Download Lecture Trends in the Periodic Table - NGHS

The properties of the elements exhibit trends. These
trends can be predicted using the periodic table and can
be explained and understood by analyzing the electron
configurations of the elements.
There are two important trends. First, electrons are
added one at a time moving from left to right across a
period. As this happens, the electrons of the outermost
shell experience increasingly strong nuclear attraction, so
the electrons become closer to the nucleus and more
tightly bound to it.
Second, moving down a column in the periodic table, the
outermost electrons become less tightly bound to the
nucleus. This happens because the number of filled
principal energy levels (which shield the outermost
electrons from attraction to the nucleus) increases
downward within each group.
These 2 trends explain the periodicity observed in the
elemental properties of atomic radius, ionization energy,
electron affinity, and electronegativity.
In order to talk about the radius of
an atom, we have to make an
arbitrary decision about where the
edge of the atom is. It is arbitrary
because the electron orbitals do not
end sharply.
Nevertheless, we can just arbitrarily
choose the radius that the electron
spends 90% of its time inside the
black line.
The atomic radius of an element is half of the distance
between the centers of two atoms of that element that
are just touching each other. Generally, the atomic radius
decreases across a period from left to right and increases
down a given group. The atoms with the largest atomic
radii are located in Group I and at the bottom of groups.
Moving from left to right across a period, electrons are
added one at a time to the outer energy shell.
Moving down a group in the periodic table, the number of
electrons and filled electron shells increases, but the
number of valence electrons remains the same.
In general the size of the atom depends on how far the outermost
valence electron is from the nucleus. With this in mind we
understand two general trends...
Remember, positive and negative attract, so as you add a proton
to the nucleus, it pulls the electrons in closer to the nucleus,
decreasing the radius. But as you add an electron to the cloud, it
takes up more space, so the radius increases.
*
Size increases down a group
The increasing principle quantum number of the valence orbitals
means larger orbitals and an increase in atomic size.
* Size generally decreases across a period from left to right
To understand this trend it is first important to realize that the more
strongly attracted the outermost valence electron is to the nucleus then
the smaller the atom will be. While the number of positively charged
protons in the nucleus increases as we move from left to right the
number of negatively charged electrons between the nucleus and the
outermost electron also increases by the same amount. Thus you might
expect there to be no change in the radius of the outermost electron
orbital since the increasing charge of the nucleus would be canceled by
the electrons between the nucleus and the outermost electron. In reality,
however, this is not quite the case. As we move across a given period
the ability of the inner electrons to cancel the increasing charge of the
nucleus diminishes and the outermost electron is more strongly
attracted to the nucleus. Hence the radius decreases from left to right.
Here is another way to visualize
the atomic radii of various
elements.
The largest element is
Cesium, in the lower left of
the periodic table. The
smallest element with more
than 2 electrons is fluorine,
in the upper right corner of
the periodic table.
Relative Size of the Atoms
The ionization energy, or ionization potential, is the
energy required to completely remove an electron from a
gaseous atom or ion.
The closer and more tightly bound an electron is to the
nucleus, the more difficult it will be to remove, and the
higher its ionization energy will be.
The first ionization energy is the energy required to
remove one electron from an atom. The second ionization
energy is the energy required to remove a second
valence electron from the ion.
Successive ionization energies increase. The second
ionization energy is always greater than the first
ionization energy.
Ionization energies increase moving from left to
right across a period (decreasing atomic radius).
Ionization energy decreases moving down a group
(increasing atomic radius). Group I elements have
low ionization energies because the loss of an
electron forms a stable octet.
Electron affinity reflects the ability of an atom to
accept an electron. It is the energy change that
occurs when an electron is added to a gaseous atom.
Atoms with stronger effective nuclear charge have
greater electron affinity.
Some generalizations can be made about the electron
affinities of certain groups in the periodic table. The
Group IIA elements, the alkaline earths, have low
electron affinity values. These elements are relatively
stable because they have filled s subshells. Group VIIA
elements, the halogens, have high electron affinities
because the addition of an electron to an atom results
in a completely filled shell. Group VIII elements, noble
gases, have electron affinities near zero, since each
atom possesses a stable octet and will not accept an
electron readily. Elements of other groups have low
electron affinities.
Electron affinity becomes less negative down a group.
Electron affinity decreases or increases across a period
depending on electronic configuration.
Lets tie it all together:
Electronegativity is a measure of the attraction of an
atom for the electrons in a chemical bond. The higher the
electronegativity of an atom, the greater its attraction for
bonding electrons. Electronegativity is related to
ionization energy.
Electrons with low ionization energies have low
electronegativities because their nuclei do not exert a
strong attractive force on electrons. Elements with high
ionization energies have high electronegativities due to
the strong pull exerted on electrons by the nucleus.
In a group, the electronegativity decreases as
atomic number increases, as a result of increased
distance between the valence electron and nucleus
(greater atomic radius). An example of an
electropositive (i.e., low electronegativity) element
is cesium; an example of a highly electronegative
element is fluorine.
Summary of Periodic Table Trends
Moving Left --> Right
*
*
*
Atomic Radius Decreases
Ionization Energy Increases
Electronegativity Increases
Moving Top --> Bottom
*
*
*
Atomic Radius Increases
Ionization Energy Decreases
Electronegativity Decreases
Each family shares chemical and physical properties.
The number of sublevels that an
energy level can contain is equal to
the principle quantum number of
that level. So, for example, the
second energy level would have two
sublevels, and the third energy level
would have three sublevels. The
first sublevel is called an s sublevel.
The second sublevel is called a p
sublevel. The third sublevel is
called a d sublevel and the fourth
sublevel is called an f sublevel.
Although energy levels that are
higher than 4 would contain
additional sublevels, these
sublevels have not been named
because no known atom in its
ground state would have electrons
that occupy them.
I. Principle Quantum Number (n)
and Sublevels
The principal quantum number (n) describes the size of the orbital.
Orbitals for which n = 2 are larger than those for which n = 1, for
example. Because they have opposite electrical charges, electrons
are attracted to the nucleus of the atom. Energy must therefore be
absorbed to excite an electron from an orbital in which the electron is
close to the nucleus (n = 1) into an orbital in which it is further from the
nucleus (n = 2). The principal quantum number therefore indirectly
describes the energy of an orbital.
The Principal Quantum Number (signified by the letter 'n'): This
quantum number was the first one discovered and it was done
so by Niels Bohr in 1913. Bohr thought that each electron was
in its own unique energy level, which he called a "stationary
state," and that each electron would have a unique value of 'n.'
In this idea, Bohr was wrong. It very quickly was discovered that more than one electron could have a given 'n'
value. For example, it was eventually discovered that when n=3, eighteen different electrons could have that value.
Keep in mind that it is the set of four quantum numbers that is important. As you will see, each of the 18 electrons
just mention will have its own unique set of n, l, m, and s.
Finally, there is a rule for what values 'n' can assume. It is:
n = 1, 2, 3, and so on.
n will always be a whole number and NEVER less than one.
One point: n does not refer to any particular location in space or any particular shape. It is one component (of four)
that will uniquely identify each electron in an atom.
The angular quantum number (l) describes the shape of the orbital. Orbitals have shapes that are best described as
spherical (l = 0), polar (l = 1), or cloverleaf (l = 2). They can even take on more complex shapes as the value of the
angular quantum number becomes larger.
There is only one way in which a sphere (l = 0) can be
oriented in space. Orbitals that have polar (l = 1) or
cloverleaf (l = 2) shapes, however, can point in different
directions. We therefore need a third quantum number,
known as the magnetic quantum number (m), to
describe the orientation in space of a particular orbital.
(It is called the magnetic quantum number because the
effect of different orientations of orbitals was first
observed in the presence of a magnetic field.)
The Azimuthal Quantum Number (signified by the letter 'l'): about 1914-1915, Arnold Sommerfeld realized that
Bohr's 'n' was insufficient. In other words, more equations were needed to properly describe how electrons behaved.
In fact, Sommerfeld realized that TWO more quantum numbers were needed.
The first of these is the quantum number signified by 'l.' When Sommerfeld started this work, he used n' (n prime),
but he shifted it to 'l' after some years. I'm not sure why, but it seems easier to print l than n prime and what if the
printer (of a textbook) accidently dumps a few prime symbols, leaving just the letter 'n?' Ooops!
The rule for selecting the proper values of 'l' is as follows:
l = 0, 1, 2, . . . , n-1
l will always be a whole number and will NEVER be as large as the 'n' value it is associated with.
The Magnetic Quantum Number (signified by the letter 'm'): this quantum
number was also discovered by Sommerfeld in the same 1914-1915 time
frame. I don't think he discovered one and then the other, I think that him
realizing the need for two runs together somewhat. I could be wrong in this, so
don't take my word for it!
The rule for selecting m is as follows:
m starts at negative 'l,' runs by whole numbers to zero and then goes to
positive 'l.'
For example, when l = 2, the m values used are -2, -1, 0, +1, +2, for a total of
five values.
The Spin Quantum Number (signified by the letter 's'): spin is a property of electrons that is not related to a sphere
spinning. It was first thought to be this way, hence the name spin, but it was soon realized that electrons cannot spin on
their axis like the Earth does on its axis. If the electron did this, its surface would be moving at about ten times the speed
of light (if memory serves correctly!). In any event, the electron's surface would have to move faster than the speed of light
and this isn't possible.
In 1925, Wolfgang Pauli demonstrated the need for a fourth quantum number. He closed the abstract to his paper this
way:
"On the basis of these results one is also led to a general classification of every electron in the atom by the principal
quantum number n and two auxiliary quantum numbers k1 and k2 to which is added a further quantum number m1 in the
presence of an external field. In conjunction with a recent paper by E. C. Stoner this classification leads to a general
quantum theoretical formulation of the completion of electron groups in atoms."
In late 1925, two young researchers named George Uhlenbeck and Samuel Goudsmit discovered the property of the
electron responsible for the fourth quantum number being needed and named this property spin.
The rule for selecting s is as follows: after the n, l and m to be used have been determined, assign the value +1/2 to one
electron, then assign -1/2 to the next electron, while using the same n, l and m values.
For example, when n, l, m = 1, 0, 0; the first s value used is +1/2, however a second electron can also have n, l, m = 1, 0,
0; so assign -1/2 to it.
Rules Governing the Allowed Combinations of Quantum Numbers
* The three quantum numbers (n, l, and m) that describe an orbital are
integers: 0, 1, 2, 3, and so on.
* The principal quantum number (n) cannot be zero. The allowed values of
n are therefore 1, 2, 3, 4, and so on.
* The angular quantum number (l) can be any integer between 0 and n - 1.
If n = 3, for example, l can be either 0, 1, or 2.
* The magnetic quantum number (m) can be any integer between -l and +l.
If l = 2, m can be either -2, -1, 0, +1, or +2.
There is only one orbital in the n = 1 shell because there is only one way in which a sphere can be oriented in
space. The only allowed combination of quantum numbers for which n = 1 is the following.
n
l
m
1
0
0
1s
There are four orbitals in the n = 2 shell.
n
l
2
0
2
1
2
1
2
1
m
0
-1
0
1
2s
2p
There is only one orbital in the 2s subshell. But, there are three orbitals in the 2p subshell because there are three
directions in which a p orbital can point. One of these orbitals is oriented along the X axis, another along the Y axis,
and the third along the Z axis of a coordinate system, as shown in the figure below. These orbitals are therefore
known as the 2px, 2py, and 2pz orbitals.
There are nine orbitals in the n = 3 shell.
n
l
3
0
m
0
3
3
3
1
1
1
-1
0
1
3p
3
3
3
3
3
2
2
2
2
2
-2
-1
0
1
2
3d
3s
There is one orbital in the 3s subshell and three orbitals in the 3p subshell. The n = 3 shell, however, also includes 3d
orbitals.
The five different orientations of orbitals in the 3d subshell
are shown in the figure below. One of these orbitals lies in
the XY plane of an XYZ coordinate system and is called the
3dxy orbital. The 3dxz and 3dyz orbitals have the same
shape, but they lie between the axes of the coordinate
system in the XZ and YZ planes. The fourth orbital in this
subshell lies along the X and Y axes and is called the 3dx2y2 orbital. Most of the space occupied by the fifth orbital lies
along the Z axis and this orbital is called the 3dz2 orbital.
The number of orbitals in a shell is the square of the principal quantum number: 12 = 1,
22 = 4, 32 = 9. There is one orbital in an s subshell (l = 0), three orbitals in a p subshell (l
= 1), and five orbitals in a d subshell (l = 2). The number of orbitals in a subshell is
therefore 2(l) + 1.
Before we can use these orbitals we need to know the number of electrons that can
occupy an orbital and how they can be distinguished from one another. Experimental
evidence suggests that an orbital can hold no more than two electrons.
To distinguish between the two electrons in an orbital, we need a fourth quantum
number. This is called the spin quantum number (s) because electrons behave as if they
were spinning in either a clockwise or counterclockwise fashion. One of the electrons in
an orbital is arbitrarily assigned an s quantum number of +1/2, the other is assigned an s
quantum number of -1/2. Thus, it takes three quantum numbers to define an orbital but
four quantum numbers to identify one of the electrons that can occupy the orbital.
The allowed combinations of n, l, and m quantum numbers for the first four shells are
given in the table below. For each of these orbitals, there are two allowed values of the
spin quantum number, s.
The Relative Energies of Atomic Orbitals
Because of the force of attraction between objects of opposite charge, the most important factor influencing the energy of
an orbital is its size and therefore the value of the principal quantum number, n. For an atom that contains only one
electron, there is no difference between the energies of the different subshells within a shell. The 3s, 3p, and 3d orbitals,
for example, have the same energy in a hydrogen atom. The Bohr model, which specified the energies of orbits in terms of
nothing more than the distance between the electron and the nucleus, therefore works for this atom.
The hydrogen atom is unusual, however. As soon as an atom contains more than one electron, the different subshells no
longer have the same energy. Within a given shell, the s orbitals always have the lowest energy. The energy of the
subshells gradually becomes larger as the value of the angular quantum number becomes larger.
Relative energies: s < p < d < f
As a result, two factors control the energy of an orbital for
most atoms: the size of the orbital and its shape, as shown in
the figure to the right.
Electron Configurations, the Aufbau Principle, Degenerate Orbitals, and Hund's Rule
The electron configuration of an atom describes the orbitals occupied by electrons on the atom. The basis of this
prediction is a rule known as the aufbau principle, which assumes that electrons are added to an atom, one at a time,
starting with the lowest energy orbital, until all of the electrons have been placed in an appropriate orbital.
A hydrogen atom (Z = 1) has only one electron, which goes into the lowest energy orbital, the 1s orbital. This is indicated
by writing a superscript "1" after the symbol for the orbital.
H (Z = 1): 1s1
The next element has two electrons and the second electron fills the 1s orbital because there are only two possible values
for the spin quantum number used to distinguish between the electrons in an orbital.
He (Z = 2): 1s2
The third electron goes into the next orbital in the energy diagram, the 2s orbital.
Li (Z = 3): 1s2 2s1
The fourth electron fills this orbital.
Be (Z = 4): 1s2 2s2
After the 1s and 2s orbitals have been filled, the next lowest energy orbitals are the three 2p orbitals. The fifth electron
therefore goes into one of these orbitals.
B (Z = 5): 1s2 2s2 2p1
When the time comes to add a sixth electron, the electron configuration is obvious.
C (Z = 6): 1s2 2s2 2p2
However, there are three orbitals in the 2p subshell. Does the second electron go into the same
orbital as the first, or does it go into one of the other orbitals in this subshell?
To answer this, we need to understand the concept of degenerate orbitals. By definition, orbitals are
degenerate when they have the same energy. The energy of an orbital depends on both its size
and its shape because the electron spends more of its time further from the nucleus of the atom as
the orbital becomes larger or the shape becomes more complex. In an isolated atom, however, the
energy of an orbital doesn't depend on the direction in which it points in space. Orbitals that differ
only in their orientation in space, such as the 2px, 2py, and 2pz orbitals, are therefore degenerate.
Electrons fill degenerate orbitals according to rules first stated by Friedrich Hund. Hund's rules can
be summarized as follows.
* One electron is added to each of the degenerate orbitals in a subshell before two electrons are
added to any orbital in the subshell.
* Electrons are added to a subshell with the same value of the spin quantum number until each
orbital in the subshell has at least one electron.
When the time comes to place two electrons into the 2p subshell we put one electron into each of
two of these orbitals. (The choice between the 2px, 2py, and 2pz orbitals is purely arbitrary.)
C (Z = 6): 1s2 2s2 2px1 2py1
The fact that both of the electrons in the 2p subshell have the same spin quantum number can be shown by
representing an electron for which s = +1/2 with an
arrow pointing up and an electron for which s = -1/2 with an arrow pointing down.
The electrons in the 2p orbitals on carbon can therefore be represented as follows.
When we get to N (Z = 7), we have to put one electron into each of the three degenerate 2p orbitals.
N (Z = 7):
1s2 2s2 2p3
Because each orbital in this subshell now contains one electron, the next electron added to the subshell must have the
opposite spin quantum number, thereby filling one of the 2p orbitals.
O (Z = 8):
1s2 2s2 2p4
The ninth electron fills a second orbital in this subshell.
F (Z = 9):
1s2 2s2 2p5
The tenth electron completes the 2p subshell.
Ne (Z = 10):
1s2 2s2 2p6
There is something unusually stable about atoms, such as He and Ne, that have electron configurations with filled
shells of orbitals. By convention, we therefore write abbreviated electron configurations in terms of the number of
electrons beyond the previous element with a filled-shell electron configuration. Electron configurations of the next
two elements in the periodic table, for example, could be written as follows.
Na (Z = 11): [Ne] 3s1
Mg (Z = 12): [Ne] 3s2
Ne
Na
Mg
II. Sublevels and Orbitals
An orbital is a space that can be occupied by up to two electrons.
Each type of sublevel holds a different number or orbitals, and therefore,
a different number of electrons. s sublevels have one orbital, which can
hold up to two electrons. p sublevels have three orbitals, each of which
can hold 2 electrons, for a total of 6. d sublevels have 5 orbitals, for a
possible total of 10 electrons. f sublevels, with 7 orbitals, can hold up to
14 electrons. The information about the sublevels is summarized in the
table below:
Orbital and Electron Capacity for the Four Named Sublevels
Su b le ve l
s
p
d
f
# of or b it a ls
1
3
5
7
Ma xi m u m nu mb er o f elec t rons
2
6
10
14
III. Total Number of Orbital and Electrons per Energy Level
An easy way to calculate the number of orbitals found in
an energy level is to use the formula n2. For example, the
third energy level (n=3) has a total of 32, or nine orbitals.
This makes sense because we know that the third energy
level would have 3 sublevels; an s sublevel with one orbital,
a p sublevel with 3 orbitals and a d sublevel with 5 orbitals. 1
+ 3 + 5 = 9, so the formula n2 works!
IV. Total Number of Electrons per Energy Level
An easy way to calculate the total number of electrons that can be held by a
given energy level is to use the formula 2n2. For example, the fourth energy
level (n=4) can hold 2(4)2 = 32 electrons. This makes sense because the
fourth energy level would have four sublevels, one of each of the named types.
The s sublevel hold 2 electrons, the p sublevel holds 6 electrons , the d
sublevel holds 10 electrons and the f sublevel holds 14 electrons. 2 + 6 + 10 +
14 = 32, so the formula 2n2 works! We can summarize this information in the
table below:
Orbitals and Electron Capacity of the First Four Principle Energy Levels
Pri n cip le en er g y
le ve l ( n )
1
2
3
4
Type o f s ub lev e l
s
s
p
s
p
d
s
p
d
f
Nu m b e r of or b ital s
pe r typ e
1
Nu m b e r of or b ital s
pe r l e ve l(n 2 )
1
Maxim u m n u m b e r
of e le ctro n s ( 2 n 2 )
2
1
4
8
1
9
18
1
16
32
V. Order of Filling Sublevels with Electrons
The next thing that you need to recall is the fact that the energy
sublevels are filled in a specific order that is shown by the arrow
diagram seen below:
Remember to start at the
beginning of each arrow, and
then follow it all of the way to the
end, filling in the sublevels that it
passes through. In other words,
the order for filling in the
sublevels becomes; 1s, 2s, 2p,
3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s,
4f, 5d, 6p, 7s, 5f, 6d,7p.
How do I read an electron configuration table?
Are you making a model of an atom and need to know how
to place the electrons around the nucleus? If so, you will
need to know how to read an element's electron
configuration table. Follow these easy directions to learn
how!
What is an electron configuration table?
An electron configuration table is a type of code that describes
how many electrons are in each energy level of an atom and
how the electrons are arranged within each energy level. It
packs a lot of information into a little space and it takes a little
practice to read. For example, this is the electron configuration
table for gold:
What do all those numbers and letters mean?
Each row of an electron configuration table is sort of like a
sentence. Each 'sentence' is made up of smaller 'words'. Each
'word' follows this format:
number - letter - superscript.
The first number is the energy level. We can tell right away that
an atom of gold contains 6 energy levels.
The lowercase letter is the sub-shell. The sub-shells are
named s, p, d and f. The number of available sub-shells
increases as the energy level increases. For example, the first
energy level only contains an s sub-shell while the second
energy level contains both an s sub-shell and a p sub-shell.
The number in superscript is the number of electrons in a subshell. Each sub-shell can hold only a certain number of
electrons. The s sub-shell can hold no more than 2 electrons,
the p sub-shell can hold 6, the d sub-shell can hold 10 and the
f sub-shell can hold as many as 14.
How many energy levels does an atom have?
Since the electron configuration table lists each energy level by
row, you can tell how many energy levels there are by seeing how
many rows there are. As was mentioned earlier, an atom of gold
contains six energy levels, as shown below:
An atom of gold contains 6 energy levels.
How many electrons are in each energy level?
The total number of electrons in an energy level is the sum of the
electrons in each sub-shell of that energy level. Just add the
numbers in superscript together to find the number of electrons in
an energy level. The number of electrons in each energy level in
an atom of gold is shown below:
The number of electrons in each energy level of gold.
The number in superscript is the number of electrons in a sub-shell. Each subshell can hold only a certain number of electrons. The s sub-shell can hold no
more than 2 electrons, the p sub-shell can hold 6, the d sub-shell can hold 10
and the f sub-shell can hold as many as 14.
This is just a combination of the previous two examples. Use
the electron configuration to find that atom's highest energy
level and then add up the numbers in superscript to find the
number of electrons that are in it. There is one electron in the
outer energy level of an atom of gold, as shown below: