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THE ATOM
Chapter
5/4/2017
8
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The Concepts of Particle and Wave
We regard objects such as a stone or
electron as particles.
 We regard the ripples in a lake as waves.
 Classical physics, the physics of chapters
1-6, treats particles and waves as
separate aspects of the reality we find in
everyday life.

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The Concepts of Particle and Wave

In the small scale world of atoms, molecules, electrons,
and nuclei there are neither particles nor waves in our
sense of these terms.

We think of electrons as particles (they have charge and mass)


We think of em waves as waves (they exhibit wave behavior
such as diffraction and interference)



Evidence exists that a moving electron is a type of wave in some
instances.
Em waves also behave as though they consist of streams of
particles.
Modern physics – refers to the physics in which waveparticle duality is central to an understanding.
It is the physics of the atomic world.
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PHOTOELECTRIC EFFECT
Can electrons be set free from atoms by light?
Refers to electrons
being emitted by a
metal surface when
light is directed onto it.
 Most
metals
need
ultraviolet light for the
photoelectric effect to
occur, but not all.

electron
 Potassium
and cesium
respond to visible light.
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Everyday Examples of the
Photoelectric Effect
Photoelectric cells measure light intensity
in a camera.
 Solar cells produce electric current when
sunlight falls on them.
 Television camera tubes convert the
image of a scene into an electric signal.

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Light

The word “light” is defined here as
“electromagnetic radiation of any
wavelength”
 X-rays,
gamma rays, uv light, microwaves,
radio waves, visible light
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The Photoelectric Effect
No Simple Explanation

The electrons are always emitted at once,
even when a faint light is used.
 According
to the electromagnetic theory of
light, the energy in an em wave is spread out
across the wave; hence, a certain period of
time should be needed for an individual
electron to gather enough energy to leave the
metal.
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The Photoelectric Effect
No Simple Explanation

A bright light causes more electrons to be
emitted than a faint light, but the average
KE of the electrons is the same.
 The
electromagnetic theory of light predicts
that the stronger the light, the greater the KE
of the electrons.
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The Photoelectric Effect
No Simple Explanation

The higher the frequency of light, the more
KE the electrons have. (blue light yields
faster electrons than red)
 According
to the electromagnetic theory of
light, the frequency should NOT matter.
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The Photoelectric Effect
The higher the frequency of light, the more KE the photoelectrons have.
The brighter the light, the more photoelectrons are emitted.
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Quantum Theory of Light

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
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Until the discovery of the photoelectric effect, the
electromagnetic theory of light completely
explained the behavior of light.
The Quantum Theory of Light arose from the
discovery of the photoelectric effect.
Created by Albert Einstein (1905)
The same year saw the birth of the Theory of
Relativity.
All of modern physics has its roots in these two
theories.
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Photons – Particles of Light
The modern concept of the photon was
developed gradually by Einstein (1905-17)
to explain experimental observations that
did not fit the classical wave (or
electromagnetic) model of light.
 Particularly, the photon model accounted
for the frequency dependence of light’s
energy.

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Photons

Einstein
proposed
that light consists of
tiny bursts of energy
called photons.
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I want to know more about
PHOTONS!

The photon is an elementary particle responsible for all
electromagnetic phenomena; they produce all electric
and magnetic fields.





In other words, photons make up all forms of light on the em spectrum.
A photon is a discrete bundle (quantum) of
electromagnetic (or light) energy.
Photons have zero mass, zero rest energy, and zero
charge.
Photons are always in motion and travel at the speed of
light (c), in free space.
Photons carry energy and momentum.

Can be slowed down or even absorbed, transferring energy and
momentum proportional to its frequency
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I want to know more about
PHOTONS!





Photons can be destroyed/created when radiation is
absorbed/emitted.
Photons have particle-like interactions (i.e. collision) with electrons
and other particles.
Photons are one of the rare particles that are identical to their
antiparticle, the antiphoton.
Photons act as both a wave and a particle all the time (even though
it’s common, but basically incorrect, to say that it’s “sometimes a
wave and sometimes a particle” depending upon which features are
more obvious at a given time).
Photons are emitted in many natural processes such as when a
charge is accelerated, when an atom or nucleus jumps from a higher
to lower energy level, or when a particle and its antiparticle are
annihilated.
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Max Planck and Quanta

Einstein’s proposal that light consists of photons came about from a
hypothesis suggested 5 years earlier by Max Planck (1858-1947), a
German physicist.

In order to explain variation of color with temperature (Figure 4-4) (i.e.
red (hot) to yellow (hotter) to white(hottest) Planck said:


The higher the temperature, the shorter the wavelength and higher the
frequency.
Planck hypothesized that warm bodies emit radiant energy in discrete
bundles, what he called quanta.


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Mass and electric charge are considered quantized, in that they consist of some
whole number of fundamental units.
Planck said the energy in each energy bundle is proportional to the
frequency of radiation.
All the quanta associated with a given frequency of light have the same
energy: E=hf
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Quantum Energy
E = hf


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E=quantum energy
h = Plank’s constant = 6.63 x 10-34 joule . Sec
f = frequency of light
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Quanta
A quantum is the smallest elemental unit
of a quantity.
 Quanta are discrete bundles in which
radiation and other forms of energy occur.

 Light
(or any form of radiant energy), is
composed of many quanta, each of which is
called a photon.
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Photoelectric Effect
EINSTEIN’S HYPOTHESIS : if light is
emitted in little packets, it should travel
through space and be absorbed in the
same little packets.
 Einstein proposed that some minimum
energy, w, is needed to pull an electron
away from a metal surface.

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Photoelectric Effect

Einstein’s formula for the photoelectric
effect can be summarized as:
hf = KE + w where
w
= minimum energy to pull an electron away from a
metal surface
 h = Planck’s constant
 f = frequency
 KE = kinetic energy
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Photoelectric Effect
 In
summation, if the frequency of the
light is too low, so that E (quantum
energy = hf) is less than w, no
electrons can come out.
The
energy of the ejected electron is
related only to the light’s frequency, not
to its intensity.
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Photoelectric Effect
 When
E is greater than w, a photon of
light striking an electron can give the
electron enough energy for it to leave
the metal with a certain amount of
kinetic energy (KE).
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Photon Example


The average frequency of light emitted by a 100-W light bulb is 5.5 x
1014 Hz. How many photons per second does the light bulb emit??
The energy of each photon can be calculated using:
E=hf
(6.63 x 10-34 J*s)(5.5 x 1014 Hz) = 3.6 x 10-19 J
Since 100 W = 100 J/s, the number of photons emitted per second is
energy / sec
100 J / s
20


2
.
8
x
10
photons / sec
19
energy / photon 3.6 x10 J / photon
Such an enormous amount of photons makes it impossible for us to experience
light as a stream of individual particles.
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What is Light??
 Light
traveling as a series of little
packets of energy is directly opposed
to the wave theory of light.
 But, in fact, Einstein suggested in
1905 that light travels through space
in the form of distinct photons.
 LIGHT can be defined as having both
wave and particle aspects.
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Light

Wave Theory of Light – accounts for the
diffraction and interference of light.
 Light
waves are spread out like waves
traveling across water.

Quantum Theory of Light – accounts for
the photoelectric effect.
 Light
travels from a source as a series of tiny
bursts of energy, each burst so small that it
can be taken up by a single electron.
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The Wave and Quantum Theories of Light
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Light

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The wave theory of light and the quantum theory of light
complement each other.
Both theories are needed to account for a single physical
phenomenon.
Wave theory (em waves) provides the only explanation
for some experiments involving light.
Quantum theory (photons) provides the only explanation
for other experiments involving light.
In any particular event light exhibits either a wave nature
or a particle nature, never both at the same time.
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X-Rays – High Energy Photons

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Wilhelm Roentgen (1845-1923) discovered xrays.
X-rays are given off whenever fast electrons are
stopped suddenly.
This is the inverse of the photoelectric effect.
 The
photoelectric effect shows that photons of light
can give energy to electrons.

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X-rays are high frequency em waves.
Electron KE is transformed into photon energy.
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An X-Ray Tube
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Matter Waves

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Is it possible for a particle, such
as an electron, to have wave
properties as well?
Yes!
Louis de Broglie (1892-1987)
proposed that moving objects
have wave properties that
complement their particle
properties.
He suggested that a particle of
mass m and speed v behaves
as though it is a wave whose
wavelength is:
h

mv
λ=de Broglie wavelength
h=Planck’s constant
mv=momentum
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Matter Waves

The more momentum (mv) a particle has,
the shorter its de Broglie wavelength λ.

Matter waves are real but are only
significant in the atomic world and are
crucial to the understanding of atomic
structure and behavior.
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Calculate the de Broglie wavelength of (a) a
46-g golf ball whose speed is 30 m/s, and
(b) an electron whose speed is 107 m/s.
34
h
6.63x10 J * s
34


 4.8 x10 m
mv (.046kg )(30m / s)
Wavelength of golf ball is small compared with its dimensions and would not
Expect to find any wave aspects in its behavior.
6.63x1034 J * s
11


7
.
3
x
10
m
31
7
(9.1x10 kg )(10 m / s)
Dimensions of atoms are comparable with wavelength (radius of hydrogen atom
Is 5.3x10-11m) Therefore, the wave character of moving electrons is important
In the world of the atom.
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Waves of Probability
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In water waves, the quantity that varies periodically is the
height of the water surface; in sound waves, it is air
pressure; in light waves, it is electric and magnetic fields.
What varies in the case of matter waves??
The quantity whose variations make up matter waves is
called the wave function, symbol  (the Greek letter psi).
The value 2 at a given place and time for a given
particle determines the probability of finding the particle
there at that time.
For this reason 2 is called the probability density of the
particle.

A large value of 2 means the strong possibility of the particle’s
presence.
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Particle and Wave Description of a Moving Object
Particle
description of
moving object.
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Wave description of same moving object.
The packet of matter waves that corresponds
to a certain object moves with the same speed v
as the object does. The waves are waves of
probability.
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Heisenberg’s Uncertainty Principle


To regard a moving particle as a wave packet suggests
that there are limits to the accuracy with which we can
measure “particle” properties such as position and
speed.
Werner Heisenberg 1901-1976


It is impossible to know both the exact position and the exact
momentum of a particle at the same time.
The narrower its wave packet, the more precisely a particle’s
position can be identified.


However the wavelength of the waves is not well defined.
The wider its wave packet, the wavelength can be precisely
identified.

However the position cannot be determined.
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Narrow and Wide Wave Packets
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Atomic Spectra

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With the Rutherford model of the atom, the
quantum theory of light, and the wave theory of
moving particles, we have what is needed to
make sense of atomic structures.
When these concepts are linked together, they
give rise to a theory of the atom that agrees with
experiment.
The starting point will be the hydrogen atom.
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Atomic Spectra

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A spectroscope is an instrument used to observe the
color components of ANY light source.
The spectroscope allows us to analyze the light emitted
by elements when they are excited by various types of
energy (current or heat, for example).
When light from glowing atoms is viewed through a
spectroscope, we see the light consists of a number of
discrete (separate) frequencies rather than a continuous
spectrum.
The pattern of frequencies formed by a given element is
called the element’s atomic spectrum.

It is the element’s finger print.
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Atomic Spectra and Spectroscope
Atomic Spectra
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Bohr Model of the Atom
Niels Bohr proposed a theory in 1913 of
the hydrogen atom that accounted for its
stability and for the frequencies of the
spectral lines.
 Bohr applied the new quantum ideas to
atomic structure to come up with the
model, even though later it was replaced
by a more complex picture.

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Bohr Model of the Atom


Bohr proposed that an electron in an atom can
circle the nucleus without losing energy only in
certain specific orbits.
Atomic electrons can have only certain particular
energies because the energy of the electron
depends on which orbit it is in.
 Innermost orbit has the least energy
 Orbits are identified by a quantum number,
n, where
n=1 is the innermost orbit.
 Each orbit represents an energy level of the atom.
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Explaining Spectral Lines

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Atoms emit or absorb only light of certain frequencies,
which we see as spectral lines.
An electron in a particular orbit can absorb only those
photons of light whose energy will allow it to jump to
another orbit farther out, where the electron has more
energy.
When an electron jumps from an orbit to a closer orbit to
the nucleus, where it has less energy, it emits a photon
of light.
Difference in energy between the two orbits is hf, where f
is the frequency of the absorbed or emitted light.
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Electron Orbits in Hydrogen Atom
(Bohr Model)
The radius of each orbit
is proportional to the square
of the orbit’s quantum
number.
Ground State
Excited States
Each electron jump gives a photon of a characteristic
frequency and appears in the spectrum as a single bright line.
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Electron Waves and Orbits:
Standing Waves in the Atom

Why does an electron only follow certain
orbits??

The de Broglie wavelength of the electron is exactly
equal to the circumference of its ground-state (n=1 orbit).
The n=1 orbit of the electron in a hydrogen atom
corresponds to one complete electron wave joined on
itself.
Electron waves in an atom are analogous to standing
waves in a wire loop and leads to the concept:
 An electron can circle a nucleus only in orbits that
contain a whole number of de Broglie wavelengths.
(fig 8-27)


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The quantum number, n, of an orbit means
it is the number of electron waves that fit into
the orbit.
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Quantum Mechanics


The preceding theory of the hydrogen atom developed
by Bohr in 1913 accounts for much experimental data.
However, there are some limitations:



It does not account for the spectra of atoms that have 2 or more
electrons each.
Most important of all, it does not give an understanding of how
individual atoms interact with one another to form molecules,
solids, and liquids.
A more general approach of the atom was required and
in 1925-26 Erwin Schrödinger, Werner Heisenberg, and
other developed quantum mechanics.
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Quantum Mechanics
Probabilities, not Certainties

The real difference between Newtonian
mechanics and quantum mechanics lies in
what they describe.
 Newtonian
Mechanics (Chap 2) deals with the
motion of an object under the influence of
applied forces.
 The
values it predicts for observable quantities agree
with the measured values of those quantities.
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Quantum Mechanics
Probabilities, not Certainties

The real difference between Newtonian
mechanics and quantum mechanics lies in what
they describe.



With quantum mechanics the uncertainty principle radically alters
the meaning of “observable quantity” in the atomic realm, and
the position and momentum of a particle cannot be
simultaneously known.
Quantum mechanics explore probabilities.
Although quantum mechanics does not give us a look into the
inner world of the atom, it does tell us everything we need to
know about the measurable properties of atoms.
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Quantum Numbers
An Atomic Electron Has 4 in All

In the Bohr model of the hydrogen atom,
the electron moves around the nucleus in
a circular orbit.
 The
only quantity that changes is it position
on the circle.
 The single quantum number, n, is enough to
specify the physical state of an electron.
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Quantum Numbers
An Atomic Electron Has 4 in All
In the quantum theory of the atom, an
electron has NO FIXED ORBIT but is free
to move about in three dimensions.
 Think of the electron as circulating in a
probability cloud that forms a certain
pattern in space.

the cloud is most dense (2 is high),
the electron is most likely to be found.
 Where
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Probability cloud for the ground
state of hydrogen. The denser
the cloud, the more likely the
electron is to be found there.
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Quantum Numbers
An Atomic Electron Has 4 in All

Three quantum numbers determine the size and
shape of the probability cloud of an atomic
electron:
Quantum Number – (n) is the chief factor
that governs the electron’s energy.
 Orbital Quantum Number – (l) determines the
magnitude of the electron’s angular momentum.
 Magnetic Quantum Number – (ml) determines the
direction of the electron’s angular momentum.
 Principal
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The right hand rule for direction of angular momentum vector.
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Quantum Numbers
An Atomic Electron Has 4 in All

Spin Magnetic Quantum Number – (ms) is
the fourth quantum number and describes
the direction of electron spin.
 Electron
aligns itself so that its spin is along a
magnetic field, in which case ms has a value
of +1/2.
 Electron aligns itself so that its spin is
opposite a magnetic field, in which case ms
has a value of -1/2.
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Spin Magnetic Quantum Number
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Exclusion Principle
A different set of quantum numbers for each electron in an atom

In 1925, Wolfgang Pauli solved the
problem of the electron arrangement in an
atom that has more than one electron with
his exclusion principle.
 Only
one electron in an atom can exist in a
given quantum state.

Each electron in an atom must have a different set
of quantum numbers n, l, ml, and ms.
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The End
This link includes all kinds of physics info but
also has good info on the atom.
http://www.colorado.edu/physics/2000/index.
pl?Type=TOC
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