4. (a) Complete electron energy-level diagrams for a potassium ion and a chloride ion.
(b) Which noble gas atom has the same electron energy-level diagram as these
ions?
Extension
5. If the historical letter designations were not used for the sublevels, what would be the
label for the following orbitals, using only quantum numbers: 1s, 2s, 2p, 3d?
NEL
Atomic Theories 191
Electron Configuration
electron configuration a method
for communicating the location
and number of electrons in
electron energy levels;
e.g., Mg: 1s 2 2s 2 2p 6 3s 2
principal
quantum
number
3p5
number of
electrons
in orbital(s)
orbital
Figure 7
Example of electron configuration
SAMPLE problem
Electron energy-level diagrams are a better way of visualizing the energies of the electrons in an atom than quantum numbers, but they are rather cumbersome to draw. We
are now going to look at a third way to convey this information. Electron configurations
provide the same information as the energy-level diagrams, but in a more concise format.
An electron configuration is a listing of the number and kinds of electrons in order of
increasing energy, written in a single line; e.g., Li: 1s2 2s1. The order, from left to right,
is the order of increasing energy of the orbitals. The symbol includes both the type of
orbital and the number of electrons (Figure 7).
For example, if you were to look back at the energy-level diagrams shown previously
for the oxygen atom, the sulfide ion, and the iron atom, then you could write the electron configuration from the diagram by listing the orbitals from lowest to highest energy.
oxygen atom, O: 1s2 2s2 2p4
sulfide ion, S22: 1s2 2s2 2p6 3s2 3p6
iron atom, Fe: 1s 2 2s 2 2p6 3s2 3p6 4s 2 3d 6
Note that some of the information is lost when going from the energy-level diagram
to the electron configuration, but the efficiency of the communication is much improved
by using an electron configuration. Fortunately, there is a method for writing electron
configurations that does not require drawing an energy-level diagram first. Let us look
at this procedure.
Writing Electron Configurations
1.
Write the electron configuration for the chlorine atom.
First, locate chlorine on the periodic table. Starting at the top left of the table, follow with
your finger through the sections of the periodic table (in order of atomic number), listing
off the filled orbitals and then the final orbital.
1s2
2s2
2p6
2s2
3p5
You now have the electron configuration for chlorine: 1s 2, 2s 2, 2p6, 3s 2, and 3p5.
Figure 8
Polonium is a very rare, radioactive natural element found in
small quantities in uranium ores.
Polonium is also synthesized in
gram quantities by bombarding
Bi-209 with neutrons. The energy
released from the radioactive
decay of Po-210, the most
common isotope, is very large
(100 W/g) — a half gram of the
isotope will spontaneously heat
up to 500°C. Surprisingly, Po-210
has several uses, including as a
thermoelectric power source for
satellites.
192 Chapter 3
2.
Identify the element whose atoms have the following electron configuration:
1s 2
2s 2 2p 6 3s 2 3p 6 4s 2 3d10 4p 6 5s 2 4d10 5p 6 6s 2 4f 14 5d10 6p 4
Notice that the highest n is 6, so you can go quickly to the higher periods in the table to
identify the element. The highest s and p orbitals always tell you the period number, and
in this case the electron configuration finishes with 6s 2 4f 14 5d 10 6p4: the element must be
in period 6. Going across period 6 through the two s-elements, the 14 f -elements, and the
10 d-elements, you come to the fourth element in the p-section of the periodic table.
The fourth element in the 6p region of the periodic table is polonium, Po (Figure 8).
Example 1
Write the electron configuration for the tin atom and the tin(II) ion.
Solution
Sn: 1s 2 2s 2 2p6 3s 2 3p6 4s 2 3d10 4p6 5s 2 4d10 5p2
Sn21: 1s 2 2s 2 2p6 3s 2 3p6 4s 2 3d 10 4p6 5s 2 4d 10
NEL
Section 3.6
Example 2
Identify the atoms that have the following electron configurations:
(a) 1s 2 2s 2 2p6 3s 2 3p6 4s 2 3d 10 4p5
(b) 1s 2 2s 2 2p6 3s 2 3p6 4s 2 3d 10 4p6 5s 2 4d 5
Solution
(a) bromine atom, Br
(b) technetium atom, Tc
Shorthand Form of Electron Configurations
There is an internationally accepted shortcut for writing electron configurations. The core
electrons of an atom are expressed by using a symbol to represent all of the electrons of
the preceding noble gas. Just the remaining electrons beyond the noble gas are shown in
the electron configuration. This reflects the stability of the noble gases and the theory that
only the electrons beyond the noble gas (the outer shell electrons) are chemically important for explaining chemical properties. Let’s rewrite the full electron configurations for
the chlorine and tin atoms into this shorthand format.
Cl: 1s 2 2s 2 2p6 3s 2 3p5
becomes Cl: [Ne] 3s2 3p5
2
2
6
2
6
2
10
6
2
10
2
Sn: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p becomes Sn: [Kr] 5s2 4d10 5p2
SAMPLE problem
Writing Shorthand Electron Configurations
Write the shorthand electron configuration for the strontium atom.
LEARNING TIP
Follow the same procedure as before, but start with the noble gas immediately preceding
the strontium atom, which is krypton. Then continue adding orbitals and electrons until
you obtain the required number of electrons for a strontium atom (two beyond krypton).
Sr: [Kr] 5s 2
Electron Configurations
for Cations
Recall that energy-level diagrams
for cations are done by first doing
the energy level for the neutral
atom, and then subtracting electrons from the highest principal
quantum number, n. Notice in this
Example that electrons are
removed from the n 5 5 orbital.
The 5p electrons are removed
before the 5s electrons.
Example
Write the shorthand electron configuration for the lead atom and the lead(II) ion.
Solution
Pb: [Xe] 6s 2 4f 14 5d 10 6p 2
Pb21: [Xe] 6s 2 4f 14 5d 10
SUMMARY
Procedure for Writing
an Electron Configuration
Step 1 Determine the position of the element in the periodic table and
the total number of electrons in the atom or simple ion.
NEL
1s
1s
2s
2p
3s
3p
Step 2 Start assigning electrons in increasing order of main energy
levels and sublevels (using the aufbau diagram, Figure 5, or the
periodic table, Figure 6).
4s
3d
4p
5s
4d
5p
Step 3 Continue assigning electrons by filling each sublevel before going
to the next sublevel, until all of the electrons are assigned.
6s
5d
6p
7s
6d
• For anions, add the extra electrons to the total number in the atom.
4f
• For cations, write the electron configuration for the neutral atom first
and then remove the required number of electrons from the highest
principal quantum number, n.
5f
Atomic Theories 193
Practice
Understanding Concepts
6. Identify the elements whose atoms have the following electron configurations:
(a)
(b)
(c)
(d)
1s2 2s2
1s2 2s2 2p5
1s2 2s2 2p6 3s1
1s2 2s2 2p6 3s2 3p4
7. Write full electron configurations for each of the Period 3 elements.
8. (a) Write shorthand electron configurations for each of the halogens.
(b) Describe how the halogen configurations are similar. Does this general pat-
tern apply to other families?
9. Write the full electron configurations for a fluoride ion and a sodium ion.
10. A fluoride ion, neon atom, and sodium ion are theoretically described as isoelec-
tronic. State the meaning of this term.
11. Write the shorthand electron configurations for the common ion of the first three
members of Group 12.
Explaining the Periodic Table
representative elements the
metals and nonmetals in the main
blocks, Groups 1-2, 13-18, in the
periodic table; in other words, the
s and p blocks
transition elements the metals
in Groups 3-12; elements filling
d orbitals with electrons
LEARNING TIP
The lanthanides are also called
the rare earths, and the
elements after uranium (the
highest-atomic-number
naturally occurring element) are
called transuranium elements.
194 Chapter 3
The modern view of the atom based on the four quantum numbers was developed using
experimental studies of atomic spectra and the experimentally determined arrangement
of elements in the periodic table. It is no coincidence that the maximum number of electrons in the s, p, d, and f orbitals (Table 5) corresponds exactly to the number of columns
of elements in the s, p, d, and f blocks in the periodic table (Figure 6). This by itself is a
significant accomplishment that the original Bohr model could not adequately explain.
Table 5 Electron Subshells and the Periodic Table
Period
Period 1
# of
elements
2
Electron distribution
groups:
1-2
13-18
orbitals: s
p
2
3-12
d
Period 2
8
2
6
Period 3
18
2
6
10
Period 4-5
18
2
6
10
Period 6-7
32
2
6
10
f
14
Groups or families in the periodic table were originally created by Mendeleev to reflect
the similar properties of elements in a particular group. The noble gas family, Group 18,
is a group of gases that are generally nonreactive. The electron configurations for noble
gas atoms show that each of them has a filled ns 2np6 outer shell of electrons (Table 6). The
original idea from the Bohr theory — filled energy levels as stable (nonreactive) arrangements — still holds, but is more precisely defined. Similar outer shell or valence electron
configurations also apply to most families, in particular, the representative elements.
Similarly, the transition elements can now be explained by our new theory as elements that are filling the d energy sublevel with electrons. The transition elements are
sometimes referred to as the d block of elements. The 5 d orbitals can accommodate 10
electrons, and there are 10 elements in each transition-metal period (Table 6).
NEL
Section 3.6
Table 6 Explaining the Periodic Table
Sublevel
Elements
Orbitals
Electrons
Series of elements
s and p
21 6 5 8
11 3 5 4
21 6 5 8
representative
d
10
5
10
transition
f
14
7
14
lanthanides and actinides
Using the same test of the theory on the lanthanides and the actinides, we can explain
these series of elements as filling an f energy level. The f block of elements is 14 elements wide, as expected by filling 7 f orbitals with 14 electrons. The success of the
quantum-number and s-p-d-f theories in explaining the long-established periodic table
led to these approaches being widely accepted in the scientific community.
lanthanides and actinides the 14
metals in each of periods 6 and 7
that range in atomic number from
57-70 and 89-102, respectively; the
elements filling the f block
Explaining Ion Charges
Previously, we could not explain transition-metal ions and multiple ions formed by
heavy representative metals. Now many of these can be explained, although some require
a more detailed theory beyond this textbook. For example, you know that zinc forms a
21 ion. The electron configuration for a zinc atom:
Zn: [Ar] 4s 2 3d10
shows 12 outer electrons. If another atom or ion removes the two 4s electrons (the ones
with the highest n) this would leave zinc with filled 3d orbitals — a relatively stable state,
like those of atoms with filled sub-shells:
Zn21: [Ar] 3d10
(Note that it is unlikely that zinc would give up 10 electrons to leave filled 4s orbitals.)
Another example that illustrates the explanatory power of this approach is the formation
of either 21 or 41 ions by lead. The electron configuration for a lead atom:
Pb: [Xe] 6s 2 4f 14 5d10 6p 2
shows filled 4f, 5d, 6s orbitals, and a partially filled 6p orbital. The lead atom could lose
the two 6p electrons to form a 21 ion or lose four electrons from the 6s and 6p orbitals
to form a 41 ion. (From the energy-level diagram (Figure 2), you can see that all of
these outer electrons are very similar in energy and it is easier to remove fewer electrons
than large numbers such as 10 and 14.) Again, our new theory passes the test of being
able to initially explain what we could not explain previously. Let’s put it to another test.
Explaining Magnetism
To create an explanation for magnetism, let’s start with the evidence of ferromagnetic
(strongly magnetic) elements and write their electron configurations (Table 7).
Table 7 Ferromagnetic Elements and Their Electron Configurations
Ferromagnetic
element
Electron
configuration
d-Orbital
filling
Pairing of d electrons
iron
[Ar] 4s 2 3d 6
1 pair; 4 unpaired
cobalt
[Ar] 4s 2 3d 7
2 pairs; 3 unpaired
nickel
[Ar] 4s 2 3d 8
3 pairs; 2 unpaired
Based on the magnetism associated with electron spin and the presence of several unpaired
electrons, an initial explanation is that the unpaired electrons cause the magnetism. However,
ruthenium, rhodium, and palladium, immediately below iron, cobalt, and nickel in the
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Atomic Theories 195
(a)
unmagnetized
(b)
periodic table (i.e., in the same groups) are only paramagnetic (weakly magnetic) and are
not ferromagnetic. The presence of several unpaired electrons may account for some magnetism, but not for the strong ferromagnetism. The eventual explanation for this anomaly
is that iron, cobalt, and nickel (as smaller, closely packed atoms) are able to orient themselves
in a magnetic field. The theory is that each atom acts like a little magnet. These atoms influence each other to form groups (called domains) in which all of the atoms are oriented with
their north poles in the same direction. If most of the domains are then oriented in the
same direction by an external magnetic field of, for example, a strong bar magnet, the ferromagnetic metal becomes a “permanent” magnet. However, the magnet is only permanent until dropped or heated or subjected to some other procedure that allows the domains
to become randomly oriented again. (Figure 9). Ferromagnetism is a based on the properties
of a collection of atoms, rather than just one atom.
Paramagnetism is also explained as being due to unpaired electrons within substances
where domains do not form. In other words, paramagnetism is based on the magnetism
of individual atoms. Again, the theory of electron configurations is able to at least partially explain an important property of some chemicals. In this case, a full description
of each electron, including its spin, is involved in the explanation.
Anomalous Electron Configurations
magnetized
Figure 9
The theory explaining ferromagnetism in iron is that in unmagnetized iron (a) the domains of atomic
magnets are randomly oriented. In
magnetized iron (b) the domains
are lined up to form a “permanent”
magnet.
LAB EXERCISE 3.6.1
Quantitative Paramagnetism
(p. 215)
Paramagnetism is believed to be
related to unpaired electrons. This
lab exercise explores this relation.
Electron configurations can be determined experimentally from a variety of sophisticated experimental designs. Using the rules created above, let’s test our ability to accurately predict the
electron configurations of the atoms in the 3d block of elements. First, the predictions:
Sc: [Ar] 4s 2 3d1
Ti: [Ar] 4s 2 3d 2
V: [Ar] 4s 2 3d3
Cr: [Ar] 4s 2 3d 4
Mn: [Ar] 4s 2 3d 5
Fe: [Ar] 4s2 3d 6
Co: [Ar] 4s2 3d 7
Ni: [Ar] 4s2 3d 8
Cu: [Ar] 4s2 3d 9
Zn: [Ar] 4s2 3d10
Then the evidence:
Sc: [Ar] 4s 2 3d1
Ti: [Ar] 4s 2 3d 2
V: [Ar] 4s 2 3d 3
Cr: [Ar] 4s1 3d 5
Mn: [Ar] 4s2 3d 5
Fe: [Ar] 4s2 3d 6
Co: [Ar] 4s2 3d 7
Ni: [Ar] 4s2 3d 8
Cu: [Ar] 4s1 3d10
Zn: [Ar] 4s2 3d10
Overall, the configurations based on experimental evidence agree with the predictions, with two exceptions — chromium and copper. A slight revision of the rules for
writing electron configurations seems to be required.
The evidence suggests that half-filled and filled subshells are more stable (lower energy)
than unfilled subshells. This appears to be more important for d orbitals compared to
s orbitals. In the case of chromium, an s electron is promoted to the d subshell to create
two half-filled subshells; i.e., [Ar] 4s2 3d 4 becomes [Ar] 4s1 3d 5. In the case of copper, an
s electron is promoted to the d subshell to create a half-filled s subshell and a filled d
subshell; i.e., [Ar] 4s 2 3d 9 becomes [Ar] 4s1 3d 10 (Figure 10). The justification is that the
overall energy state of the atom is lower after the promotion of the electron. Apparently,
this is the lowest possible energy state for chromium and copper atoms.
Predicted
Figure 10
The stability of half-filled and filled
subshells is used to explain the
anomalous electron configurations
of chromium and copper.
196 Chapter 3
Cr: [Ar]
Actual
Cr: [Ar]
Cu: [Ar]
Cu: [Ar]
4s
3d
4s
3d
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Section 3.6
Section 3.6 Questions
14. Carbon, silicon, and germanium all form four bonds. Explain
Understanding Concepts
1. Determine the maximum number of electrons with a prin-
cipal quantum number
(a) 1
(c) 3
(b) 2
(d) 4
Applying Inquiry Skills
15. The ingenious Stern-Gerlach experiment of 1921 is famous
2. Copy and complete Table 8.
Table 8 Orbitals and Electrons in s, p, d, and f Sublevels
Sublevel
symbol
(a) s
Value of l
Number of
orbitals
Max. # of
electrons
0
(b) p
1
(c) d
2
(d) f
3
this property, using electron configurations.
for providing early evidence of quantized electron spin. The
experimental design called for a beam of gaseous silver
atoms from an oven to be sent through a nonuniform magnetic field. There were two possible results: one predicted
by classical and one by quantum theory (Figure 11).
(a) Which of the expected results is likely the classical
prediction and which is likely the quantum theory prediction? Explain your choice.
(b) Use quantum theory, the Pauli exclusion principle, and
the electron configuration of silver to explain the
results of the Stern-Gerlach experiment.
3. State the aufbau principle and describe two methods that
oven
can be used to employ this principle.
4. If four electrons are to be placed into a p subshell, describe
the procedure, including the appropriate rules.
magnet pole
5. (a) Draw electron energy-level diagrams for beryllium,
magnesium, and calcium atoms.
(b) What is the similarity in these diagrams?
slit to
focus beam
beam of
silver atoms
N
6. The last electron represented in an electron configuration
is related to the position of the element in the periodic
table. For each of the following sections of the periodic
table, indicate the sublevel (s,p,d,f) of the last electron:
(a) Groups 1 and 2
(b) Groups 3 to 12 (transition metals)
(c) Groups 13 to 18
(d) lanthanides and actinides
non-uniform
magnetic field
S
photographic
plate
magnet pole
field off
7. (a) When the halogens form ionic compounds, what is the
two possible results for
field on
ion charge of the halide ions?
(b) Explain this similarity, using electron configurations.
8. The sodium ion and the neon atom are isoelectronic; i.e.,
have the same electron configuration.
(a) Write the electron configurations for the sodium ion
and the neon atom.
(b) Describe and explain the similarities and differences in
properties of these two chemical entities.
9. Use electron configurations to explain the common ion
charges for antimony; i.e., Sb31 and Sb51.
10. Predict the electron configuration for the gallium ion, Ga31.
Provide your reasoning.
11. Evidence indicates that copper is paramagnetic, but zinc is
not. Explain the evidence.
12. Predict the electron configuration of a gold atom. Provide
your reasoning.
13. Use electron configurations to explain the
(a) 31 charge on the scandium ion
(b) 11 charge on a silver ion
(c) 31 and 21 charges on iron(III) and iron(II) ions
(d) 11 and 31 charges on the Tl11 and Tl31 ions
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Figure 11
The Stern–Gerlach experiment expected two possible results: one
predicted from classical magnetic theory in which all orientations
of electron spin are possible and the other predicted from
quantum theory in which only two orientations are possible.
Making Connections
16. Prior to 1968 Canadian dimes were made from silver rather
than nickel. A change was made because the value of the
silver in the dime had become greater than ten cents and
the dimes were being shipped out of the country to be
melted down.
(a) Why were the dimes shipped out of Canada before
being melted?
(b) If you had a box full of Canadian dimes and you
wanted to efficiently separate the silver from the nickel
ones, what empirical properties of silver and nickel
learned in this section could assist you in completing
your task?
Atomic Theories 197
(c) Use theoretical concepts learned in this section to
explain your separation technique.
17. Electron spin resonance (ESR) is an analytical technique
that is based on the spin of an electron. State some examples of the uses of ESR in at least two different areas.
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18. Magnetic Resonance Imaging (MRI) is increasingly in
demand for medical diagnosis (Figure 12).
(a) How is this technique similar to and different from
electron spin techniques?
(b) Provide some examples of the usefulness of MRI
results.
(c) What political issue is associated with MRI use?
GO
198 Chapter 3
www.science.nelson.com
Figure 12
MRI was developed
using the quantum
mechanical model
of the atom.
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Wave Mechanics and Orbitals
After many revisions, the quantum theory of the atom produced many improvements
in the understanding of different electron energy states within an atom. This was very
useful in explaining properties such as atomic spectra and some periodic trends. However,
these advances did not address some fundamental questions such as, “What is the electron doing inside the atom?” and "Where does the electron spend its time inside the
atom?” Scientists generally knew that a planetary model of various orbits was not correct because an atom should collapse, according to known physical laws. We know that
this is not true; atoms are generally very stable. Bohr’s solution to this problem was to
state that an electron orbit is somehow stable and doesn’t obey the classical laws of
physics. Even Bohr knew that this was not a satisfactory answer because it does not offer
any explanation of the behaviour of the electron.
The solution to this dilemma of electron behaviour came surprisingly in 1923 from
a young graduate student, Louis de Broglie (Figure 1). By 1923, the idea of a photon as
a quantum of energy was generally accepted. This meant that light appeared to have a
dual nature—sometimes it behaved like a continuous electromagnetic wave and sometimes it behaved like a particle (photon). De Broglie’s insight was essentially to reverse
this statement—if a wave can behave like a particle, then a particle should also be able
to behave like a wave. Of course, he had to justify this hypothesis and he did this by
using a number of formulas and concepts from the work of Max Planck and Albert
Einstein. At first, this novel idea by de Broglie was scorned by many respected and established scientists. However, like all initial hypotheses in science, the value of the idea must
be determined by experimental evidence. This happened a few years later. Clinton
Davisson accidentally discovered evidence for the wave properties of an electron, although
he did not realize what he had done at first. Shortly after Davisson’s report, G. P. Thomson
(son of J. J. Thomson) independently demonstrated the
n=3
wave properties of an electron.
n=2
Davisson and Thomson shared the
Nobel prize in 1937 for their experimental confirmation of de Broglie’s
hypothesis.
When Erwin Schrödinger heard
λ2
of de Broglie’s electron wave, it
immediately occurred to him that
this idea could be used to solve the problem of electron
λ3
behaviour inside an atom. Schrödinger and others created the physics to describe electrons behaving like waves inside an atom. Schrödinger’s
proposed wave mechanics was firmly based on the existing quantum concepts, and for
this reason is usually referred to as quantum mechanics. According to Schrödinger, the
electron can only have certain (quantized) energies because of the requirement for only
whole numbers of wavelengths for the electron wave. This is illustrated in Figure 2.
Electron Orbitals
Schrödinger’s quantum or wave mechanics provided a complete mathematical framework
that automatically included all four quantum numbers and produced the energies of all electron orbitals. But what does it tell us about where the electrons are and what they are
doing? A significant problem in trying to answer these questions is the difficulty in picturing
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3.7
Figure 1
Louis de Broglie obtained his first university degree in history. After serving
in the French army, he became interested in science and returned to university to study physics. De Broglie
was a connoisseur of classical music
and he used his knowledge of basic
tones and overtones as inspiration for
electron waves. In spite of the fact
that his hypothesis was ridiculed by
some, he graduated with a doctorate
in physics in 1924.
quantum mechanics the current
theory of atomic structure based on
wave properties of electrons; also
known as wave mechanics
λ4
Figure 2
Schrödinger envisaged electrons as
stable circular waves around the
nucleus.
ACTIVITY 3.7.1
Modelling Standing
Electron Waves (216)
Standing waves on a string are
interesting, but standing waves on a
circular loop are very cool.
Atomic Theories 199
electron probability density a
mathematical or graphical representation of the chance of finding an
electron in a given space
DID YOU KNOW
?
Crazy Enough?
Niels Bohr had this to say to
Heisenberg and Pauli when
reporting his colleagues’ response
to their theory: "We are all agreed
that your theory is crazy. The question that divides us is whether it is
crazy enough to have a chance of
being correct. My own feeling is that
it is not crazy enough."
ACTIVITY 3.7.2
Simulation of Electron Orbitals
(p. 217)
Computers are necessary to do calculations in quantum mechanics
and can quickly provide electron
probability densities.
Figure 3
A 1s orbital. The concentration of
dots near each point provides a
measure of the probability of finding
the electron at that point. The more
probable the location, the more dots
per unit volume. The same information, only in 2-D (like a slice into the
sphere), is shown by the graph.
200 Chapter 3
Radial probability distribution
Heisenberg uncertainty principle
it is impossible to simultaneously
know exact position and speed of a
particle
a particle as a wave. This seems contrary to our experience and we really have no picture
to comfort us. A way around this problem is to still retain our picture of an electron as a
particle, but one whose location we can only specify as a statistical probability; i.e., what
are the odds of finding the electron at this location? This probabilistic approach was shown
to be necessary as a result of the work by Werner Heisenberg, a student of Bohr and
Sommerfeld. Heisenberg realized that to measure any particle, we essentially have to “touch”
it. For ordinary-sized objects this is not a problem, but for very tiny, subatomic particles
we find out where they are and their speed by sending photons out to collide with them.
When the photon comes back into our instruments, we can make interpretations about the
particle. However, the process of hitting a subatomic particle with a photon means that the
particle is no longer where it was and it has also changed its speed. The very act of measuring changes what we are measuring. This is the essence of the famous Heisenberg’s
uncertainty principle, in which he showed mathematically that there are definite limits to
our ability to know both where a particle is and its speed. Because it is impossible to know
exactly where an electron is, we are stuck with describing the likelihood or probability of
an electron being found in a certain location.
We do not know what electrons are doing in the
atom — circles, ellipses, figure eights, the mambo....
In fact, quantum mechanics does not include any
description of how an electron goes from one point to
another, if it does this at all. In terms of a location, all
that we know is the probability of finding the electron in a particular position around the nucleus of
an atom. (This is somewhat like knowing that the
caretaker is somewhere in the school doing something, but we do not know where or what.) Since we
can never know what the electrons are doing, scientists use the term orbital (rather than orbit) to describe
the region in space where electrons may be found.
Fortunately, the wave equations from quantum
mechanics can be manipulated to produce a threedimensional probability distribution of the electron in an orbital specified by the quantum numbers.
This is known as an electron probability density
and can be represented in a variety of ways. The
electron probability density for a 1s orbital of the
hydrogen atom (Figure 3) shows a spherical shape
with the greatest probability of finding an electron
at rmax. Interestingly, this distance is the same as the
one calculated by Bohr for the radius of the first
circular orbit. Notice, however, that the interpretation of the electron has changed substantially. The
probability densities of other orbitals, such as p and
d orbitals, can also be calculated; some of these are
presented in Figure 4. Looking at these diagrams,
you can see why orbitals are often called “electron
clouds.”
0
2
4
r (10210m)
1s orbital
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Section 3.7
(a)
(b)
(d)
z
1s
Pz
y
2s
2pz
x
Radial probability distribution
2py
2px
z
(c)
d xy
y
1s, 2s, 2p
x
0
2
4
6
8
r (10210m)
2s orbital
Problems with Quantum Mechanics
As is the case with all theories, there are areas of quantum mechanics that are not well
understood. There is evidence of quantum phenomena that are not explainable with
our current concepts. As chemists examine larger and more complicated molecules, the
analysis of the structure becomes mathematically very complex. Also, Werner Heisenberg
pointed out in his uncertainty principle that there is a limit to how precise we can make
any measurement. Many scientists (Einstein among them) have found this concept disturbing, since it means that many rules thought to be true in our normal world may
not be true in the subatomic world, including the basic concept of cause and effect.
Technology requires that something works, not necessarily that we understand why it
works. A typical technology used without complete understanding is superconductivity.
In 1911 Heike Kamerlingh-Onnes first demonstrated, using liquid helium as a coolant,
that the electrical resistance of mercury metal suddenly decreased to zero at 4.2 K. Since
then, science has discovered many superconducting materials, and technology has found
them to be incredibly useful. A good example is the coil system that produces the magnetic field for MRIs. If the electromagnets were not superconducting, the current used could
not be nearly as great, and the magnetic field would not be nearly strong enough to work.
A Nobel prize was awarded for an “electron-pairing” superconductor quantum theory
in 1972, to John Bardeen, William Cooper, and John Schrieffer (B, C, S). However, there
are still many aspects of superconductivity that are not explained by the BCS theory. The
most notable point is that their theory sets an upper temperature limit for superconductivity of 23 K, and recently, materials have been found that are superconducting at
temperatures that are much higher (Figure 5). Some superconductors work at temperatures over 150 K, and oddly enough, recently produced superconducting substances are
not even conductors at room temperature. Why they should become superconducting
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Figure 4
Some of the electron clouds representing the electron probability
density.
(a) In the cross-section, the darker
the shading, the higher the
probability of finding the
electron.
(b) A 2pz orbital
(c) A dx y orbital
(d) A superposition of 1s, 2s, and
2p orbitals
Figure 5
Levitation of magnets suspended
above a superconducting ceramic
material at the temperature of
boiling nitrogen (77 K) has become
a common science demonstration in
high schools and universities.
Atomic Theories 201
as the temperature drops is the subject of several current theories, none of which is complete enough to have general acceptance by the scientific community. What does seem certain is that superconductivity is a quantum effect, and it seems to support the argument
that at subatomic levels, we don’t necesarily know what the rules are.
Section 3.7 Questions
Understanding Concepts
1. Briefly state the main contribution of each of the following
scientists to the development of quantum mechanics:
(a) de Broglie
(b) Schrödinger
(c) Heisenberg
2. What is an electron orbital and how is it different from an
orbit?
3. State two general characteristics of any orbital provided by
the quantum mechanics atomic model.
4. What information about an electron is not provided by the
quantum mechanics theory?
5. Using diagrams and words, describe the shapes of the 1s,
2s, and three 2p orbitals.
Making Connections
6. Statistics are used in many situations to describe past
events and predict future ones. List some examples of the
use of statistics. How is this relevant to quantum
mechanics?
7. When the police use a radar gun to measure a car’s speed,
bounce back to the radar gun. If you got a speeding ticket,
could you use Heisenberg’s uncertainty principle in your
defence? Explain briefly.
8. Dr. Richard Bader and his research group at McMaster
University are well known for their work on atomic and
molecular structure. Find out the nature of their work and
give a brief, general description of how it relates to
quantum mechanics.
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9. There are many present and projected technological appli-
cations for superconductivity. Research these applications
and make a list of at least four, with a brief description of
each.
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10. Research for the highest temperature at which supercon-
ductivity has been achieved. What substance is used for
this highest temperature?
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photons are fired at the car. The photons hit the car and
202 Chapter 3
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