Download Unit 4 Periodicity

Unit 4
Periodicity
Chem 020, R. R. Martin
A. Wave-Particle Duality of Light
Light travels as an electromagnetic wave with a wavelength (λ).
The amplitude is the intensity (brightness)
The number of cycles that pass a given point per unit time is the
frequency (c/λ). One Hertz (Hz) is one cycle per second.
The speed (c) at which light moves through space is a constant,
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−1
2.998 × 10 m s . Therefore, Frequency = c/λ
Electromagnetic waves span a spectrum, but our eyes can only
see around 400 – 700 nm. White light from the sun consists of all
wavelengths between this range (and more).
Work by Max Planck and Albert Einstein in the early 1900’s
demonstrated that light can also be considered as a stream of particles
known as photons, which have the energy:
1
E = (hc)/ λ
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where h = Planck’s constant, 6.626 × 10 J s
• Note that the energy of the photon is directly proportional to
frequency, yet inversely proportional to wavelength.
o Shorter wavelength = higher frequency = higher energy
o Exposure to ultraviolet light and x-rays can cause cancer!
B. Atomic Spectra
Recall that white light consists a continuum of all wavelengths
between 400 – 700 nm (the visible region).
However, the spectra given off by atoms of gaseous elements
consist of lines that are at specific wavelengths, so we obtain a line
spectrum (not a continuum).
Atomic spectra are characteristic to the element in question, and
the spectra can be used for identification purposes.
For example, the atomic spectrum of hydrogen can be produced
2
by striking electric discharge through H2. This energy breaks the bond
and forms gaseous H atoms.
The emission is then passed through a prism, which splits the
light into its component wavelengths, giving a line spectrum.
Photons are produced when an electron moves from one energy
level to another, and the energy difference between the levels is
released as light energy (photons).
Energy levels for electrons in atoms are limited to specific values,
i.e. they are quantized.
With the H atom, four lines of specific wavelength were produced.
Since wavelength is related to photon energy, it follows that the H atom
emits only those four energies.
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C. The Bohr Model
In the 1910’s, Neils Bohr developed a Nobel-prize-winning theory
to explain the hydrogen spectrum. (While the theory was completely
incorrect, it opened doors to the development of the current and
accepted quantum mechanical model).
Bohr’s assumption was that the electron particle moved in a
circular orbit around a central proton and that there were orbits at
distinct radial distances (levels) from the proton.
Energy would then be released or absorbed as the electron
changed orbit levels.
Moving the electron further away from the proton requires the
addition of energy to overcome the electrostatic forces. Light energy is
absorbed (termed excitation).
When an electron moves to a lower level, light energy is released
(termed emission). The energy of the photon emitted corresponds to
the difference in energy between the two levels involved.
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D. The Quantum Mechanical Model
Although Bohr’s model was highly successful in explaining the line
spectrum of the H atom, it failed for everything else. This failure is
because Bohr treated the electron like a particle (particles have welldefined paths that can be predicted).
•
In 1924, Louis de Broglie suggested that perhaps electrons
and light could behave in a similar manner, i.e. perhaps electrons could
also behave as both particles and waves
o The paths of waves cannot be accurately predicted.
This new idea was experimentally confirmed in 1927 at Bell Labs
and led to a whole new discipline: quantum mechanics.
•
This model differs from the Bohr model in two important ways:
1. Because of the particle-wave duality, it is impossible to specify
the precise location of an electron at any instant.
•
We cannot predict the actual path it takes (not an orbit), and
we can only estimate the probability of its position
2. The kinetic energy of the electron is inversely related to the
volume of the region to which it is confined
•
Smaller volume = closer to nucleus. In the smaller volume,
electrostatic energy decreases and the kinetic energy decreases
The QMM uses complex mathematics to describe the particlewave behaviour of electrons. However, we won’t look these details…
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only the results!
The chemical properties of an atom are determined by its
electronic configuration, i.e. number of electrons and how they are
arranged in the atom. This information can also be obtained from an
element’s location in the periodic table.
Four quantum numbers identify each electron in an atom
1. Principal Quantum Number (n)
where n = any positive integer (1, 2, 3, 4…).
Derived from the Bohr model, this number defines the principle
energy level for the electron
As the level n increases, so does the energy of the electron and its
distance from the nucleus.
Within each n level are sublevels designated ℓ.
2. Orbital Quantum Number (ℓ)
where ℓ = any integer between 0 and (n – 1).
For example, if n = 2, then ℓ = 0 or 1.
•
ℓ describes the shape of the electron cloud (the
probability of an electron being there 90% of the time): ℓ = 0 Æ s
electrons ℓ = 1 Æ p electrons ℓ = 2 Æ d electrons ℓ = 3 Æ f electrons
All n allow for s electrons, so we have 1s, 2s, 3s…
For p electrons, n must be at least 2, so 2p, 3p, 4p…
For d electrons, n must be at least 3, so 3d, 4d, 5d…
For f electrons, n must be at least 4, so 4f and 5f
3. Magnetic Quantum Number (mℓ)
where mℓ = any integer between –ℓ through 0 to +ℓ.
e.g. if ℓ = 1 (p electron), then mℓ = –1, 0, or +1.
mℓ represents the electron’s magnetic moment, which is the spatial
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direction of the electron cloud
If ℓ = 0 (s electron), mℓ = 0, and there can only be one possible
orientation of the s orbital.
If ℓ = 1 (p electron), mℓ = –1, 0, or +1, and there are three p
orbitals each with different orientation
4. Spin Quantum Number (ms)
where ms = +½ or –½ regardless of what the other quantum
numbers are
When electrons come together, their spins may be the same (both
+ or both –) or opposite (one + and one –).
These are respectively called parallel spins or opposite spins, and
are denoted by arrows pointing up or down.
(parallel, not allowed)
(opposite, allowed)
• Parallel spins are not allowed because the Pauli Exclusion
Principle says that in any one atom, no two electrons may
have the same four quantum numbers.
Important note: Each orbital (cloud) can hold two electrons. Thus,
if two electrons are in the same orbital, three of their quantum numbers
th
would be the same. Therefore, to make the 4 number different, they
must have different spins.
The max number of electrons for any principle number n is given
2
−
by 2n . (e.g. if n = 2, we have one s + three p = 8 e )
a. Shape of s orbitals
If ℓ = 0 (s electrons), mℓ = 0, and there can be only one s orbital at
any given principle quantum number n.
Recall that a cloud or orbital defines the probability of finding an
electron at a particular point (indicated by the dot density). This is
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represented by a three-dimensional plot.
s orbitals are spherically symmetric. i.e. most of the time, an s
electron is found within the sphere drawn on the plot.
Realize that every level n has an s orbital and that each one of
these orbitals can hold a maximum of two electrons.
o Notation: if, for example, the s orbital on level n = 2 has just one
1
electron, we denote this by the notation 2s . If it has two
2
electrons (must have opposite spins), then 2s .
b. Shape of p orbitals
If ℓ = 1 (p electrons), mℓ = +1, 0, and −1, then there are three p
orbitals at every level n ≥ 2. (ℓ = 1 and n = 1 not possible).
Each p orbital holds a maximum two electrons, and since there
are three of these orbitals, we can have six p electrons at any of the
allowed levels (n ≥ 2).
Each p orbital lies on a different axis and features two lobes.
Since they are on different axes, they are 90° apart.
If, for example, we have six electrons in the p orbitals of level n =
6
2, we say that it has the configuration 2p . If only five electrons are
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5
present, then 2p , hence unfilled p orbitals.
E. Electronic Configurations
As mentioned earlier, in a group of electrons having the same
value of n, sometimes referred to as shell, the maximum number of
2
electrons that can be accommodated is 2n .
•
The chart below summarizes the possible orbital types (ℓ),
sometimes called subshells or sublevels, at various n levels.
o How many s, p, d, and f orbitals are at each level?
•
For n = 1, we only have 1s, so a maximum of 2 electrons.
1
2
o e.g. H is 1s and He is 1s
•
For n = 2, we have 2s (two electrons) and 2p (six electrons)
o e.g. C has six electrons. Two are in 1s, which leaves four
nd
electrons for the 2 level, two in 2s and two in 2p. We denote this
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2
2
2
configuration as 1s 2s 2p
o
With C, are those two 2p electrons in the same 2p orbital or
are they in separate ones? (recall three 2p orbitals)
Hund’s Rule states that electrons occupy orbitals of equal energy
in such a way that the number of unpaired electrons is at a maximum,
thus minimizing inter-electronic repulsion.
•
Therefore, in the case of carbon, where we only have two
electrons in the 2p orbitals, those two electrons must reside in different
2p orbitals.
o This is denoted by: 2p ____ ____ ____
2
2
4
•
Oxygen has 8 electrons, configured 1s 2s 2p .
o Using Hund’s Rule: 2p ____ ____ ____
The filling of orbitals using Hund’s Rule gives us the lowest-energy
configuration, also called the ground state.
•
Other arrangements consistent with the Pauli principle are
possible, but are of higher energy. These are called excited states.
o Virtually any configuration is possible in an excited state, but
the number of electrons does not change.
2
1
0
1
2
o An excited state for oxygen could be 1s 2s 2p 3s 3p
Isoelectronic species are those with the same number of electrons
arranged similarly. For example, these all have the same configuration
has the noble gas Ne (all filled):
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2−
−
+
2+
3+
2
2
6
o O , F , Ne, Na , Mg , Al are all 1s 2s 2p or [Ne]
a. Orbital energies
In order to write a ground-state configuration, we need to know the
energies of the orbitals, or more precisely, the energies of the electrons
in the orbitals.
There is no absolute fixed energy order, but this is a trend:
•
However, in simple cases, we can place electrons into the
orbitals in increasing order of n, and for the same n, in increasing order
of the orbital quantum number (ℓ).
o This approach works for the first 18 electrons. Example:
2
2
6
2
6
Argon ground state = 1s 2s 2p 3s 3p
•
Subsequent electrons must fill the 4s level before the 3d.
2
2
6
2
6
1
1
o Example: K is 1s 2s 2p 3s 3p 4s shorthand [Ar] 4s
Note: Electrons in the highest n are called valence electrons. The
rest are the core electrons.
Transition metals, however, behave differently…
•
For example, the electronic configuration of Cr (24 electrons)
o We would normally predict that the six electrons over the [Ar]
2
4
core are arranged 4s 3d
(not the case)
o However, if the 3d orbitals could be exactly half-filled, the 3d
and 4s become approximately equal in energy. An electron from the 4s
moves to the 3d, and this scenario also obeys Hund’s Rule and
minimizes repulsions.
Likewise, completely full 3d orbitals are favourable, e.g. Cu. The
energy of the 3d falls below that of the 4s because of the increased
1
10
nuclear charge. Cu configuration = [Ar] 4s 3d
Cr and Cu are in the first series of the transition metals. With
these, promotion of one electron will always occur if it results in a halffilled or completely filled d orbital.
Transition metals in the second series behave similarly.
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b. Cationic species
When an atom loses electrons to form a cation, the electrons are
always lost from the valence shell, that with the highest n.
Thus, for transition metals, the electrons remaining over the noblegas core are always found in the 3d orbitals.
2+
•
Example: write the configurations for the V atom and V
o
We lose the 4s electrons because the greater nuclear charge
(more protons in the nucleus) lowers the energy of the 3d below that of
the 4s.
2+
3+
Example: write the configurations for Fe, Fe , and Fe
3+
Although the V atom and Fe have the same number of electrons,
they are not isoelectronic pairs. Their electronic arrangements are
different.
•
This scheme is an interesting way to remember the orbital
filling order. How to redraw this on an exam…
o Write out the orbital subshells possible for each n on separate
lines; e.g. for n=2 we have 2s 2p
o The filling order is from the upper-right corner
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o Of course, this requires you to know that s holds two
electrons, p holds six, d holds ten, and f holds fourteen. However, this
same information can be obtained from the periodic table.
F. The Periodic Table and Electronic Configurations
The periodic table is divided into four blocks according to the
subshell (ℓ) being filled. It is useful because it allows you to easily
determine electronic configuration and which elements may have
similar chemical properties.
Going across = Groups. Going down = Periods.
Main-group elements are those with s or p subshells being filled,
with other subshells being full or empty.
Those with d orbitals being filled are termed transition elements.
Each d sublevel holds 10 electrons.
Elements in the f block are those with f orbitals being filled. These
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orbitals hold 14 electrons. The lanthanides are those with the 4f orbitals
being filled, and actinides, 5f.
Earlier, we examined the definitions of valence shell (outer) and
core electrons (inner). The valence shell is important because these
electrons influence the element’s properties. It is also these valence
electrons that are used to form bonds.
We can determine valence-shell configuration by reading the
periodic table from left to right. Using P as an example…
2
2
6
2
3
P has the configuration 1s 2s 2p 3s 3p
2
3
In shorthand notation, [Ne] 3s 3p
•
The number of valence electrons is the number of electrons
occupying the highest n level, and in this case five electrons.
• Now repeat with the element As
2
2
6
2
6
2
10
3
P has the configuration 1s 2s 2p 3s 3p 4s 3d 4p
2
10
3
In shorthand notation, [Ar] 4s 3d 4p
Number of valence electrons? 5
Notice that As is directly underneath P. Both of these elements are
in the same group, #5A (#15).
The valence electrons for all elements in the same group have a
similar valence configuration. The only difference lies in the identity of n
that holds these valence electrons.
Since elements in any one group have the same number of
valence electrons, it is no surprise that they have similar chemical
properties.
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15
1
Group 1A Alkali metals valence config = ns Li, Na, K, Rb, Cs, Fr
2
Group 2A Alkali earths valence config = ns Be, Mg, Ca, Sr, Ba,
Ra
2
1
2
2
Group 3A (13)
valence config = ns np B, Al, Ga, In, Tl
Group 4A (14)
valence config = ns np C, Si, Ge, Sn, Pb
Group 5A (15)
2
3
valence config = ns np N, P, As, Sb, Bi
2
4
Group 6A (16) Chalcogens valence config = ns np O, S, Se, Te, Po
2
5
Group 7A (17) Halogens valence config = ns np F,Cl, Br, I, At
2
6
2
Group 8A (18) Noble Gases valence config = ns np He (1s ), Ne,
Ar, Kr, Xe, Rn All noble gases have a full valence shell
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•
Noble gases are extremely stable and not very reactive due to
their full valence shell. Other elements can lose or gain electrons to
attain the same electronic configuration as these noble gases.
o Example: K tends to give away one electron, and Cl can
accept an electron to attain the Ar configuration.
•
Write electronic configurations for…
−
o
I
2+
o
Sn
3+
o
Ru
Which one of these has the greatest number of unpaired electrons
3+
−
in the ground state? Ge, Cl, Sc , Br , N
12.21
G. Periodic Properties of Atoms
1. Atomic Size
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Atomic size, or more correctly, atomic radius, assumes a spherical
atom.
For an elemental substance (typically metals), the atomic radius is
one-half the shortest distance of approach between atoms.
Cu
In covalent bonding, atomic radius is easier to define. The covalent
radius is the contribution that the atom makes to the internuclear
distance (bond length).
Cl2
Ionic radius is used to describe ion sizes.
o Anions are always larger than their parent atoms because the
additional electrons exert a repulsive force upon each other and
increase the radius
o Cations are always smaller than their parent atoms, because
they have lost electrons.
o Assume that charge dominates in an isoelectronic series (all
have the same electronic configuration)
•
2−
−
+
2+
atomic size: O > F > Ne > Na > Mg
• Comparison between atoms and ions
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• In general, atomic size decreases across a period from left to right,
and increases down a group.
12.23
These trends can be explained by the concept of effective nuclear
charge (Zeff). The outer valence electrons are attracted to the nucleus,
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but are also repelled by the core electrons.
So, the actual charge that the valence electrons feel is somewhat
diminished, and we say that they are shielded by the core electrons.
For any electron, Zeff is approximately Z − S, where Z is the actual
nuclear charge (atomic number) and S is the number of core electrons.
i.e. Zeff = atomic number − # core electrons
Na
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Mg
12
Al
13
Only core electrons shield… valence electrons do not!
As Zeff increases across a row, valence electrons are pulled in
more tightly, resulting in a smaller atomic size.
Going down a group, the number of core electrons increases,
which increases the shielding of valence electrons. These valence
electrons are less attracted, so size increases.
2. Ionization Energy
•
The ionization energy (IE) is the energy required to remove an
electron completely (infinite separation) from a gas atom
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+
−
M(g) M (g) + e (always endothermic)
•
An atom with several electrons will have successive IE’s
First IE M(g)
+
Second IE M (g)
+
−
2+
−
M (g) + e
M (g) + e
Successive IE values always increase in magnitude because of
increasing ionic charge. It is more difficult to remove an electron when
the atom already has a positive charge.
There are general trends:
•
Going down a group, atomic size increases (more shielding),
so the valence electrons are further away from the nucleus and more
easily removed. And, these electrons are in a higher n shell, which
have higher energy.
H 1312 kJ/mol
Li 520 kJ/mol
Na 496 kJ/mol
K 419 kJ/mol
Going across a row, Zeff increases, which makes the electrons
harder to remove.
Some interesting exceptions to the trend
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2
2
Be (1s 2s ) 900 kJ/mol
2
2
1
B (1s 2s 2p ) 800 kJ/mol
1
o The electron lost in B is the 2p , which is higher in energy than
2
the 2s . High-energy electrons are more easily lost.
• As the next five electrons are added to the 2p orbitals (going
from B to Ne), IE increases with nuclear charges. EXCEPT: N 2p
____ ____ ____ 1402 kJ/mol
3
4
O 2p ____ ____ ____ 1314 kJ/mol
o The electron lost from O is pushed out by the extra
repulsion from the second electron in the same 2px.
3. Electron Affinity
•
Electron affinity (EA) is the opposite of IE. EA is when a
gaseous atom gains an electron.
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−
−
M(g) + e
M (g)
This can be exothermic or endothermic.
If a valence shell is being completed (filled), then it is a favourable
process (it has a higher affinity)
H(g) + e
F(g) + e
−
−
H (g) −73 kJ
−
Cl(g) + e
−
−
F (g) −328 kJ
−
Cl (g) −349 kJ
o These anions are formed when the element reacts with a very
reactive metal that donates an electron, e.g. Li
• Addition of a second electron is always unfavourable because of likecharge repulsion.
O(g) + e
−
−
O (g) + e
−
−
O (g)
2−
O (g) −328 kJ
2−
o Nonetheless, the O ion is very common and is stabilized
by attraction to cations in solids, e.g. MgO.
• Trend: More negative value (higher affinity and easier to add an
electron) when going up a column (less repulsion from existing
electrons) and across a row (valence being filled). However, Noble
gases have very positive values.
4. Electronegativity
Electronegativity is the tendency of an atom in a covalently bonded
molecule to attract the bonding electron pair to itself.
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It follows the same trend as electron affinity, where it increases as
going up a group and across a row. Values are relative and not
absolute.
The greatest electronegativity values are found with small nonmetals. F is the most electronegative element.
Electronegativity is important in bonding, because a bond between
−
two atoms of different electronegativity is polarized, and the e pair is
closer to the more electronegative atom.
Examples: H2 and HCl
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A Little Summary
Electrons in atoms are defined by four quantum numbers:
1. n, the Principle Quantum Number has values in integer steps: n= 1,2 3, etc.
The higher the value of n, the farther (on average) the electron is from the nucleus.
2. l, the Orbital Quantum Number, helps define the shape of the orbital. The value of l is related to the value of n,
it can have values from 0 to (n-1) in integer units
If n=1 l = (n-1) = 0
If n = 2 possible values of l are: 0 and 1 (n-1)
If n=3 the possible values of l are: 0,1,2 ((n-1)
Orbitals with electrons having values l values 1,2,3,4 etc are assigned letters (from old spectroscopic notation)
l = 0 are s orbitals (from Sharpe lines in spectra)
l = 1 are p orbitals (from the Principle line)
l = 2 are d orbitals (from Diffuse lines)
l = 3 are f orbitals (from Fine lines in spectra).
3. The Magnetic Quantum Number, gives the orientation of the magnetic field associated with the electrons motion
in space.
The symbol is ml, its value depends on the value of l.
Values of ml vary from –l to +l in integer values.
If l = 1 the available values of ml are: -1, 0, +1
If l = 2 the available values of ml are: -2, -1, 0, +1, +2
4. The Spin Quantum Number is associated with the electron, given the symbol ms it can have only one of two
values; +1/2 or -1/2
We can use these quantum numbers to construct the Ground State electron configuration (lowest energy state) of an
atom using:
The Aufbau principle, which essentially states that we start with the lowest quantum # (n=1) add all the required
electrons, move to the next highest quantum # ( n = 2) and add all the required electrons and so on until the number of
electrons equals the atomic # of the elements. When doing this we must obey:
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The Pauli Exclusion Principle:
No two electrons in the same atom can have the same set of all four quantum numbers.
And
Hund’s Rule:
Electrons occupy orbitals of equal energy so that the number of unpaired electrons (electrons with the same
spin) is a maximum.
Thus for H n =1, l=0, ml = 0, ms = + or -1
l = 0 yields an s orbital so the ground state for H has the electronic configuration: 1s1 or 1s ↓ where the arrow
indicates the direction of the electron spin note the spin could be +1/2 or -1/2 ( 1s ↑) in this case these are equivalent
and will have the same energy (the two staes are said to be degenerate)
For N, atomic # 7
We have n=1, l= 0, ml = 0, ms = + or -1
Configuration so far : 1s2
And can use two electrons, as long as they have opposite spins, with two to go.
Now set n = 2
Values of l = 0 or 1
For l =0, ml = 0, ms = + or -1
or 2s2
So that we now have accommodated 4 electrons with a ground state 1s2 2s2
We still have three electrons left we can add them with l = 1 (a p state) with ml = -1, 0, or 1
We must also apply Hund’s rule and the three electrons we add must have the same spin
We get 1s2 2s2 2p3 as the ground state for N
Note showing the spins with arrows yields;
1s2 ↑↓ 2s2 ↑↓ 2p3 ↑ ↑ ↑ or 1s ↑↓ 2s ↑↓ 2p ↓ ↓ ↓
These states are degenerate.
Oxygen atomic # 8 would be:
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1s2 ↑↓ 2s2 ↑↓ 2p4 ↑↓ ↑ ↑
And so on, however note;
1. The 3d levels have lower energy than the 4p so that 3d electrons are added after filling the 4 s but before
filling the 4p.
2. Cu atomic # 29 is an exception, by the time Cu is reached the energy of the 3d level has fallen below the 4s
(due to increased nuclear charge) so that the ground state for Cu in 3d10 4s1. Cr exhibits a similar anomaly, we
would expect Ar3d44s2, however Ar3d54s1 with 6 unpaired electrons is the lower energy (ground) state for Cr.
3. When electrons are lost from a transition metal atom (an atom with d, but no f electrons), any electrons
remaining over the noble gas core are always found in the d orbitals.
Example: V has the ground state [Ar] 3d3 4s2 , V2+ has ground state [Ar] 3d3 4s0 .
4. Isoelectronic Species have the same number of electrons arranged in the same way:
F- and Na+ are Isoelectronic, both 2s2 2p6.
5. Atomic size increases from the top to the bottom of a group and decreases across a period. For Isoelectronic ions
the size deceases as the atomic number increases.
6. The three principle parts of the periodic table:
I Main Group Elements ns and np orbitals are being filled. They have 1-8 electrons in their valence shell.
II Transition Elements (or d-block elements) the d orbitals are being filled.
By convention Zn, Cd, and Hg are considered to be transition elements.
III Inner Transition Elements f orbitals are being filled, the 4f series are also called lanthanides (since La immediately
precedes them, the 5f are called actinides (preceded by Ac).
7. The first ionization energy, defined for:
A(g) → A(g)+ + eIncreases from left to right across the table and decreases from top to bottom in any group.
With increasing charge on the ion Ionization energies increase.
8. Electron affinity is the energy released (or absorbed) for:
A(g) + e- →
A(g)-
This reaction becomes more favorable across any period and less favorable from the top to bottom of any group.
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9. Electronegativity is the most loosely defined term: “The tendency of an atom in a molecule to attract electrons to
itself”. The concept allows us to identify polar molecules which have essentially positive an negative ends, for
instance:
relatively positive H---Br relatively negative
Linus Pauling, somewhat arbitrarily defined the Electronegativity of F (the most electronegative element) as 4, with a
sequence F > O > Cl > N > I > Se.
In general Electronegativity increases from left to right and decreases from top tp bottom of the main group elements.
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