Electron Configurations

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Electron Configurations
8 Periodic Table
8-1 Electron Configurations
8-2 The Periodic Table and Electron Configurations
8-3 Using the Periodic Table to Write Electron
8-4 Atomic and Ionic Radii
8-5 Ionization Energy
8-6 Electron Affinity
8-7 Chemical Properties and the Periodic Table
8.1 Electron Configurations
• Armed with knowledge of the relative energies of orbitals
and the Pauli exclusion principle, we are in a position to
consider the arrangements of electrons in atoms.
• Electron configuration:The way electrons are
distributed among the various orbitals of an atom.
Three principles of electron configuration
• Principle of the Lowest Energy:The orbitals are filled in
order of increasing energy.
• The Pauli exclusion principle:No more than two
electrons per orbital.
• Hund’s Rule:For degenerate orbitals, the lowest energy
is attained when the number of electrons having the same
spin is maximized.
Orbitals and Their Energies
• In hydrogen the energy of an
orbital depends only on its
principal quantum number, n.
• For a one-electron hydrogen
atom, orbitals on the same
energy level have the same
• The 3s, 3p, and 3d subshells all
have the same energy.
 1 
En    RH   2  (n  1, 2,3, 4 )
n 
In a multi-electron atom the
electron–electron repulsions cause
the various subshells in a given
shell to be at different energies.
Notice also that all orbitals of a given
subshell (such as the five 3d orbitals) have
the same energy as one another. Orbitals with
the same energy are said to be degenerate.
The important idea is this: In a multi-electron atom, for a
given value of n, the energy of an orbital increases with
increasing value of l.
General energy ordering of orbitals for a multi-electron atom
Three-electron atom——lithium Li
• The number of electrons in a neutral atom equals its
atomic number.
• The ls orbital can accommodate two of the electrons.
The third one goes into the next lowest energy orbital,
the 2s.
• We can represent any electron configuration by writing
the symbol for the occupied subshell and adding a
superscript to indicate the number of electrons in that
Orbital Diagram
• We can also show the arrangement of the electrons as
• In this representation, which we call an orbital diagram.
• Each box represents one orbital.
• Half-arrows represent the electrons, each electron by a
half arrow .
• The direction of the arrow represents the spin of the
electron (ms = +½, -½).
Paired and unpaired electron
• Electrons having opposite spins are said to be paired
when they are in the same orbital
• An unpaired electron is one not accompanied by a
partner of opposite spin.
Hund’s Rule
• Consider now how the electron configurations of the
elements change as we move from element to element
across the periodic table.
• The choice of a spin-up electron here is arbitrary; It is
customary to show unpaired electrons with their spins
Electron Spin and the Pauli Exclusion
Electron Spin and the Pauli Exclusion
• Since electron spin is quantized, we define ms = spin
quantum number =  ½.
• Pauli’s Exclusions Principle: no two electrons can have
the same set of 4 quantum numbers.
Therefore, two electrons in the same orbital must have
opposite spins.
Electron Configurations:
Hund’s Rule
• Electron configurations tells us in which orbitals the
electrons for an element are located.
• Three rules:
electrons fill orbitals starting with lowest n and moving
no two electrons can fill one orbital with the same spin
for degenerate orbitals, electrons fill each orbital singly before
any orbital gets a second electron (Hund’s rule).
Energy of orbitals in a ____________ electron atom
Energy depends only on principal quantum number n
En = -RH (
Energy of orbitals in a ___________-electron atom
Energy depends on n and l
n=3 l = 2
n=3 l = 0
n=2 l = 0
n=3 l = 1
n=2 l = 1
n=1 l = 0
Fill lowest energy orbitals first (______________ principle)
H 1 electron
H 1s1
Fill lowest energy orbitals first (Aufbau principle)
He 2 electrons
He 1s2
Fill lowest energy orbitals first (Aufbau principle)
Li 3 electrons
Li 1s22s1
Fill lowest energy orbitals first (Aufbau principle)
Be 4 electrons
Be 1s22s2
Fill lowest energy orbitals first (Aufbau principle)
B 5 electrons
B 1s22s22p1
Fill lowest energy orbitals first (Aufbau principle)
C 6 electrons
C 1s22s22p2
______________: The most stable arrangement of electrons in subshells is the one
with the greatest number of parallel spins.
C 6 electrons
C 1s22s22p2
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
N 7 electrons
N 1s22s22p3
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
N 7 electrons
N 1s22s22p3
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
O 8 electrons
O 1s22s22p4
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
F 9 electrons
F 1s22s22p5
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
Ne 10 electrons
Ne 1s22s22p6
Order of orbitals (filling) in multi-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
What is the electron configuration of Mg?
Mg 12 electrons
1s < 2s < 2p < 3s < 3p < 4s
___________________ 2 + 2 + 6 + 2 = 12 electrons
Abbreviated as [Ne]______
[Ne] is 1s22s22p6
What are the possible quantum numbers for the
last (outermost) electron in Cl?
Cl 17 electrons
1s < 2s < 2p < 3s < 3p < 4s
____________________ 2 + 2 + 6 + 2 + 5 = 17 electrons
Last electron added to 3p orbital
ml = -1, 0, or +1
ms = ½ or -½
8-2 The Periodic Table and Electron Configurations
The Periodic Table
Reading the Periodic Table
• Columns in the periodic table are called groups (numbered
from 1A to 8A or 1 to 18).
• Rows in the periodic table are called periods.
• Metals are located on the left hand side of the periodic
table (most of the elements are metals).
• Non-metals are located in the top right hand side of the
periodic table.
• Elements with properties similar to both metals and nonmetals are called metalloids and are located at the interface
between the metals and non-metals.
Properties of the Periodic Table
• Some of the groups in the periodic table are given special
• These names indicate the similarities between group
Group 1A: Alkali metals.
Group 2A: Alkaline earth metals.
Group 6A: Chalcogens.
Group 7A: Halogens.
Group 8A: Noble gases.
Description of the Modern Periodic Table
• The vertical groups bring together elements with similar
• The horizontal periods of the table are arranged in order of
increasing atomic number from left to right. The groups are
numbered at the top. and the periods at the extreme left in the
periodic table on the inside front cover.
• The first two groups--the s block- and the last six groups--the
p block-together constitute the main-group elements.
• The d-block elements are known as the transition elements.
The f-block elements, sometimes called the innertransition
elements, would extend tile table to a width of 32 members
if incorporated in the main body of the table. The table
would generally be too wide to fit on a printed page, and so
the f-block elements are extracted from the table and placed
at the bottom. The 14 elements following lanthanum (Z = 57)
are called the lanthanides, and the 14 following actinium
( Z = 89) are called the actinides.
Ground State Electron Configurations of the Elements
• The electron configurations of the
elements correspond to their
locations in the periodic table.
• Elements in the same column of the
table have related outer-shell
(valence) electron configurations.
• All 2A elements have an ns2 outer
configuration, and all 3A elements
have an ns2np1 outer configuration,
with the value of n increasing as we
move down each column.
• As shown in figure, the periodic table can be divided into
four blocks based on the filling order of orbitals.
• Two blue columns of elements, known as the alkali metals
(group 1A) and alkaline earth metals (group 2A), are
those in which the valence s orbitals are being filled.
These two columns make up the s block of the periodic
• On the right is a block of six pink columns that comprises
the p block, where the valence p orbitals are being filled.
• The s block and the p block elements together are the
representative elements (main-group elements).
• The orange block has ten columns containing the transition
metals. These are the elements in which the valence d
orbitals are being filled and make up the d block.
• These elements are known as either transition elements or
transition metals.
• The elements in the two tan rows containing 14 columns
are the ones in which the valence f orbitals are being filled
and make up the f block.
• In most tables, the f block is positioned below the periodic
table to save space:
• The number of columns in each block corresponds to
the maximum number of electrons that can occupy
each kind of subshell.
• s, p, d, and f subshells → the numbers of electrons.
• The s block has 2 columns, the p block has 6, the d block
has 10, and the f block has 14.
• Recall also that ls is the first s subshell, 2p is the first p
subshell, 3d is the first d subshell, and 4f is the first f
• Using these facts, you can write the electron
configuration of an element based merely on its position
in the periodic table.
• Let’s use the periodic table to write the electron
configuration of selenium (Se, element 34).
8-4 Atomic and Ionic Radii
General definition
Atomic Radii
The covalent radius is one-half the distance between
the nuclei oftwo identical atoms joined by a single
covalent bond.
The ionic radius is based on the distance between the
nuclei of ions joined by an ionic bond.
The metallic radius is one-half the distance between
the nuclei of two atoms in contact in the crystalline
solid metal.
Covalent radius
Metallic radius
Ionic radius
Ionic Radius
A comparing
of atomic and
ionic sizes
Metallic radii
are shown for
Na and Mg and
ionic radii for
Na+ and Mg2+.
8-5 Ionization Energy
The first ionization energy (I1) of magnesium is 738 kJ/mol.
The second ionization energy (I2) is 1450 kJ/mol. The amount
of energy required increased for the second ionization. It is
more difficult to remove an electron from a positively charged
ion than it is to remove one from a neutral atom. This is a
direct consequence of Coulomb's law, which states, in part,
that the force of attraction between oppositely charged
particles is directly proportional to the magnitudes of the
First ionization energies (I1) for many of the elements are
plotted in the following figure.
In general, the farther an electron is from the nucleus, the
more easily it can be extracted.
General Trend in First Ionization Energies
Increasing First Ionization Energy
Increasing First Ionization Energy
8-7 Chemical Properties and the Periodic Table
Atomic Properties
Electron affinity
Atomic radius
Atomic properties and the periodic table—a summary
Electron affinity
Atomic radius
Ionization energy
Ionization energy
8-6 Electron Affinity
Electron Affinity
Electron affinity, EA, is a measure of the energy change that
occurs when a gaseous atom gains an electron.
F(g) + e- → F-(g)
EA = -328kJ/mol
When a F atom gains an electron, energy is given off. The process
is exothermic, the electron affinity is a negative quantity.
When a F atom gains an electron to become F-, the F
atom acquires the very stable electron configuration
of the noble gas neon (Ne). That is,
F(ls22s22p5) + e- → F- (ls22s22p6)
Even metal atoms can form negative ions in the gaseous state, for
example, where the added electron enters the half-filled 2s orbital.
Li(g) + e- → Li- (g) EA = -59.6 kJ/mol
For some atoms, there is no tendency
to gain an electron
The noble gases
In considering the gain of a second electron by a nonmetal atom,
Positive electron affinities can be encountered.
• The electronic structure of an atom describes the energies and
arrangement of electrons around the atom. Much of what is known
about the electronic structure of atoms was obtained by observing
the interaction of light with matter. Visible light and other forms
of electromagnetic radiation (also known as radiant energy) move
through a vacuum at the speed of light, c = 3.00×108 m/s.
Electromagnetic radiation has both electric and magnetic
components that vary periodically in wavelike fashion. The wave
characteristics of radiant energy allow it to be described in terms of
wavelength,λ, and frequency,ν, which are interrelated:
c  
• Planck proposed that the minimum amount of radiant energy that
an object can gain or lose is related to the frequency of the
E  h. This smallest quantity is called a quantum of
energy. The constant h is called Planck’s constant: h =
6.626×10-34Js. In the quantum theory, energy is quantized,
meaning that it can have only certain allowed values. Einstein used
the quantum theory to explain the photoelectric effect, the
emission of electrons from metal surfaces when exposed to light.
He proposed that light behaves as if it consists of quantized energy
packets called photons. Each photon carries energy,
E  h.
• Dispersion of radiation into its component wavelengths produces
a spectrum. If the spectrum contains all wavelengths, it is called a
continuous spectrum; if it contains only certain specific
wavelengths, the spectrum is called a line spectrum. The
radiation emitted by excited hydrogen atoms forms a line
• Bohr proposed a model of the hydrogen atom that explains its line
spectrum. In this model the energy of the electron in the hydrogen
atom depends on the value of a quantum number, n. The value of
n must be a positive integer (1, 2, 3, . . .), and each value of n
corresponds to a different specific energy, En.
• The energy of the atom increases as n increases. The lowest energy
is achieved for n = 1; this is called the ground state of the
hydrogen atom. Other values of n correspond to excited states.
Light is emitted when the electron drops from a higher-energy
state to a lower-energy state; light is absorbed to excite the
electron from a lower energy state to a higher one.
• The frequency of light emitted or absorbed is such that
the difference in energy between two allowed states.
• De Broglie proposed that matter, such as electrons, should exhibit
wavelike properties——Wave-Particle Duality. This hypothesis of
matter waves was proved experimentally by observing the
diffraction of electrons. An object has a characteristic wavelength
that depends on its momentum, mv:
  h / mv
• Discovery of the wave properties of the electron led to
Heisenberg’s uncertainty principle, which states that there is an
inherent limit to the accuracy with which the position and
momentum of a particle can be measured simultaneously.
• In the quantum mechanical model of the hydrogen atom, the
behavior of the electron is described by mathematical functions
called wave functions, denoted with the Greek letter Ψ. Each
allowed wave function has a precisely known energy, but the
location of the electron cannot be determined exactly; rather, the
probability of it being at a particular point in space is given by the
probability density, Ψ2. The electron density distribution is a map
of the probability of finding the electron at all points in space.
• The allowed wave functions of the hydrogen atom are called
orbitals. An orbital is described by a combination of an integer
and a letter, corresponding to values of three quantum numbers.
• n, l, and ml, to describe an orbital.
• The principle quantum number——the energy of the orbital,
and the distance from the nucleus
• The azimuthal quantum number defines the shape of the orbital.
• The magnetic quantum number describes the orientation of the
orbital in space.
• Contour representations are useful for visualizing the shapes of
the orbitals. Represented this way, s orbitals appear as spheres
that increase in size as n increases.
• The radial probability function tells us the probability that the
electron will be found at a certain distance from the nucleus.
• The wave function for each p orbital has two lobes on opposite
sides of the nucleus. They are oriented along the x, y, and z axes.
• Four of the d orbitals appear as shapes with four lobes around the
nucleus; the fifth one, the orbital, is represented as two lobes
along the z axis and a “doughnut” in the xy plane.
Regions in which the wave function is zero are called nodes.
There is zero probability that the electron will be found at a node.
• In many-electron atoms, different subshells of the same electron
shell have different energies. For a given value of n, the energy
of the subshells increases as the value of l increases: ns<np<nd
<nf. Orbitals within the same subshell are degenerate, meaning
they have the same energy.
• Electrons have an intrinsic property called electron spin, which is
quantized. The spin magnetic quantum number, ms, can have two
possible values, +1/2 and -1/2, which can be envisioned as the two
directions of an electron spinning about an axis. The Pauli
exclusion principle states that no two electrons in an atom can
have the same values for n, l, ml, and ms. This principle places a
limit of two on the number of electrons that can occupy any one
atomic orbital. These two electrons differ in their value of ms.
• The drawing below shows part of the orbital diagram for
an element.
• (a) As drawn, the drawing is incorrect. Why?
• (b) How would you correct the drawing without changing
the number of electrons?
• (c) To which group in the periodic table does the element
• Calculate the wavelength of electromagnetic radiation given its
frequency or its frequency given its wavelength.
• Order the common kinds of radiation in the electromagnetic
spectrum according to their wavelengths or energy.
• Explain what photons are and be able to calculate their energies
given either their frequency or wavelength.
• Calculate the wavelength of a moving object.
• Relate the quantum numbers to the number and type of orbitals
and recognize the different orbital shapes.
• Draw an energy-level diagram for the orbitals in a manyelectron atom and describe how electrons populate the orbitals
in the ground state of an atom, using the Pauli exclusion
principle and Hund’s rule.
• Use the periodic table to write condensed electron
configurations and determine the number of unpaired electrons
in an atom.
c  
E  h
 1 
En    RH   2  (n  1, 2,3, 4 )
n 
 1
1 
E  E final  Einitial  RH  2  2   h 
n n 
f 
 i
1. State where in the periodic table these elements appear:
• (a) elements with the valence-shell electron configuration
• (b) elements that have three unpaired p electrons
• (c) an element whose valence electrons are 4s24p1
• (d) the d-block elements
• (a) Calculate the energy of a photon of electromagnetic radiation
whose frequency is 6.75×1012 s-1.
(b) Calculate the energy of a photon of radiation whose
wavelength is 322 nm.
• (c) What wavelength of radiation has photons of energy
• The visible emission lines observed by Balmer all involved nf
= 2.
• (a) Explain why only the lines with were observed in the
visible region of the electromagnetic spectrum.
• (b) Calculate the wavelengths of the first three lines in the
Balmer series—those for which ni = 3, 4, and 5—and identify
these lines in the emission spectrum of H atom
• Sketch the shape and orientation of the following types
of orbitals: (a) s, (b) pz, (c) dxy, (d)
, (e) d 2 .
d x2  y 2
• Write the condensed electron configurations for the following
atoms, using the appropriate noble-gas core abbreviations: (a)
Cs(55), (b) Ni(28), (c) Se(34), (d) Cd(48), (e) Pb(82), (f)
Cu(29), (g) Cr(24).
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