What gives fireworks their different
colors?
The Atom and Unanswered Questions
• Recall that in Rutherford's model, the
atom’s mass is concentrated in the nucleus
and electrons move around it.
• The model doesn’t explain how the electrons
were arranged around the nucleus.
• The model doesn’t explain why negatively
charged electrons are not pulled into the
positively charged nucleus.
The Atom and Unanswered Questions
(cont.)
• In the early 1900s, scientists observed
certain elements emitted visible light when
heated in a flame.
• Analysis of the emitted 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, a form of energy that exhibits
wave-like behavior as it travels through
space.
• All waves can be described by several
characteristics.
The Wave Nature of Light (cont.)
• The wavelength (λ) is the shortest
distance between equivalent points on a
continuous wave.
• The frequency (ν) is the number of waves
that pass a given point per second.
• The amplitude is the wave’s height from the
origin to a crest.
The Wave Nature of Light (cont.)
The Wave Nature of Light (cont.)
• Wavelengths represented by λ (lambda).
• Expressed in meters
• Frequency represented by v (nu)
• Expressed in waves per second
• Hertz (Hz) is SI unit = one wave/second
• Speed of light represented by c
• This is a constant value in a vacuum
The Wave Nature of Light (cont.)
• The speed of light (3.00  108 m/s) is the
product of its wavelength and frequency c = λν.
• λ and v are inversely proportional
The Wave Nature of Light (cont.)
• Light from a green leaf is found to have a
wavelength of 4.90 x 10-7 m (or 490 nm or
4,900Å) Note: Å = ångström = 10-10 m. What is
the frequency of the light?
• c = λν where c= 300 million meters/second
• c/λ = ν
• 3.00*108 m/s / 4.90 x 10-7 m = ν
• ν = 6.12 * 1014 Hz
The Wave Nature of Light (cont.)
• Sunlight contains a continuous range of
wavelengths and frequencies.
• A prism separates sunlight into a continuous
spectrum of colors.
• The electromagnetic spectrum includes all
forms of electromagnetic radiation.
The Wave Nature of Light (cont.)
Visible Spectrum
Color
Frequency
Wavelength
violet
668–789 THz
380–450 nm
blue
631–668 THz
450–475 nm
cyan
606–630 THz
476–495 nm
green
526–606 THz
495–570 nm
yellow
508–526 THz
570–590 nm
orange
484–508 THz
590–620 nm
red
400–484 THz
620–750 nm
The Particle Nature of Light
• The wave model of light cannot explain all
of light’s characteristics.
• German physicist Max Planck observed in 1900
that 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
• Energy of a quantum:
• Equantum = hv
• Planck’s constant (h) has a value of
6.626  10–34 Joules ● second.
• Found that energy can only be emitted or
absorbed in whole number multiples of hv (e.g.
3hv or 8hv).
The Particle Nature of Light (cont.)
• Albert Einstein proposed in 1905 that light
has a dual nature.
• A beam of light has wavelike and particlelike
properties. Think of light as a stream of tiny
packets of energy called photons.
• A photon is a particle of electromagnetic
radiation which carries a quantum of energy,
but has no mass. Thus:
Ephoton = h
Ephoton represents energy of light
h is Planck's constant.
 represents frequency.
The Particle Nature of Light (cont.)
• The photoelectric effect is when electrons are
emitted from a metal’s surface when light of a
certain frequency shines on it. Thus, depends
on Ephoton of light, not intensity (brightness).
The Particle Nature of Light (cont.)
• Calculate the quantum of energy associated with
purple light of 380 nm.
• v = c/λ = 3*108 m/s / 3.80 x 10-7 m = 7.9 x 1014 Hz
• Ephoton = h = 6.626  10–34 J*sec x (7.9 x 1014/sec)
= 5.2 x 10-19 J
Atomic Emission Spectra
• Since the energy of a beam of light is related to
its frequency, we can determine its energy by
measuring its frequency or wavelength.
• Thus the
(i.e. wavelength) tells
us about its energy level.
• For example, light in a neon sign is produced
when electricity is passed through a tube filled
with neon gas and excites the neon atoms.
• The excited neon atoms emit light to release
energy. Only colors related to the quantum of
energy released will be generated.
Atomic Emission Spectra (Discrete)
Atomic Emission Spectra (cont.)
• The atomic emission spectrum of an
element is the set of wavelengths of the
electromagnetic waves emitted by the
atoms of the element.
• Each element’s atomic emission spectrum is
unique.
Atomic Emission Spectra (cont.)
• The Emission Spectra for Calcium (top)
and Sodium (bottom).
Assessment
What is the smallest amount of energy
that can be gained or lost by an atom?
A. electromagnetic photon
B. beta particle
C. quantum
D. wave-particle
A.
B.
C.
D.
A
B
C
D
Assessment
What is a particle of electromagnetic
radiation with no mass called?
A. beta particle
B. alpha particle
C. quanta
D. photon
A.
B.
C.
D.
A
B
C
D
Bohr's Model of the Atom
Bohr's Model of the Atom
• Bohr correctly predicted the frequency lines
in hydrogen’s atomic emission spectrum.
• His new model built a relationship between
location of electrons and their energy levels.
• The lowest allowable energy state of an atom
and its electrons is called its ground state.
• When an atom gains energy, it is said to be in
an excited state.
Bohr's Model of the Atom (cont.)
• Bohr suggested that an electron moves
around the nucleus only in certain allowed
circular orbits.
Bohr's Model of the Atom (cont.)
• Each orbit was given a number, called the
quantum number.
Bohr's Model of the Atom (cont.)
• Hydrogen’s single electron is in the n = 1
orbit in the ground state.
• When energy is added, the electron moves to
the n = 2 orbit or higher (excited state).
• When the electron is no longer excited by an
outside force, it drops back down to a lower
energy level.
• When it “falls” it
form of electromagnetic radiation.
in the
Bohr's Model of the Atom (cont.)
Bohr's Model of the Atom (cont.)
Electron Energy Transformations
• Bohr’s atomic model attributes hydrogen’s emission
spectrum to electrons dropping from higher-energy to
lower-energy orbits closer to the nucleus.
∆E = E higher-energy orbit - E lower-energy orbit = E photon = hν = hc/λ
• Bohr determined that the energy of each level was:
E = -2.178 x 10-18 J x (Z2 / n2)
• Where Z = the nuclear charge (= +1 for Hydrogen) and
• n = orbit level
Electron Energy Transformations
• If an electron moves from n=6 to n =1 (ground state),
energy released would equal:
• n=6: E6 = -2.178 x 10-18 J x (12/62) = -6.050 x 10-20 J
• n=1: E1 = -2.178 x 10-18 J x (12/12) = -2.178 x 10-18 J
• ∆E = energy of final state – energy of initial state
• ∆E = (-2.178 x 10-18 J) – (-6.050 x 10-20 J) =
= -2.117 x 10-18 J (atom released energy)
λ = hc/ ∆E = (6.626x10-34J*s x 3.0x108m/s) / -2.117 x 10-18 J
= 9.383 x10-8 m or 93.83nm (ultraviolet light emitted)
Bohr's Model of the Atom (cont.)
• Bohr’s model explained the hydrogen’s
spectral lines, but failed to explain any
other element’s lines and their chemical
reactions.
• The behavior of electrons is still not fully
understood, but substantial evidence shows
they do not move around the nucleus in
circular orbits like planets.
The Quantum Wave Mechanical Model
• While the Bohr model was not perfect, its
idea of quantum energy levels was on the
right track.
• Louis de Broglie (1892–1987) noted that
Bohr’s quantized energy orbits had
similarities to “standing” waves.
• He proposed that electron particles also
behaved like waves as they moved around
the nucleus.
The Quantum Wave Mechanical Model (cont.)
• The next figure illustrates that waves with
fixed endpoints, like the vibrations of a
guitar string, can only vibrate in certain
wavelengths (or else they don’t “fit”).
• Waves going around a circle can only
vibrate in whole-number wavelengths.
• And only ODD numbers of whole
wavelengths can fit around a circle or orbit.
The Quantum Wave Mechanical Model (cont.)
• The de Broglie equation predicts that all
moving particles, including baseballs and
electrons, have wave characteristics.
 represents wavelengths
h is Planck's constant.
m represents mass of the particle.
 represents velocity.
• Since electrons can only move in specific
wavelengths around the nucleus, and
wavelength/frequency determines energy,
we now have a mathematical reason for
Bohr’s quantum energy levels.
The Quantum Wave Mechanical Model (cont.)
• Heisenberg showed it is impossible to take
any measurement of an object without
disturbing it.
• The Heisenberg uncertainty principle
states that it is fundamentally impossible to
know precisely both the velocity and position
of an electron particle at the same time.
• The only quantity that can be known is the
probability for an electron to occupy a certain
region around the nucleus. These regions
are called “Orbitals”.
The Quantum Wave Mechanical Model (cont.)
• Building on de Broglie’s work, Erwin
Schrödinger derived an equation in 1926
that treated electrons as waves.
• His new model was called the quantum
wave mechanical model of the atom.
• Schrödinger’s wave equation applied equally
well to elements other than hydrogen, thus
improving on the Bohr Model.
The Quantum Wave Mechanical Model (cont.)
• The Schrodinger wave function defines a threedimensional region of electron location
probability called the atomic orbital.
90%
Electron
Probability
Every Electron needs an Orbital it can call Home
• All the electrons for each element must
occupy a specific orbital – there can be no
overlap.
• The Quantum Model describes the different
types and energies of orbitals using various:
– Sizes
– Shapes
– Orientations
– Spins
Atomic Orbitals
• Principal quantum number (n) indicates the
relative size and energy of atomic orbitals.
• “n” specifies the atom’s major energy levels,
called the principal energy levels.
• These are similar to Bohr’s orbit levels.
• n: 1-7 represent the seven principal energy
levels for electrons of all known elements
Atomic Orbitals (cont.)
• Principal levels have multiple sublevels
The number of sublevels = n and relate the
shape of the orbital.
Atomic Orbitals (cont.)
• Each energy sublevel relates to orbitals of
different shape. Spacial orientation can
increase the number of sublevels.
Atomic Orbitals (cont.)
• Each Orbital has a unique set of “Quantum
Numbers” defining its energy and position.
• ‘n’ = Principal Quantum Number (size /energy)
• ‘l’ = Angular Momentum Quantum Number.
Shape of orbital. There are “n” shapes from 0 to n-1.
Also referred to letters based on early spectral
descriptions (0=s,1=p,2=d,3=f).
• ml = Magnetic Quantum Number. Orientation of
orbital. Has values between –l and l .
• ms = Electron Spin Quantum Number. Electrons can
spin in two directions: ½ and -½ or “up” and “down”
Quantum Numbers for first Four Levels of Orbitals
n
l
(level) (shape)
(shell) (subshell)
1
2
3
4
m
l
Orbital
Number of
(orientations)
Name
Orbitals
ms
(spin)
Number of Electrons
Electrons per level
0
1s
0
1
-1/2, +1/2
2
0
2s
0
1
-1/2, +1/2
2
2
8
1
2p
-1,0,+1
3
-1/2, +1/2
6
0
3s
0
1
-1/2, +1/2
2
1
3p
-1,0,+1
3
-1/2, +1/2
6
2
3d
-2,-1,0,+1,+2
5
-1/2, +1/2
10
0
4s
0
1
-1/2, +1/2
2
1
4p
-1,0,+1
3
-1/2, +1/2
6
18
32
2
4d
-2,-1,0,+1,+2
5
-1/2, +1/2
10
3
4f
-3,-2,-1,0,+1,+2,+3
7
-1/2, +1/2
14
Quantum Numbers (cont.)
•
•
What are the quantum numbers for the hydrogen’s lone
electron in its ground state?
•
n=1, l=0, ml=0, ms=1/2
•
Usually written as: (1,0,0,1/2)
Only certain quantum numbers are allowed
•
•
If n=1, then can’t have l=3, for example.
Would the following be allowed?
•
(3,2,-3,1/2)
•
•
No: level n=3 can have ml=-2,-1,0,1,2 only
(2,1,-1,-1/2)
•
Yes
Quantum Numbers (cont.)
•
What is the maximum number of electrons with quantum number
of (n=5, l=4)?
•
If l = 4, then can have 9 orbitals of ml = -4,-3,-2,-1,0,1,2,3,4
and within each orbital, can have two electrons of spin ½ and -½
•
Thus there is room for 9x2 = 18 electrons
•
These 18 electrons will have quantum numbers starting with (5,4)
1.
5,4,-4, ½
2.
5,4,-4, -½
3.
5,4,-3, ½
4.
5,4,-3, -½
5.
etc.
Atomic Orbitals Summary
• Principal quantum number (n) = size and
energy of atomic orbitals.
• n= 1-7 energy levels or “shells”
• Subshells (l) = shape of atomic orbitals
• Subshell quantum no.:
0, 1, 2, 3
• Subshell orbital letters:
s, p, d, f
• Orientation (ml): different directions
increases the number of orbitals per level.
• Number of orbitals for each subshell:
s=1; p=3; d=5; f=7.
Assessment
Heisenberg proposed the:
A. Atomic Emission Spectrum
B. Quantum Leap
C. Wave theory of light
D. Uncertainty Principle
A.
B.
C.
D.
A
B
C
D
Assessment
Who proposed that particles could also
exhibit wavelike behaviors?
A. Bohr
B. Einstein
C. Rutherford
D. de Broglie
A.
B.
C.
D.
A
B
C
D
Assessment
Which atomic suborbitals have a
“dumbbell” shape?
A. s
B. f
C. p
D. d
A.
B.
C.
D.
A
B
C
D
Assessment
Which set of quantum numbers are not
allowed and why?
A. (2,1,-1,1/2)
B. (4,1,2,1/2) If l=1, ml can only be from -1 to 1
C. (3,2,-2,-1/2)
D. (1,0,0,1/2)
A.
B.
C.
D.
A
B
C
D
Assessment
The set of quantum numbers (4,1,-1,1/2)
has which orbital name?
A. 4s
B. 5s
C. 4p
D. 4d
A.
B.
C.
D.
A
B
C
D
Electron Configuration
• Determine how electrons are organized around
the nucleus for each element =
“Electron Configuration”
• Apply the
• Pauli exclusion principle,
• the aufbau principle, and
• Hund's rule to properly determine electron
configurations using orbital diagrams and electron
configuration notation.
Ground-State Electron Configuration
• The arrangement of electrons in the atom
is called the electron configuration.
• The aufbau principle states that each
electron occupies the lowest energy orbital
available.
Ground-State Electron Configuration
(cont.)
• The Pauli exclusion principle states that
a maximum of two electrons can occupy a
single 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
the same energy level
orbitals.
Ground-State Electron Configuration
(cont.)
Electron Configuration (cont.)
• Some electron configurations don’t appear
to follow the rules, such as those for
chromium, copper, and several other
elements.
• Their configurations reflect the increased
stability of half-filled and completely filled
sets of s and d orbitals.
• Chromium: 1s2 2s2 2p6 3s2 3p6 4s1 3d5
• Copper: 1s2 2s2 2p6 3s2 3p6 4s1 3d10
Electron Configuration (cont.)
• Noble gas notation – shorthand configuration.
Period Table Blocks – Valence Electrons
Valence Electrons
• Valence electrons are defined as
electrons in the atom’s outermost orbitals—
those associated with the atom’s highest
principal energy level.
• Electron-dot structure consists of the
element’s symbol representing the nucleus,
surrounded by dots representing the
element’s valence electrons.
Valence Electrons (cont.)
Assessment
In the ground state, which orbital does an
atom’s electrons occupy?
A. the highest available
B. the lowest available
C. the n = 0 orbital
D. the d suborbital
A.
B.
C.
D.
A
B
C
D
Assessment
The outermost electrons of an atom are
called what?
A. suborbitals
B. orbitals
C. ground state electrons
D. valence electrons
A.
B.
C.
D.
A
B
C
D
Assessment
Which Periodic Table Group will have its
valence electrons in a s2 p3 configuration?
A. The Alkali Metals
B. The Halogens
C. The Noble Gases
D. Group 15
A.
B.
C.
D.
A
B
C
D