Unit 4 - Electrons in
Atoms
Background information:
• Early research focused on the nucleus
• How are the electrons arranged?
• Why weren’t the electrons pulled into the
nucleus?
• Why are there differences in chemical
behavior?
• Certain elements emitted light when heated in
a flame that could be related to the
arrangement of the electrons
Wave Nature of Light
• Electromagnetic radiation is a form of energy
that exhibits wavelike behavior as it travels
through space.
• Waves have three primary characteristics:
• Wavelength – distance between equivalent
points on a continuous wave (m or cm)
• Frequency – number of waves that pass a
point in a given second (s-1)
• Amplitude – height of the wave measured
form the origin to the top of a crest
- All electromagnetic waves travel at the same speed, but
they have different wavelengths and frequencies.
- This gives the waves different properties.
- Visible light is a small portion of the electromagnetic
spectrum.
- The electromagnetic spectrum encompasses all forms of
radiation.
- The energy of the radiation increases with increasing
frequency and the resultant decreasing wavelength.
Infrared image:
Ultraviolet light images:
X-ray images:
The three characteristics of electromagnetic
radiation are related to one another through
the equation:
c = λυ
speed of light = wavelength x frequency
𝑐𝑚
𝑠
= cm ● s-1
𝑐𝑚
𝑠
𝑚
8
10
𝑠
c = 3.00 x 1010
c = 3.00 x
Determine the wavelength, in cm, of a
microwave that has a frequency of 3.44 x
109 s-1.
Use the speed of light equation
c = λν
3.00 x 1010 = λ ∙ 3.44 x 109
λ=
3.00 𝑥 1010
3.44 𝑥 109
λ = .872 x 101 = 8.72 cm
Determine the frequency of green light. It
has a wavelength of 4.90 x 10-7 m.
Use the speed of light equation
c = λν
3.00 x 108 = ν ∙ 4.90 x 10-7
ν=
3.00 𝑥 108
14
=
6.12244898
x
10
4.90 𝑥 10−7
ν = 6.12 x 1014 s-1
Now solve the following examples on your
whiteboard:
• Calculate the wavelength
of the red light used in a
bar code reader that has
a frequency of
4.62 x 1014 s-1.
• A laser used to dazzle the
audience in a rock
concert emits a blue light
with a wavelength of
5.15 x 10-7 m. Calculate
the frequency of this light.
SOLUTIONS:
• Calculate the wavelength
of the red light used in a
bar code reader that has
a frequency of
4.62 x 1014 s-1.
c = λν
3.00 x 108 = λ ∙ 4.62 x 1014
λ=
3.00 𝑥 108
=
14
4.62 𝑥 10
6.493506494 x 10-7
λ = 6.49 x 10-7 m
• A laser used to dazzle the
audience in a rock
concert emits a blue light
with a wavelength of
5.15 x 10-7 m. Calculate
the frequency of this light.
c = λν
3.00 x 108 = ν ∙ 5.15 x 10-7
ν=
3.00 𝑥 108
=
−7
5.15 𝑥 10
5.825242718 x 1014
ν = 5.83 x 1014 s-1
PARTICLE NATURE OF LIGHT
• Considering light as a wave does not explain much of its
everyday behavior.
• It fails to describe some important aspects of light’s
interactions with matter.
• The wave model does not explain why heated objects
emit only certain frequencies of light at a given
temperature.
FLAME TEST:
It cannot explain why some metals emit electrons
when colored light of a specific frequency is shined
on them.
THE QUANTUM CONCEPT
• Remember that temperature is a measure of the average
kinetic energy a substance’s particles. As a metal gets
hotter, it possesses a greater amount of kinetic energy
and emits different colors of light.
• The colors correspond to different frequencies and
wavelengths.
• The wave model could not explain this.
Max Planck
• Max Planck studied this
phenomenon and it led
him to a startling
conclusion: matter can
gain or lose energy only
in small, specific amounts
called quanta.
• A quantum is the
minimum amount of
energy that can be
gained or lost by an atom.
Planck’s Equation:
• Planck developed a mathematical relationship between
the energy and frequency of emitted radiation:
E = hν
Energy = Planck’s constant ∙ frequency
Energy is measured in Joules (J)
The unit for frequency is s-1
h = 6.63 x 10-34 J ∙ s
Planck’s Equation – another version:
• Another version of Planck’s equation is:
E=
ℎ𝑐
λ
In this version we use wavelength (λ) and the speed
of light instead of frequency.
THE PHOTOELECTRIC EFFECT
• In the photoelectric effect,
electrons, called
photoelectrons, are
emitted from the surface
of a metal when light of a
certain frequency is
shined on the surface.
THE PHOTOELECTRIC EFFECT
• No matter how long it
shines, light with a
frequency below that
required will not cause
electrons to be ejected
from the surface of the
metal.
• Once the correct
frequency is reached,
even a dim light will
cause the electrons to be
ejected.
THE PHOTOELECTRIC EFFECT
• Einstein proposed that electromagnetic radiation has
both wave-like and particle-like properties.
• While a beam of light has many wave-like
characteristics, it can also be thought of as a stream of
tiny particles, or bundles of energy, that Einstein called
photons.
• A photon is a particle of electromagnetic radiation with
no mass that carries a quantum of energy.
• The energy of a photon is: E = hν
Examples:
• Determine the energy of
a photon from the violet
portion of the rainbow if it
has a frequency of
7.23 x 1014 s-1.
E = hν
• The wavelength of red
light from the heliumneon laser is
6.328 x 10-7 m.
Determine the energy of
this light.
E=
= (6.63 x 10-34) ∙ (7.23 x 1014)
= 4.79349 x 10-19
= 4.79 x 10-19 J
ℎ𝑐
λ
(6.63 𝑥 10−34 )(3.00 𝑥 108 )
=
(6.328 𝑥 10−7 )
= 3.1431732 x 10-19
= 3.143 x 10-19 J
Another example:
• Calculate the wavelength, in m, of a photon in the red
spectra line of lithium that has an energy of
2.96 x 10-19 J.
E=
ℎ𝑐
λ
2.96 x 10-19 =
λ=
6.63 𝑥 10−34 (3.00 𝑥 108)
λ
(6.63 𝑥 10−34 )(3.00 𝑥 108)
2.96 𝑥 10−19
λ = 6.71 x 10-7 m
Now solve the following examples on your
whiteboard:
• Calculate the frequency
of a photon in yellow light
whose energy is
3.37 x 10-19 J.
• A radio station broadcasts
on a frequency of 9.83 x
106 s-1 . Determine the
energy of the photons
traveling through the
atmosphere.
Atomic Emission Spectra
• The atomic emission spectra of an element is the set of
frequencies of the electromagnetic spectrum emitted by
atoms of the element.
• The element’s atomic emission spectrum consists of
several individual lines of color, not a continuous range
of colors as seen in the visible spectrum.
Atomic Emission Spectra
Atomic Emission Spectra
• Each element’s atomic emission spectrum is unique and
can be used to determine if that element is part of an
unknown compound.
• The fact that only certain colors appear in an element’s
atomic emission spectrum means that only certain
specific frequencies of light are emitted. Because those
emitted frequencies of light are related to specific energy
levels, it can be concluded that only photons having
specific energies are emitted.
Atomic Emission Spectra
• Scientists were still confused. They had not expected
line spectra. They had expected a continuous series of
colors and energies as excited electrons lost energy and
spiraled toward the nucleus. But, the electrons weren’t
doing this.
QUANTUM THEORY AND THE ATOM
The Bohr Model of the Atom
• Niels Bohr, a Danish physicist, attempted to explain why
the emission spectrum of the hydrogen atom was not
continuous.
Bohr Model of the Atom
• Bohr proposed, using Planck’s and Einstein’s concepts,
that the hydrogen atom has only certain allowable
energy states for its electron.
• He suggested that the single electron in a hydrogen
atom moves around the nucleus only in certain allowed
circular orbits.
• The smaller the electron’s orbit, the lower the atom’s
energy state. The higher the electron’s orbit, the higher
the atom’s energy state.
Bohr Model of the Atom
• Bohr assigned a quantum number, n, to each orbit. The
higher the value of “n”, the higher the corresponding
energy level.
Hydrogen’s Line Spectrum
• Bohr suggested that when hydrogen is in the ground
state, the lowest energy state, the electron is in the n = 1
orbit. In this state, the atom does not radiate energy.
• If energy is added (absorbed), the electron moves to a
higher energy orbit. The atom is now in an excited state.
• Since nature likes being in the lowest energy state
possible, the atom will return to the ground state. This
happens when the electron returns to the n = 1 orbit. In
the process a photon of energy is emitted.
Hydrogen’s Line Spectrum
• According to Bohr’s model, only certain atomic energies
are possible, therefore only certain frequencies of
electromagnetic radiation are emitted.
Hydrogen’s Line Spectrum
• Bohr’s model explained the hydrogen atom, but failed to
explain the emission spectrum of any other element.
• Bohr’s model did not fully account for the chemical
behavior of atoms.
• Also, unlike the models developed to this point, evidence
was mounting that the electrons do not move around the
nucleus in circular orbits.
THE QUANTUM MECHANICAL MODEL OF
THE ATOM: Electrons as Waves
• Louis De Broglie thought that Bohr’s quantized orbits
had characteristics similar to those of waves.
ELECTRONS AS WAVES
• His question: if waves can have particle-like behavior,
could the opposite also be true? Can particles like
electrons behave like waves?
ELECTRONS AS WAVES
• If an electron has a wavelike motion and it’s restricted to
a circular orbit of fixed radius, then the electron is
allowed only certain possible wavelengths, frequencies,
and energies.
ELECTRONS AS WAVES
• De Broglie proposed an equation that could be used to
calculate the wavelength of a particle:
λ=
ℎ
𝑚𝑣
λ is the wavelength
h = 6.63 x 10-34 J∙s
m = the mass of the particle
v = the velocity of the particle
Experiments that followed proved that electrons
and other moving particles do have wave
characteristics.
THE HEISENBERG UNCERTAINTY
PRINCIPLE
Werner Heisenberg developed a
mathematical system of matrices that
led to the modern version of quantum
mechanics. This led to the uncertainty
principle:
The more precisely the position of a
particle is determined, the less precisely its momentum
can be known, and vice versa.
SCHRODINGER WAVE EQUATION
S
Erwin Schrodinger through the use of
wave mechanics developed a wave
equation that treated hydrogen’s
electron as a wave.
SCHRODINGER WAVE EQUATION
• The wave equation is quite complex and each solution is
known as a wave function.
• The wave function is related to the probability of finding
the electron within a particular volume of space around
the nucleus.
• The wave function predicts a three-dimensional region
around the nucleus called an atomic orbital that
describes the electron’s probable location.
SCHRODINGER WAVE EQUATION
• The atomic orbital can be though of as a fuzzy cloud
where the density of the cloud at a given point can be
thought of as proportional to the probability of finding the
electron at that point.
HYDROGEN’S ATOMIC ORBITALS
• The boundary of an atomic orbital is fuzzy, so orbitals do
not have a defined size.
• Chemists draw an orbital’s surface to contain 90% of the
electron’s total probability distribution.
• Just as the Bohr model assigned a quantum number to
the electron’s orbit, the quantum mechanical model does
the same.
HYDROGEN’S ATOMIC ORBITALS
• The first is the
• principal quantum number (n)
• The principal quantum number indicates the relative
sizes and energies of the atomic orbitals. As “n”
increases, the orbital becomes larger; the electron
spends more time farther away from the nucleus; and
the atom’s energy level increases.
• Therefore, “n” specifies the atom’s major energy levels,
called the
• principal energy levels
LABELING ELECTRONS IN ATOMS
• In quantum theory each electron in an atom is assigned
a set of four quantum numbers.
• Three of the numbers act like coordinates to describe the
location while the fourth describes the electron’s
orientation in the orbital. The first is the
• principal quantum number (n)
• This number describes the energy level that the electron
occupies. It is assigned a positive integer, starting with
one:
• n= 1, 2, 3, 4, …
LABELING ELECTRONS IN ATOMS
• The larger the value of “n”, the further the electron is
from the nucleus and the more energy it will have.
• Quantum numbers are used to describe the shapes of
atomic orbitals.
• The second quantum number is the
• azimuthal or angular quantum number
• It is designated by the letter l
• “l” has numerical values ranging from:
• l = 0, 1, 2, 3, … n-1
LABELING ELECTRONS IN ATOMS
• While “l” does have numerical values, the shapes of the
orbitals are often described using letters:
l
letter
0
s
1
p
2
d
3
f
LABELING ELECTRONS IN ATOMS
• The lowest energy orbital is the “s” orbital. It is the
closest to the nucleus and shaped like a sphere:
There is an “s” orbital in each energy level.
LABELING ELECTRONS IN ATOMS
• The next higher orbital is the “p” orbital. There are three
“p” orbital orientations at each energy level above n = 1.
LABELING ELECTRONS IN ATOMS
• Orbitals designated “d” and “f” have more complex
shapes and even higher energy.
• The “d” orbitals exist at n = 3 and above.
LABELING ELECTRONS IN ATOMS
• The “f” orbitals exist at n = 4 and above
LABELING ELECTRONS IN ATOMS
LABELING ELECTRONS IN ATOMS
• A third quantum number, the magnetic quantum number,
is designated
• ml
• The value of ml tells one the electron’s position by
designating the spatial orientation of the orbital that the
electron occupies.
LABELING ELECTRONS IN ATOMS
• So while multiple electrons within an atom may have the
same values of “n” and “l”, they may not necessarily
have the same values of “ml”.
• These electrons are said to be in the same sublevel of
the atom.
LABELING ELECTRONS IN ATOMS
• The relationship between “l”, and “ml” is:
Value of l
Letter
designation
Range of ml
0
s
0
1
2
1
p
-1, 0, 1
3
6
2
d
-2, -1, 0, 1, 2
5
10
3
f
-3,-2,-1,0,1,2,3,
7
14
Number of Maximum
orientations number of
electrons
LABELING ELECTRONS IN ATOMS
• The fourth quantum number describes the motion of the
electron
• It is the spin quantum number
• ms
1
1
• “ms” has values of: + and 2
2
ELECTRON CONFIGURATION
• The arrangement of the electrons in an atom is called
the atom’s
• electron configuration
• Since low energy systems are more stable than high
energy systems, electrons tend to assume the
arrangement that gives them the lowest possible energy.
ELECTRON CONFIGURATION
• Three rules, or principles, define how electrons can be
arranged in the orbitals of an atom:
• Aufbau Principle
• Pauli Exclusion Principle
• Hund’s Rule
ELECTRON CONFIGURATION
• The Aufbau Principle states that each electron will
occupy the lowest energy orbital available.
• The Pauli Exclusion Principle states that a maximum of
two electrons may occupy a single atomic orbital; but
only if the electrons have opposite spins.
• Hund’s Rule states that single electrons with the same
spin must occupy each equal energy orbital before
additional electrons with opposite spins can occupy
those same orbitals.
ELECTRON CONFIGURATION
• As stated earlier, an electron configuration is the
arrangement of the electrons within an atom. This
diagram, known as the diagonal rule will help you
sequence the proper filling of the atomic orbitals.
ELECTRON CONFIGURATION
ELECTRON CONFIGURATION
• To write an electron configuration, follow these steps:
(1) Locate the element whose electron configuration
you wish to write.
(2) Fill in the orbitals in the proper order with
electrons. Use the diagonal rule.
(3) Check that the total number of electrons matches
the atomic number.
ELECTRON CONFIGURATION
• Write the electron configuration for nickel.
Ni = 28 electrons
1s22s22p63s23p64s23d8
or
1s22s22p63s23p63d84s2
ELECTRON CONFIGURATION
• You can also create your own guide from a blank
periodic table:
ELECTRON CONFIGURATION
• Add in the electron configuration information:
ELECTRON CONFIGURATION
• Fill in the details:
ELECTRON CONFIGURATION
• There is a shorthand method of writing electron
configurations known as the noble gas electron
configuration.
• By using the noble gas just before the element in
question and then adding the remaining electron
configuration, one can write an abbreviated form of the
electron configuration.
ELECTRON CONFIGURATION
• Write the noble gas electron configuration for silicon.
Si = 14 electrons
Write the preceding noble gas inside a set of
brackets:
[Ne]
Then, add the remaining electrons:
[Ne]3s23p2
ELECTRON CONFIGURATION
• On your white board write the complete electron
configuration for the following elements:
rhenium
arsenic
ELECTRON CONFIGURATION
• On your white board write the complete electron
configuration for the following elements:
rhenium
1s22s22p63s23p64s23d104p65s24d105p66s24f145d5
1s22s22p63s23p63d104s24p64d104f145s25p65d56s2
arsenic
1s22s22p63s23p64s23d104p6
1s22s22p63s23p63d104s24p6
ORBITAL DIAGRAMS
• Orbital diagrams are used to show how electrons are
distributed within sublevels and to show the direction of
spin.
• Each orbital is represented by either a box, circle, or line:
_______
The electrons are represented by arrows: ↑↓
The direction of spin is represented by the
direction of the arrow.
ORBITAL DIAGRAMS
• Construct the orbital diagram for oxygen
• The electron configuration for oxygen is:
• 1s22s22p4
• ↑↓ ↑↓ ↑↓ ↑ ↑
1s2 2s2 2p4
ORBITAL DIAGRAMS
• Electrons are arranged in accordance with Hund’s Rule.
This rule states that orbitals of equal energy are each
occupied by one electron before any pairing occurs by
adding a second electron.
• This way repulsion is minimized.
• All electrons in singly occupied orbitals must have the
same spin.
• When two electrons occupy the same orbital, they must
have opposite spins.
ORBITAL DIAGRAMS
• Construct an orbital diagram for aluminum
• The electron configuration for aluminum is:
• 1s22s22p63s23p1
↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ __ __
1s2 2s2
2p6
3s2
3p1
ORBITAL DIAGRAMS
• Construct an orbital diagram for iron.
• The electron configuration for iron is:
1s22s22p63s23p64s23d6
First write:
↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ ↑ ↑ ↑
1s2 2s2
2p6
3s2
3p6
4s2
3d5
Then add the last electron:
↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ ↑ ↑
1s2 2s2
2p6
3s2
3p6
4s2
3d6
ORBITAL DIAGRAMS
• On your whiteboard, construct the orbital diagram for
• Arsenic
• Vanadium