Chapter 5
Electrons in Atoms
I. Wave Nature of Light
• In the early 1900s, scientists observed certain
elements emitting visible light when heated
• Study of the emitted light revealed that an
element’s chemical behavior is related to the
arrangement of its electrons
• Electromagnetic radiation is a form of energy
that exhibits wavelike behaviors as it travels
through space
Increased Energy
• Waves have several primary characteristics
1. Wavelength (λ, lambda)
• Shortest distance between equivalent
points on a continuous wave
2. Frequency (ν, nu)
• Number of waves that pass a given point
per second
• One hertz (Hz) is the SI unit for frequency
- one hertz equals one wave per second
652 Hz = 652 waves/second = 652/s = 652s-1
High Frequency
Low Frequency
• Wavelength and frequency are inversely
related
- as one quantity increases, the other
decreases
• All electromagnetic waves travel at a speed of
3.00x108 m/s
• Although waves may travel at the same speed,
they may have different wavelengths and
frequencies
• The speed of light, c, is the product of
wavelength and frequency
C = λν
3. Amplitude
• The wave’s height from the origin to a crest,
or from the origin to a trough
• Visible light contains a continuous range of
wavelengths and frequencies that separates
into a spectrum of colors
• The visible light spectrum is only a small
portion of the complete electromagnetic
spectrum
Increased Energy
• The electromagnetic spectrum encompasses
all forms of electromagnetic radiation
• Each type of radiation has its own wavelength
and frequency
• Energy increases with increasing frequency
Increased Energy
II. Particle Nature of Light
A. The Quantum Concept
• Some objects emit certain frequencies of
light (radiation) at a given temperature
• Different colors correspond to different
frequencies and wavelengths
• Max Planck concluded that matter can gain or
lose energy only in small, specific amounts
called quanta
• Planck proposed that objects emit light energy
in a quantized, or steplike, manner
• This energy of a quantum is related to
frequency of emitted radiation by the
equation
Equantum = hν
Equantum = quantum energy
H = Planck’s constant = 6.626x10-34J·s
ν = frequency of emitted radiation
• This explains why energy increases with
increasing frequency
Increased Energy
B. The photoelectric effect
• Some metals emit electrons when colored
light of a specific frequency shines on them
- this is called the photoelectric effect
• Metals will not eject photoelectrons when
the colored light has too low of a
frequency
• Albert Einstein proposed that electromagnetic
radiation has both wavelike and particlelike
characteristics
- a beam of light can be thought of as a
stream of tiny particles, called photons
• A photon has no mass but carries a quantum
of energy
• A photon’s energy also depends on its
frequency
Ephoton = hν
• In order for the photoelectric effect to occur a
photon must possess, at a minimum, the
energy required to free an electron from an
atom
Photon
III. Atomic Emission Spectra
• The set of frequencies of the
electromagnetic waves emitted by atoms of
an element
• An element’s atomic emission spectrum
consists of several individual lines of color,
not a continuous range of colors as seen in
the visible spectrum
Hydrogen
Helium
Mercury
Uranium
• Atoms absorb energy and become excited and
release energy by emitting light
• The fact that only certain colors appear in an
element’s atomic emission spectrum means
that only certain frequencies of light (or
energy) are emitted
IV. Bohr Model of the Atom
A. Energy states of hydrogen
• Niels Bohr studied why hydrogen’s
atomic emission spectra is discontinuous
• When an atom gains energy, it is said to
be in an excited state
• Although hydrogen has only one
electron, it is capable of having many
different excited states
• The lowest allowable energy state of an atom
is called its ground state
• Bohr related these energy states to the
motion of the electron within the atom
• He suggested that electrons move around the
nucleus in certain circular orbits
Ground State
• The smaller the electrons orbit,
the lower the atom’s energy
state
• The larger the electrons orbit,
the higher the atoms energy
state
• Bohr assigned a quantum
number, n, to each orbit
• The orbits, or energy levels, are
not evenly spaced
B. An explanation of hydrogen’s
line spectra
• The hydrogen atom is in
the ground state when its
electron is in the n=1 orbit
• When energy is added,
the electron “raises” to an
excited state and moves to
the n=2 orbit
• At an excited state the
electron can drop to a
lower-energy state
• When an electron transitions to a lower
energy-state the atom emits a photon
corresponding to the difference between the
energy associated with the two orbits
ΔE = Ehigher-energy orbit – Elower-energy orbit
ΔE = Ephoton
Ephoton = hν
• Transitions from
higher-energy orbits
to the second orbit
(n=2) account for all
of hydrogen’s visible
lines
- the series of visible
lines is called the
Balmer series
• Transitions from
higher-energy orbits
to the ground state
(n=1) account for
hydrogen’s ultraviolet
series, or Lyman
series
• Transitions from
higher-energy orbits
to the third orbit
(n=3) account for
hydrogen’s infrared
series, or Pashen
series
V. The Quantum Mechanical Model of the Atom
A. Electrons as waves
• Louis de Broglie thought that Bohr’s
quantized electron orbits had
characteristics similar to waves
• Einstein had proposed waves have
particlelike behavior
• de Broglie thought the opposite to be
true that particles, including electrons,
have wavelike behavior
• From Bohr’s model, de Broglie knew that an
electron is restricted to circular orbits of fixed
radius
• For an electron to also have wave-like motion,
it is only allowed certain wavelengths,
frequencies, and energies
VI. The Heisenberg Uncertainty Principle
• It is fundamentally impossible to know
precisely both the velocity and position of a
particle at the same time
• It is impossible to make any measurement
on an object without disturbing it at least a
little
A. Hydrogen’s Atomic Orbitals
• The boundary of an atomic orbital is
unclear
• Chemists arbitrarily draw an orbitals
surface to contain 90% of the electron’s
total probability distribution
B. The Schrӧdinger wave equation
• The quantum mechanical model of the
atom proposed by Erwin Schrӧdinger is a
model in which electrons are treated as
waves
• Applies equally well to atoms of other
elements
-Bohr’s model only applied to Hydrogen
• Limits an electron’s energy to certain values
but does not attempt to describe the
electron’s path around the nucleus
• A three-dimensional region around the
nucleus called the atomic orbital describes the
electron’s probably location
• Each orbital, or energy level, contains energy
sublevels
1. n = 1
sublevels = s
2. n = 2
sublevels = s and p
3. n = 3
sublevels = s, p, and d
4. n = 4
sublevels = s, p, d, and f
• S sublevel
- spherical
• P sublevel
- dumbbell shaped
- 3 orbitals of equal energy
2px, 2py, and 2pz
• D sublevel
- 5 orbitals of equal energy
dxy, dxz, dyz, dx2-y2, dz2
• 4 have identical shapes but different
orientations
• Fifth orbital shaped and oriented differently
• F sublevel
- 7 orbitals of equal energy
• Each orbital contains at most 2 electrons
VII. Ground-State Electron Configurations
• The arrangement of electrons in an atom is
called the atom’s electron configuration
• Most electrons assume the arrangement
that gives the atom the lowest possible
energy, or the ground-state configuration
A. The aufbau principle
• States that each electron occupies the lowest
energy orbital available
• The aufbau diagram shows the sequence of
atomic orbitals from lowest energy to highest
energy
1. All orbitals related to an energy sublevel are
of equal energy
2. In a multi-electron atom, the energy sublevels
within a principal energy level have different
energies
3. In order of increasing energy, the sequence of
energy sublevels within a principal energy
level is s, p, d, and f
4. Orbitals related to energy sublevels within
one principal energy level can have higher
energy than orbitals related to energy
sublevels within a higher principal level
ex. 3d sublevel has more energy than 4s
sublevel
B. The Pauli exclusion principle
• Each electron in an atom has an associated
spin
• Electrons are only able to spin in one of two
directions ↑ or ↓
• 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
VIII. Orbital Diagrams and Electron Configuration
Notations
A. Orbital Diagram
• A box represents each of the atom’s
orbitals
• Each box is labeled with the principal
quantum number and sublevel
associated with the orbital
↑↓ ↑↓ ↑↓
Pz
Px
Py
B. Electron Configuration Notation
• Designates the principal energy level (1,2,3)
and energy sublevel (s,p,d,f)
• A superscript represents the number of
electrons in the orbital
Carbon: 1s22s22p2
• Noble-gas notation represents electron
configurations of noble gases using symbols in
brackets
Neon: 1s22s22s6 or [Ne]
• Noble-gas notation is a short hand for
elements with long electron configurations
- The electron configuration for an element can
be represented using the noble-gas notation
for the noble gas in the previous period and
the electron configuration for the energy level
being filled
Aluminum: 1s22s22p63s23p1
= [Ne]3s23p1
C. Sublevel Diagram
• Produces the
sublevel sequence
shown in the
aufbau diagram
D. Exceptions to predicted configurations
• The aufbau diagram can be used to write
electron configurations only to elements
with an atomic number of 23 or less (up to
Vanadium)
IX. Valence Electrons
• Valence electrons are defined as electrons
in the atom’s outermost orbitals
• Group numbers on the periodic table help
tell you how many valence electrons are in
those elements in that group
- Group 1 elements have 1 valence electron
- Group 18 elements have 8 valence
electrons
A. Electron-dot structures
• An atom’s electron-dot structure consists of
the element’s symbol surrounded by dots
representing the atom’s valence electrons
• Dots representing valence electrons are placed
one at a time on the four sides of the symbol
and then paired up until all are used
• Dot structures are important in showing
valence electrons because it is these electrons
that are available for forming chemical bonds