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The Electronic
Structure of Atoms
Electromagnetic Radiation
Early atomic scientists studied the
interaction of matter with electromagnetic radiation.
Electromagnetic radiation, or radiant energy,
includes visible light, infrared, micro and radio
waves, and X-rays and ultraviolet light.
Electromagnetic Radiation
Electromagnetic radiation travels in waves.
The waves of radiant energy have three
important characteristics:
1. Wavelength - λ - (lambda)
2. Frequency – ν – (nu)
3. Speed – c – the speed of light
Wavelength, λ, is the
distance between two
adjacent peaks or troughs
in a wave.
The units may range
from picometers to
kilometers depending
upon the energy of the
Frequency, ν, is
the number of waves
(or cycles) that pass a
given point in space
per second.
The units are
cycles/s, s-1 or hertz
The Speed of Light
All electromagnetic radiation travels at the
same speed. The speed of light ( c ) is:
c = 2.9979 x 108 m/s
Wavelength and Frequency
Wavelength and
frequency are
inversely related.
That is, waves with a
low frequency have a
long wavelength.
Waves with a high
frequency have short
Properties of Light - Amplitude
Waves of electromagnetic radiation are bent
or diffracted with they a passed through an
obstacle or a slit with a size comparable to their
Electromagnetic Radiation
The relationship between wavelength and
frequency is:
λν= c
Matter and Energy
By 1900, physicists thought that the nature
of energy and matter was well understood and
Matter, a collection of particles, have mass
and a defined position in space. Radiant energy,
as waves, is massless and delocalized.
It was also believed that particles of matter
could absorb or emit any energy, without
Planck & Black Body Radiation
Max Planck (1858-1947) studied the
radiation emitted by objects heated until they
glowed. He found that the energy emitted was
not continuous, but instead was released in
multiples of hν.
∆E = nhν
where n=integer
ν = frequency
h = 6.626 x 10-34 J-s (Planck’s constant)
Planck & Black Body Radiation
∆E = nhν
Planck’s work showed that when matter and
energy interact, the energy is quantized, and can
occur only in discrete units or bundles with
energy of hν. Each packet or bundle of energy is
called a quantum. A fraction of a quantum is
never emitted.
Einstein – Photoelectric Effect
Albert Einstein (1879-1955) won a Nobel
Prize for his explanation of the photoelectric effect.
When light of sufficient energy strikes the
surface of a metal, electrons are emitted from
the metal surface. Each metal has a
characteristic minimum frequency, νo , called the
threshold frequency, needed for electrons to be
The Photoelectric Effect
1. No electrons are emitted if the frequency of
light used is less than νo, regardless of the
intensity of the light.
2. For light with a frequency≥ νo , electrons are
emitted. The number of electrons increases
with the intensity of the light.
3. For light with a frequency > νo , the electrons
are emitted with greater kinetic energy.
Einstein proposed that light is quantized,
consisting of a stream of “particles” called
If the photon has sufficient energy, it can
“knock off” an electron from the metal surface.
If the energy of the photon is greater than that
needed to eject an electron, the excess energy is
transferred to the electron as kinetic energy.
The Photoelectric Effect
Ephoton= hν = hc/λ
If incident radiation with a frequency νi is used:
KEelectron = hνi -hνo = ½ mv2
The kinetic energy of the electron equals the
energy of the incident radiation less the
minimum energy needed to eject an electron.
Particle-Wave Duality
Einstein’s work suggested that the incident
photon behaved like a particle. If it “hits” the
metal surface with sufficient energy (hνi), the
excess energy of the photon is transferred to the
ejected electron.
In the atomic scale, waves of radiant energy
have particle-like properties.
Particle-Wave Duality
Einstein also combined his equations:
Ephoton= hc/λ
to obtain:
m= 2 = c2
m= λc
Particle-Wave Duality
The apparent mass of radiant energy can be
calculated. Although a wave lacks any mass at
rest, at times, it behaves as if it has mass.
Einstein’s equation was confirmed by
experiments done by Arthur Compton in 1922.
Collisions between X-rays and electrons
confirmed the “mass” of the radiation.
Louis de Broglie
Einstein showed that waves can behave like
particles. In 1923, Louis de Broglie (1892-1987)
proposed that moving electrons have wave-like
Louis de Broglie
Using Einstein’s equation:
where v is the velocity of the particle,
de Broglie rearranged the equation to calculate
the wavelength associated with any moving
Louis de Broglie
de Broglie’s equation was tested using a
stream of electrons directed at a crystal. A
diffraction pattern, due to the interaction of
waves, resulted. The experiment showed that
electrons have wave-like properties.
Wave-Like Nature of the Electron
Particle-Wave Duality
It is important to note that the wavelike
properties of moving particles are insignificant
in our everyday world. A moving object such as
a car or a tennis ball has an incredibly small
wavelength associated with it.
It is on the atomic scale that the dual nature
of particles and light become significant.
Emission Spectrum of Hydrogen
When atoms are
given extra energy,
or excited, they give
off the excess
energy as light as
they return to their
original energy, or
ground state.
Emission Spectrum of Hydrogen
Scientists expected atoms to be able to
absorb and emit a continuous range of energies,
so that a continuous spectrum of wavelengths
would be emitted.
Emission Spectrum of Hydrogen
A continuous spectrum in the visible range,
would look like a rainbow, with all colors visible.
Instead, hydrogen, and other excited atoms emit
only specific wavelengths of light as they return
to the ground state. A line spectrum results.
Emission Spectrum of Hydrogen
Emission Spectrum of Hydrogen
Instead, only a few wavelengths of light are emitted,
creating a line spectrum. The spectrum of hydrogen
contains four very sharp lines in the visible range.
Emission Spectrum of Hydrogen
The discrete lines in the spectrum indicate that
the energy of the atom is quantized. Only
specific energies exist in the excited atom, so
only specific wavelengths of radiation are
The Bohr Atomic Model
In 1913, Niels Bohr (1885-1962) proposed
that the electron of hydrogen circles the nucleus
in allowed orbits.
That is, the electron is in its ground state in
an orbit closest to the nucleus. As the atom
becomes excited, the electron is promoted to an
orbit further away from the nucleus.
The Bohr Atomic Model
Classical physics
dictates that an electron
in a circular orbit must
constantly lose energy
and emit radiation.
Bohr proposed a
quantum model, as the
spectrum showed that
only certain energies are
absorbed or emitted.
The Bohr Atomic Model
Bohr’s model of the hydrogen atom was
consistent with the emission spectrum, and
explained the distinct lines observed.
The Bohr Atomic Model
The Bohr Atomic Model
Bohr also developed an equation, using the
spectrum of hydrogen, that calculates the energy
levels an electron may have in the hydrogen
E=-2.178 x 10-18J(Z2/n2)
Where Z = atomic number
n = an integer
The Bohr Atomic Model
The Bohr model didn’t work for atoms other
than hydrogen. Though limited, Bohr’s
approach did attempt to explain the quantized
energy levels of electrons.
Later developments showed that any attempt
to define the path of the electron is incorrect.
The Quantum Mechanical Model
The quantum mechanical atomic model was
developed based on the theories of Werner
Heisenberg (1901-1976), Louis de Broglie (18921987) and Erwin Schrödinger (1887-1961).
They focused on the wave-like nature of the
moving electron.
The Quantum Mechanical Model
The electron in an
atom was viewed as a
standing wave. For an
energy level to exist,
the wave must
reinforce itself via
constructive interference.
The Quantum Mechanical Model
Schrödinger developed complex equations
called wave functions ( Ψ). The wave functions
can be used to calculate the energy of electrons,
not only in hydrogen, but in other atoms.
The Quantum Mechanical Model
The wave functions also describe
various volumes or spaces where electrons
of a specific energy are likely to be found.
These spaces are called orbitals.
The Quantum Mechanical Model
Orbitals are not orbits.
The wave functions provide no information
about the path of the electron. Instead, it
provides the space in which there is a high
probability (90%) of finding an electron with a
specific energy.
The Heisenberg Uncertainty
Werner Heisenberg showed that, due to the
wave nature of the electron,
It is impossible to know both the precise position and the
momentum of the electron at the same time.
This is known as the Heisenberg Uncertainty
The Heisenberg Uncertainty
It is impossible to know both the precise position and
the momentum of the electron at the same time.
In mathematical terms, the principle is:
(Δx) (Δmv) ≥ (h/4π)
The Heisenberg Uncertainty
It is impossible to know both the precise position and
the momentum of the electron at the same time.
The Heisenberg Uncertainty
(Δx) (Δmv) ≥ (h/4π)
There is a limit to how well we can
determine position (x), if mass and velocity are
known precisely.
For large particles, the uncertainty is
insignificant. However, on the atomic scale, we
cannot know the exact motion of an electron.
The Heisenberg Uncertainty
(Δx) (Δmv) ≥ (h/4π)
For an electron in a hydrogen atom, the
uncertainty in the position of the electron is
similar in size to the entire hydrogen atom.
Thus the location of the electron cannot be
The Schrödinger equation is used to describe
the space in which it is likely to find an electron
with a specific energy.
The equation provides us with a probability
distribution, or an electron density map. It is
important to remember that the resulting shape
does not give us any information about the path
of the electrons.
The orbital of lowest
energy is the 1s orbital.
The probability
distribution shows
electron density in all
directions, creating a
spherical shape.
The first energy level of hydrogen (n=1)
consists of a 1s orbital.
The second energy level of hydrogen (n=2)
consists of a 2s orbital and 2p orbitals.
The third energy level of hydrogen (n=3)
consists of a 3s orbital, 3p orbitals, and 3d
As the value of n
increases, the orbitals,
on average, become
larger, with more
electron density
farther from the
The “white rings”
in the drawings are
nodes. This is the
region where the
wave function goes
from a positive value
to a negative value.
p orbitals are “dumbbell” shaped, with two
lobes. In one lobe, the wave function is
positive, in the other lobe, it is negative.
p orbitals come in sets of three, called a subshell.
The three orbitals are designated as px, py and pz,
because the electron density lies primarily along
either the x, y or z axis.
All three orbitals have the exact same energy.
Orbitals with the same energy are called
n=3 level
contains s,
p and d
The d
orbitals are
The n=4
level contains
s, p, d and f
orbitals. The f
orbitals are
Quantum Numbers
In addition to n, the principal quantum
number, there are three additional quantum
numbers which describe the type of orbital ( l
) , the spatial orientation of the orbital (ml ) ,
and the spin of the electron (ms ) .
Energy Levels
In any atom or ion
with only 1 electron,
the principal quantum
number, n,
determines the energy
of the electron. For
n=2, the 2s and 2p
orbitals all have the
same energy.
Energy Levels
Likewise, the 3s,
3p and 3d orbitals are
all degenerate, with
the same energy.
Energy Levels
In a multi-electron atom, there is interaction
between electrons. As a result of this
interaction, the various subshells of a principal
quantum level will vary in energy.
Energy Levels
Energy Levels
Energy Levels
The energy
diagram for the first
three quantum levels
shows the splitting
of energies.
Energy Levels
For a given value
of n, the energies of
the subshells is as
Energy Levels
The subshells
have different
energies due to the
penetrating ability for
each type of orbital.
Electrons in a 2s
orbital can get nearer
to the nucleus than
those in a 2p orbital.
Energy Levels
The electrons in
the 3s orbital (top
diagram) have higher
probability to be
found near the
nucleus, and thus
greater penetrating
ability than those in
3p or 3d orbitals.
Multi-electron Atoms
Orbitals of any
type can be empty, or
have 1 or two
Experimental data
indicate that if two
electrons are in the
same orbital, they will
spin in opposite
Multi-electron Atoms
Electron configurations are a way of noting
which subshells of an atom contain electrons.
Although much of the periodic table was
developed before the concept of electron
configurations, it turns out that the position of
an element on the periodic table is directly
related to its electron configuration.
Multi-electron Atoms
Magnetic Properties of Atoms
Rotating electrons create a magnetic field. If
electrons are unpaired, the atom will be attracted
to a magnetic field and be paramagnetic.
If all of the electrons in an atom are paired, the
atom will be weakly repelled by a magnetic field,
and be diamagnetic.
Magnetic Properties of Atoms
Hund’s Rule states that electrons will occupy
degenerate orbitals singly with parallel spins.
The Pauli Exclusion Principle states that two
electrons occupying the same orbital will have
opposite spins.
Representation of Orbitals
Orbitals are usually represented by a horizontal
line, with the electrons appearing as arrows.
Arrows up and down indicate electrons of
opposite spins.
Multi-electron Atoms
The electron configuration for N is: 1s22s22p3
N atoms have 3 unpaired electrons: __ __ __
Multi-electron Atoms
The electron configurations for Cr and Cu differ
from that expected based on their positions in
the periodic table.
Cr and Cu
The electron configuration for Cr is:
[Ar] 4s13d5 with 6 unpaired electrons
The electron configuration for Cu is:
[Ar] 4s13d10 with the unpaired electron in the 4s
Valence Electrons
The electrons in the highest occupied
quantum level are called valence electrons. These
are the electrons that are involved in bonding.
Elements in the same family or group all
have the same number of valence electrons and
thus exhibit similar chemical behavior.
Valence Electrons
All of the group IA elements have a single
valence electron (ns1). Group IIA elements
have two valence electrons, etc. The noble gases
all have eight valence electrons(ns2np6).
When the main group elements form ions,
they usually lose or gain enough electrons to
attain the same electron configuration as a noble
Periodic Trends
Many of the properties of atoms show clear
trends in going across a period (from left to
right) or down a group.
In going across a period, each atom gains a
proton in the nucleus as well as a valence
Periodic Trends
The increase of positive charge in the
nucleus isn’t completely cancelled out by the
addition of the electron.
Electrons added to the valence shell don’t
shield each other very much. As a result, in
going across a period, the effective nuclear charge
(Zeff) increases.
Effective Nuclear Charge
The effective nuclear charge (Zeff) equals the
atomic number (Z) minus the shielding factor
Zeff= Z-σ
Effective Nuclear Charge
Zeff= Z-σ
Effective Nuclear Charge
Electrons in the
valence shell are
partially shielded
from the nucleus by
core electrons.
Effective Nuclear Charge
Electrons in p or d
orbitals don’t get too
close to the nucleus, so
they are less shielding
than electrons in s
orbitals. As a result,
effective nuclear charge
increases across a period.
Periodic Trends
In going down a group or family, a full
quantum level of electrons, along with an equal
number of protons, is added.
As n increases, the valence electrons are, on
average, farther from the nucleus, and
experience less nuclear pull due to the shielding
by the “core” electrons. As a result, Zeff
decreases slightly going down a group.
Periodic Trends
Trends- Atomic Radii
Atomic radii are obtained in a variety of ways:
1. For metallic elements, the radius is half the
internuclear distance in the crystal, which is
obtained from X-ray data.
2. For diatomic molecules, the radius is half the
bond length.
3. For other elements, estimates of the radii are
Trends- Atomic Radii
Atomic radii follow trends directly related to
the effective nuclear charge. As Zeff increases
across a period, the electrons are pulled closer to
the nucleus, and atomic radii decrease.
As Zeff decreases down a group, the valence
electrons experience less nuclear attraction, and
the radius increases.
TrendsAtomic Radii
Atomic size roughly
halves across a
period, and doubles
going down a group.