Atomic Theory, the Quantum
Revolution
Max Planck’s work on black body
radiation

In 1900, Max Planck
was investigating why
opaque hot objects will
glow red hot, yellow
hot, white hot, but
not ultraviolet hot.
(He wanted to find why
there is a maximum
energy of radiated
light.)
Classical physics had predicted the
ultraviolet catastrophe…

…where the spectrum of light emitted from a
blackbody should show unlimited intensity at
high frequency, yet a maximum limit in the
spectrum was observed, and that could not
be explained.
Eventually, Max Planck was able to
explain this…
Planck assumed that light was
emitted in small packages of
energy he called quanta
(singular: quantum)

He received the Nobel prize in 1918.
The quantized energy existed in
integral multiples of
E = hu


(Energy = Planck's constant x
frequency of radiation).
Planck made a deduction of this formula
while renouncing classical physics and
introducing the revolutionary idea of
quantized energy.
Planck’s constant (h) =
6.626 x 10-34 J.s

Problem:
What is the energy of green light with a
frequency of 6.0 x 1014 s-1?

E = hu

E = (6.626 x 10-34 J.s)(6.0 x 1014 s-1)
 E = 4.0 x 10-19 J

The Nature of Light:
Is light a particle or a wave?


In 1690, Christian Huygens
published his wave theory of
light. He observed many
wave properties of light, such
as the bending (refraction) of
light through a prism.
He correctly predicted that
light should propagate slower
in a denser medium.
Light as a wave
The Nature of Light:
Is light a particle or a wave?

At the same time as Huygens
Isaac Newton, already famous
for his theory of gravity, was
working on his particle theory
of light. He made many
observations of light behaving
as particles, such as reflecting
as it bounced off mirrors, and
creating straight line
shadows.
By the way:


Newton is considered the greatest
scientist ever because he was the first to
incorporate experiment and theory as a
way of defining science: proposing
something and then using experiments to
confirm it or not.
All of science after him works in the same
exact way.
By 1820, light is
considered a wave…

Newton’s particle theory of light
dominated for 50 years, until
1819, with the mathematical work
of Fresnel, when the wave theory
of light became firmly established
for the next 100 years.
Einstein and the Photoelectric Effect

Einstein received a Nobel
Prize in 1921 for his
explanation of the
photoelectric effect, a
phenomenon that occurs
when you shine a light
upon certain metals and a
stream of electrons is
emitted from that metal.
Einstein and the Photoelectric Effect
The emitted electrons have been
found to have certain properties:



The number of electrons emitted by the metal
depends on the intensity of the light beam applied
on the metal; more intense the beam, higher the
number of electrons emitted.
The emitted electrons move with greater speed if
the applied light has a higher frequency.
No electron is emitted until the light has a threshold
frequency, no matter how intense the light is.
Einstein and the Photoelectric Effect

These observations baffled physicists for
many decades, since they cannot be
explained if light is thought of only as a
wave.

If light were to be a wave, both the energy
and the number of the electrons emitted
from the metal should increase with the
intensity of light. Observations contradicted
this prediction.
Einstein and the Photoelectric Effect
Einstein described light as composed of quanta,
now called photons, rather than continuous
waves.
 Based on Planck’s theory, Einstein found that
the energy in each photon was equal to its
frequency multiplied by Planck’s constant
(E(photon) = hu).

This discovery led to the quantum
revolution in physics.
So, is light ultimately a wave,
or a stream of photons?

The answer is: both. Light behaves as
a wave under certain conditions, and as
a stream of particles under others. It is
said to have a dual nature: we can
understand it as either wave or particle,
depending on our context of
observation.
Dual nature of light
Light as a wave
Light as a photon (quantum of light energy)
Standing Waves


If you tie down a string at both ends (as
on a guitar) and pluck the string, it will
vibrate as a standing wave.
At the fixed ends, the amplitude is zero.
The wave does not appear to travel down
the line.
Standing waves occur in wholenumber multiples of ½ l
Standing Waves


There are always two or more places
where the vibrating string never moves,
the amplitude is zero at these points,
called nodes.
The distance between nodes is always
½ l.
Standing Waves


An important property of standing waves
is you can't have any frequency you want
because ends are fixed. When the ends
are fixed only certain discrete wavelengths
(frequencies) are allowed.
Standing waves are an example of
quantized energy (energy in discrete
packets).
Standing Waves
The Bohr Model

In 1912, Niels
Bohr adapted
Rutherford's
atomic model to
Planck’s quantum
theory and so
developed his
theory of atomic
structure.
Atoms can give off light


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Bohr’s model explained the atomic
emission spectrum of hydrogen. For this he
received the Nobel Prize in 1922. His
atomic model is based on these ideas.
The atomic emission spectrum of an
element is emission of particular
frequencies (colors) of light by energized
atoms of that element.
Each atom's atomic emission spectrum is
unique.
Atomic emission spectrum and
absorption spectrum
The emission spectrum of
hydrogen:



The most prominent spectral lines are
violet, blue, blue-green, and red.
Which of the lines has the lowest frequency?
Which of the lines has the shortest wavelength?
Atomic emission spectrum and
absorption spectrum
The Energies of Electrons

The energy of an atom changes
as the electrons absorb or release
energy
 Ground state – atom in the
lowest possible energy state
 Excited state – atom with
excess energy
When an H atom absorbs energy
from an outside source it enters an
excited state.
The excited electrons emit photons
of light and return to the low
energy ground state.
Atoms can give off light
Flame Test Colors
Barium Pale green
Cesium Blue
Iron Gold
Lithium Magenta
Sodium Intense yellow
Calcium Orange/red
Copper Blue/green
Potassium Lavender
Magnesium Bright white
Strontium Crimson
Firework Colorants

Red: strontium salts, lithium salts

Orange: calcium salts

Gold: incandescence of iron

Yellow: sodium nitrate, cryolite

Electric White: white-hot metal, barium oxide

Green: barium compounds

Blue: copper compounds + chlorine producer


Purple: mixture of strontium and copper compounds

Silver: burning aluminum, titanium, or magnesium
Bohr’s Model

In 1913, Bohr
proposed his model
of the atom. He
determined that
electrons can be
located in certain
discrete energy
states, called energy
levels.
Energy levels


The principal energy level is an important
part of Bohr’s model that remains
important in the modern model of the
atom.
The letter n is used to represent the
energy level (n = 1, 2, 3, etc.). It is
referred to as the principal quantum
number.
Bohr related his model to a ladder…


As person can stand on one rung of a
ladder or the next, yet it is impossible for
a person to stand between the rungs... an
electron can be found in one energy level
or the next, but not between levels.
The only way for the electron to jump to
the next level is for it to have a quantum
leap, which is the leap from one energy
level to another.



The energy of the electron has a definite
value in a stationary orbit. The electron
can jump from one stationary orbit to
another.
If it jumps from an orbit of lower energy
E1 to an orbit of higher energy E2 , it
absorbs a photon.
If it jumps from an orbit of higher energy
E2 to an orbit of lower energy E1, it emits
a photon.
The Energy Levels of Hydrogen

Energy level diagram
• The amount of energy released is the same amount
of energy absorbed by the atom to reach the
excited state.

How many
emission
lines are
possible for a
hydrogen
atom
considering
energy levels
1 through 7?
The Bohr Model of the Atom
Quantized energy
levels
 Electron moves in a
circular orbit
 Electron jumps
between levels by
absorbing or
emitting photon of a
particular
wavelength

Bohr's atomic model was ultimately
not successful.


Bohr’s model considered the electron as a
particle, and classical physics shows that a
charged particle accelerating around a
circular path would lose energy, and so
the electrons would fall into the nucleus.
The modern model of the atom considers
the electron, not as a particle, but as a
matter-wave.
Bohr's atomic model was ultimately
not successful.


There was a major defect in the Bohr model.
It did not explain the behavior of atoms with
more than one electron.
Electrons as waves



In 1925, Victor de Broglie
proposed the WaveParticle Duality Theory.
If light can sometimes be
considered waves and
other times particles, why
doesn’t matter behave
similarly?
He received a Nobel Prize in
1929.
Electrons as waves

De Broglie’s theory stated that a tiny
particle, such as an electron, also
exhibits wave properties in some
experiments.
Unstable wave orbit
Stable wave orbit
De Broglie’s equation
l
= h
(mv)
This equation was revolutionary!
 It linked particle properties [mass x
velocity (mv )] with wave properties
[wavelength (l)].


Remember h = 6.626 x 10-34 J . s
(Planck’s constant)
Question:

Calculate the wavelength associated with an
electron of mass m = 9.109 x 10-31 kg
traveling at 1.20 x 108 m/s.
= h
(mv)

l

l =
6.626 x 10-34 J . s
(9.109 x 10-31 kg)(1.20 x 108 m/s)
= 6.06 x 10-12 m
(which is 1/20th the diameter of the H atom)
Electrons as waves
Heisenberg’s Uncertainty Principle


Werner Heisenberg expanded
on de Broglie’s ideas; he
stated that the exact location
of the electron couldn’t be
determined. However, he
could predict a region in space
where the probability of
finding the electron is high.
Heisenberg received a Nobel
Prize in 1932.
Heisenberg’s Uncertainty Principle


On the basis of Heisenberg’s idea, the
Uncertainty Principle says that if we
choose to know the energy of an electron
in an atom with only a small uncertainty,
then we must accept a correspondingly
large uncertainty about it’s position in the
space around the atom’s nucleus.
We can only calculate the probability of
finding the electron (of given energy)
within a given space.
Schrödinger’s Wave Mechanical
Model

Erwin Schrödinger
combined de Broglie’s
equation with classical
equations for wave
motion to derive the
wave equation (which we
call the Schrödinger
equation) used to predict
electron behavior.
Schrödinger’s Wave Mechanical
Model


In the equation, Schrödinger provides a
three dimensional picture of the electron
matter-wave (called atomic orbital).
Schrödinger's theory of the atom is our
current model of the atom.
Anyone who is not shocked by
quantum theory has not
understood it"
- Niels Bohr
Atomic Orbitals


An atomic orbital is a region around the
nucleus where there is a high probability
(90%) of finding an electron.
Orbitals of the same shape grow larger as
the principal energy level (n) increases
Atomic Orbitals

Each principal energy level is divided into
sublevels.
– Labeled with numbers and letters
– Indicate the shape of the orbital
Orbital Shapes and Energies
The s - Orbital
s - orbital shape: Spherical


Occur in all energy levels, n = 1, 2, 3, etc.
Sublevel s consists of 1 spherical orbital
Orbital Shapes and Energies
Three p - Orbitals




p - orbital shape: Two lobes each
Occur in levels n = 2 and greater
Each orbital lies along an axis (2px, 2py, 2pz)
Sublevel p consists of 3 dumbbell shaped orbitals
Atomic Orbitals – s and p orbitals
Size increases as energy level increases
s and p orbitals
Orbital Shapes and Energies
Five d - Orbitals



d - orbital shape: Complex
Occur in levels n=3 and greater
Sublevel d consists of 5 complex orbitals
Orbital Shapes and Energies
Seven f - Orbitals


f - orbital shape:
Highly complex
Occur in levels
n=4 and greater
Electron configurations

The ways in which electrons are arranged
around the nuclei of atoms are called
electron configurations.
Three rules tell you how to find
electron configurations of atoms:
1.
2.
3.
The aufbau principle
The Pauli exclusion principle
Hund’s rule
The Aufbau Principle

Electrons enter
orbitals of lowest
energy first.
The Pauli Exclusion Principle


An orbital can hold only
two electrons, and they
must have opposite
spins.
Wolfgang Pauli received the
Nobel Prize in 1945.
Hund's Rule

When electrons enter orbitals of equal
energy, one electron enters each orbital
until all the orbitals contain one electron
with parallel spins.
Exceptions to the aufbau order

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
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

Copper and chromium have exceptional electron
configurations.
One electron in the 4s sublevel is promoted to
the 3d sublevel. This makes the atoms more
stable.
Your text explains that half filled and completely
filled sublevels are more stable than partially
filled sublevels.
Instead of the aufbau order…
Cu: 1s2, 2s2, 2p6, 3s2, 3p6, 3d5, 4s2
The actual configuration is….
Cu: 1s2, 2s2, 2p6, 3s2, 3p6, 3d6, 4s1