Electrons in Atoms
Chapter 5
Chapter Big Idea
• The atoms of each element have a unique
arrangement of electrons.
Section 1: Light and
Quantized Energy
Essential Questions & Vocabulary
• How do the wave and particle natures of light compare?
• What is a quantum of energy and how is it related to an
energy change of matter?
• How do continuous electromagnetic spectra and atomic
emission spectra compare and contrast?
Vocabulary
Electromagnetic Radiation
Wavelength
Frequency
Amplitude
Electromagnetic Spectrum
Quantum
Planck’s constant
Photoelectric effect
Photon
Atomic emission spectrum
Unanswered Questions
• In Rutherford’s model,
the atom’s mass is
concentrated in the
nucleus and electrons
move around it.
Unanswered Questions
• This model doesn’t explain how the electrons
were arranged around the nucleus.
• This model also doesn’t explain why negatively
charged electrons aren’t pulled into the positively
charged nucleus.
The Wave Nature of Light
• In the early 1900s, scientists observed that certain
elements emitted visible light when heated in a
flame.
• Analysis of this light revealed that an element’s
chemical behavior is related to the arrangement of
the electrons in its atoms.
The Wave Nature of Light
• Visible light is a type of electromagnetic radiation.
• Electromagnetic radiation: a form of energy that
exhibits wave-like behavior as it travels through space.
• Light is a type of energy that travels through space
at a constant speed of 3.0 × 108 m/s (186,000 mi/s).
The Wave Nature of Light
• The electromagnetic spectrum
includes all forms of electromagnetic
radiation:
The Wave Nature of Light
• All waves can be described by several
characteristics:
• The wavelength (λ) is the shortest distance between
adjacent wave crests.
The Wave Nature of Light
• The frequency (v) is the number of waves
that pass a given point per second.
• Wavelength and frequency are inversely
related—the shorter the wavelength, the
higher the frequency.
The Wave Nature of Light
• The amplitude of a wave is the wave’s height
from the origin to the crest, or from the origin to
a trough.
• Wavelength and frequency DO NOT affect the
amplitude of a wave.
The Wave Nature of Light
• The amplitude is the wave’s height from the origin
to a crest.
Wavelength & Frequency
c = 3.0 x 108 m/s
Speed of ALL light waves
λ = wavelength
Measured in meters
If nm, multiply by 10-9
𝒄 = 𝝀𝝂
ν = frequency
Measured in hertz (Hz)
or inverse seconds (s-1)
The Particle Nature of Light
• The wave model of light CANNOT explain
all of light’s characteristics.
• Example: Why heated objects emit only
certain frequencies of light at a given
temperature.
The Particle Nature of Light
• In 1900, German physicist Max Planck (1858-1947)
began searching for an explanation by studying the
light emitted by heated objects.
The Particle Nature of Light
• Planck’s study 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.
The Particle Nature of Light
The Particle Nature of Light
• Prior belief is that energy
could be absorbed and
emitted in continually varying
quantities
•
•
Heating Water: The water’s
temperature increases by
infinitesimal steps as its
molecules absorb quanta of
energy
Because the steps are so small,
the temperature seems to rise in
continuous rather than a
stepwise manner.
The Particle Nature of Light
• The energy of a quantum is given by the product of
Planck’s constant and the frequency.
𝒉 = 𝟔. 𝟔𝟐𝟔𝒙𝟏𝟎−𝟑𝟒 𝑱 · 𝒔
• According to Planck’s theory, for a given frequency,
v, matter can emit or absorb energy only in whole
number multiples of hv
The Particle Nature of Light
• The photoelectric effect is when electrons are
emitted from a metal’s surface when light of a
certain frequency shines on it.
The Dual Nature of Light
• In 1905, Albert Einstein proposed that light
has a dual nature
• A beam of light has wavelike and particlelike
properties.
• A photon is a particle of electromagnetic
radiation with no mass that carries a quantum of
energy.
𝒉 = 𝟔. 𝟔𝟐𝟔𝒙𝟏𝟎−𝟑𝟒 𝑱 · 𝒔
The Dual Nature of Light
• A photon of red light (relatively long wavelength) carries
less energy than a photon of blue light (relatively short
wavelength) does.
The Dual Nature of Light
• Every object gets its color by reflecting a certain portion of
incident light. The color is determined by the wavelength of
the reflected photons, thus by their energy. What is the
energy of a photon from the violet portion of the Sun’s light if
it has a frequency of 7.230 x 10 -14 Hz?
h = 6.626 x 10-34 𝐽 · 𝑠
𝝂 = 𝟕. 𝟐𝟑𝟎 × 𝟏𝟎−𝟏𝟒 𝑯𝒛
E= ? J
𝑬 = 𝒉𝝂
E = 6.626 × 10−34 𝐽 ∙ 𝑠 × 7.230 𝑥10−14 𝐻𝑧
𝑬 = 4.79 x 10-47 J
Atomic Emission Spectra
• The atomic emission spectrum of an element is the
set of frequencies of the electromagnetic waves
emitted by the electrons as they come back down
to the ground state.
• The energy of the photon being released corresponds to
different wavelengths of light. A higher energy photon
might be blue in color while a lower energy photon might
be red in color.
Atomic Emission Spectra
• Light in a neon sign is produced
when electricity is passed through a
tube filled with neon gas.
•
The neon atoms become excited.
•
The excited atoms return to their stable
state by emitting light to release
energy.
Atomic Emission Spectra
• A white-light spectrum is continuous, with
some radiation emitted at every
wavelength.
• The emission spectrum of an individual
element includes only certain specific
wavelengths.
Atomic Emission Spectra
• Each element’s atomic emission spectrum
is unique.
Section 2: Quantum
Theory and the Atom
Essential Questions & Vocabulary
•
•
•
How do the Bohr and quantum mechanical models of the atom
compare?
What is the impact of de Broglie’s wave-particle duality and the
Heisenberg uncertainty principle on the current view of electrons
in atoms?
What are the relationships among a hydrogen atom’s energy
levels, sublevels, and atomic orbitals?
Vocabulary
Ground state
Atomic orbital
Quantum number
Principal quantum number
De Broglie Equation
Principal energy level
Heisenberg uncertainty principle
Energy sublevel
Quantum mechanical model of the atom
Unanswered Questions
• Einstein’s theory of light’s dual nature accounted
for several unexplainable phenomena by not why
atomic emission spectra of elements were
discontinuous rather than continuous.
Bohr’s Model of the Atom
• In 1913, Neils Bohr, a Danish physicist working in
Rutherford’s laboratory, proposed a quantum model
for the hydrogen atom that seemed to answer this
question.
• Bohr correctly predicted the frequency lines in
hydrogen’s atomic emission spectrum.
Bohr’s Model of the Atom
• Bohr suggested that an electron moves around
the nucleus only in certain allowed circular orbits.
Bohr’s Model of the Atom
• Ground state: the lowest allowable energy state of
an atom
• Excited State: an atom that has gained energy
Bohr’s Model of the Atom
• Each orbit was given a number, called the quantum
number.
• Hydrogen’s single electron in the n=1 orbit in the
ground state.
• When energy is added, the electron moves to the n=2
orbit.
Bohr’s Model of the Atom
• Ground State: first energy level
•
Atom does NOT radiate energy.
• When external energy is added, the electron moves to a higherenergy orbit (excited state)
•
•
The electron eventually drops from the higher energy orbit to a lowerenergy orbit.
Emits a photon corresponding to the energy difference between the two
energy levels
Balmer Series
Limits of Bohr’s Model
• It explained hydrogen’s spectral lines but failed to
explain any other element’s spectral lines.
• Bohr’s model did not fully account for chemical
behavior of atoms
• Behavior of electrons is still not fully understood
but evidence indicates they do not move around
the nucleus in circular orbits
De Broglie (1892-1987)
If waves can have
particlelike
behavior, could the
opposite also be
true?
Quantum Mechanical Model
• Louis de Broglie hypothesized that particles, including
electrons, could also have wavelike behaviors.
• Electrons orbit the nucleus only in whole-number
wavelengths.
Quantum Mechanical Model
• The de Broglie Equation predicts that all moving
particles have wave characteristics.
• Impossible to notice the wavelength of a fast
moving car but it can for an electron moving at
the same speed.
Werner Heisenberg (1901 – 1976)
• Balloon in Dark Room
• It is impossible to take any
measurement of an object without
disturbing the object.
• Heisenberg Uncertainty principle
states that it is fundamentally
impossible to know precisely both the
velocity and position of a particle at
the same time.
Quantum Mechanical Model
• When a photon interacts with an electron, both the
velocity and the position of the electron are modified.
• The only quantity that can be known is the probability for
an electron to occupy a certain region around the nucleus.
Erwin Schrodinger (1897 – 1961)
• Furthered the wave-particle theory by deriving an
equation that treated the hydrogen’s electron as a
wave.
• Unlike Bohr, Schrodinger’s equation also applied
to other elements.
• Quantum Mechanical model of the atom –
model in which electrons are treated as waves.
• Does NOT attempt to describe electron’s
path; simply describes the PROBABILITY of
finding an electron.
Atomic Orbitals
• A three-dimensional area around the nucleus which
describes the electron’s probable location.
• Each dot represents the electron’s location at an
instant in time.
• The high density of dots near the nucleus indicates the
electron’s most probable location.
Atomic Orbitals
• Principal Quantum Number – (n) indicates the
relative size and energy of atomic orbitals
• As n increase, the orbital size and energy increase and
electron spends more time away from the nucleus
• Principal Energy Level – (n) specifies the atom’s
major energy levels
• Energy Sublevels are contained within the
principal energy levels.
Orbital Shapes
• Each energy sublevel relates to orbitals of different shapes
•
s (1), p (3), d (5) , or f (7)
• Each orbital can contain, at most, 2 electrons
Principal Energy Levels
Total
Number of
electrons
by sublevel
Total Number
of Electrons in
Principal
Energy Level
(2n2)
Principal
Quantum
Number
(n)
Sublevels
(Types of
Orbitals)
Number of
Orbitals
related to
sublevel
Total number
of Orbitals
related to
Principal Level
(n2)
1
s
1
1
2
2
2
s
p
1
3
4
2
6
8
3
s
p
d
1
3
5
9
2
6
10
18
4
s
p
d
F
1
3
5
7
16
2
6
10
14
32
Section 3: Electron
Configuration
Essential Questions & Vocabulary
• How are the Pauli exclusion principle, the aufbau
principle, and Hund’s rule used to write electron
configurations using orbital diagrams and electron
configuration notation?
• What are valence electrons, and how do electron-dot
structures represent an atom’s valence electrons?
Vocabulary
Electron configuration
Hund’s Rule
Aufbau principle
Valence electron
Pauli exclusion principle
Electron-dot structure
Ground-State Electron
Configuration
• Electron Configuration – the arrangement of
electrons in an atom.
• Low-energy systems are more stable than highenergy systems
• Electrons in an atom tend to arrange in a manner
that gives the atom the LOWEST energy
possible.
aufbau Principle
• German roots meaning “to build up” or “arrange”
• Each electron occupies the lowest energy orbital
available
Aufbau Diagrams
• Describes the sequence in which orbitals are filled
with electrons, however, atoms are NOT built up
electron by electron
Pauli Exclusion Principle
• A maximum of two electrons can occupy a single
atomic orbital, but only if the electrons have
opposite spins.
Hund’s Rule
• Single electrons with the SAME spin must occupy each
equal-energy orbital before additional electrons with
opposite spins can occupy the same orbitals.
• Remember: orbitals within the same sublevel have the same
energy.
Electron Configuration: Neon
Orbital
Diagram
Electron Configuration
Notation
• Designates the principal energy level and energy
sublevel associated with each of the atom’s orbitals
and includes a superscript representing the number of
electrons in the orbital.
Electron Configuration
Noble-Gas Notation
• A shorthand method that uses bracketed symbols
around the noble gas symbol that appears last
before the element of interest.