MODERN PHYSICS

1
MODERN PHYSICS
Electrons J.J. Thompson Robert
Millikan Photons Max Planck Albert
Einstein Photoelectric Effect Experiment The
Graph Energy Levels Absorption/Emission
Spectra Bohr Model De Broglie Wavelength Compton
Scattering
Nuclear Notation Energy-Mass Equivalence Nuclear
Decay Fission Fusion
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The Electron in Brief
We will mainly deal with Electrons and Photons in
this unit. Therefore, We will start with some
properties of each particle.
1897 J.J. Thomson Discovered the electron and
measured the properties of the particle (the
electron). However, his instruments were
crude. He could only measure the charge to mass
ratio, and not the charge or mass itself.
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J.J. Thomsons Experiment
In the year 1896 J.J. Thomson conducted an
experiment by which he defined the connection of
particles charge and its mass the Charge to
Mass ratio (q/m). He turned the cathode rays
beam on the collector. The beam transferred its
charge to the collector and warmed it. He knew
collector's mass, its specific heat and the heat
gain. He measured the temperature of the
collector using a light thermosteam fastened to
the collector. He measured the total charge
gathered on the collector using a very sensitive
electrometer.
  He obtained a value of q/m 11011 coulombs
per kilogram.
Today, the accepted value is 1.768 x1011 coulombs
per kilogram
4
The Electron in Brief
We will mainly deal with Electrons and Photons in
this unit. Therefore, We will start with some
properties of each particle.
1897 J.J. Thomson Discovered the electron and
measured the properties of the particle (the
electron). However, his instruments were crude.
He could only measure the charge to mass ratio,
and not the charge or mass itself.
1906 Robert Millikan devised an experiment to
measure the charge of the electron ( q
-1.6x10-19 C). This experiment is the famous
Millikan Oil Drop Experiment
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Millikan Oil Drop Experiment
An atomizer sprayed a fine mist of oil droplets
into the upper chamber. Some of these tiny
droplets fell through a hole in the upper floor
into the lower chamber of the apparatus. Millikan
first let them fall until they reached terminal
velocity due to air resistance. Using the
microscope, he measured their terminal velocity
and calculated the mass of each oil drop.
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Millikan Oil Drop Experiment
Next, Millikan applied a charge to the falling
drops by irradiating the bottom chamber with
x-rays. This caused the air to become ionized
(air particles lost electrons). A part of the
oil droplets captured one or more of those extra
electrons and became negatively charged.
By attaching a battery to the plates of the lower
chamber he created an electric field between the
plates that would act on the charged oil drops
he adjusted the voltage untill the electric field
force would just balance the force of gravity on
a drop, and the drop would hang suspended in
mid-air. Some drops have captured more electrons
than others, so they will require a higher
electrical field to stop.
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Millikan Oil Drop Experiment
When a drop is suspended, its weight  m g  is
exactly equal to the electric force applied, the
product of the electric field and the charge q
E. m g q E Millikan then simply solved
for q, the charge of the electron q (m g)
/E q -1.6x10-19 C
8
The Electron in Brief
We will mainly deal with Electrons and Photons in
this unit. Therefore, We will start with some
properties of each particle.
1897 J.J. Thompson Discovered the electron and
measured the properties of the particle (the
electron). However, his instruments were crude.
He could only measure the charge to mass ratio,
and not the charge or mass itself.
1906 Robert Millikan devised an experiment to
measure the charge of the electron ( q
-1.6x10-19 C). This experiment is the famous
Millikan Oil Drop Experiment
With Thompsons charge to mass ratio, and
Millikans charge, the mass of the electron could
then be calculated m 9.11x10-31 kg
9
The Photon
blackbody radiation

In the late 1800s scientists had been working a
way to describe how hot objects cool by giving
off light in various parts of the electromagnetic
spectrum. The study of this effect is known as
blackbody radiation.
Blackbody An ideal object that emits and
absorbs radiation Blackbody Radiation The
electromagnetic radiation given off by a
blackbody at a given temperature
You have seen blackbody radiation. Any
object That is hot enough gives off light
(blackbody radiation)
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The Photon
blackbody radiation

If an object is hotter than its surroundings it
will cool by giving off light. In order to study
this effect scientist had to eliminate the other
modes of cooling. Blocks of graphite were
hollowed and a small hole was drilled into the
carbon. Although the outside of the carbon block
would cool by convection as well as radiation,
the inside would cool by mostly radiation alone.
The intensity of each wavelength of light emitted
by the inside of the hot, black boxes was
studied, hence the name- blackbody radiation.
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blackbody radiation
James Clark Maxwell had discovered the equations
that governed the production and transmission of
these waves through space and time.

A serious problem arose when the electromagnetic
spectrum emitted by a radiating body did not
match the spectrum that should be produced from
the mathematical model of light. The fact that
the classical theory did not match the actual
spectrum emitted by blackbodies came to be known
as the ultra-violet catastrophe.

• Classical Model, as Energy increases,
• the intensity should increase

Real Life
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blackbody radiation
1900 Max Planck developed a mathematical model
that fit the blackbody radiation data without
using any known theory. The idea was to find
what function worked and then determine what the
theory would be. Much to the surprise of Planck,
the mathematical model that worked called for
light to be jumping off the hot objects in bits
and pieces like particles instead of waves.

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Energy of a photon
In order to avoid the UV catastrophe, Plank
discovered light is emitted in Discrete energy
units (quanta)
E hf
E the energy f the frequency of light h a
constant (Plancks Constant) 6.63x10-34 j s
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Energy of a photon
E hf
E the energy f the frequency of light h a
constant (Plancks Constant) 6.63x10-34 j s
Since Plancks constant is so small, another way
to express It is in terms of the electronvolt
(eV). 1 eV is equal to the amount of kinetic
energy gained by a single electron when it
accelerates through an electric potential
difference of one volt. Thus it is 1 volt (1
j/C) multiplied by the electron charge
(1.610-19 C). Therefore, one electron volt is
equal to 1.610-19 J
h Plancks constant 6.63x10-34 j s
4.14x10-15 eV s
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Enter Einstein
1905 Albert Einstein, while working on his
theory of relativity, discovered a few more
properties of light. 1. Photons travel at v c
in a vacuum. c 3x108 m/s
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Enter Einstein
1905 Albert Einstein, while working on his
theory of relativity, discovered a few more
properties of light. 1. Photons travel at v c
in a vacuum. c 3x108 m/s 2. Although photons
are particles, photons have no rest mass
(rest mass is the mass of a stationary
object) (no rest mass is
unique to photons, everything else has a mass)
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Enter Einstein
1905 Albert Einstein, while working on his
theory of relativity, discovered a few more
properties of light. 1. Photons travel at v c
in a vacuum. c 3x108 m/s 2. Although photons
are particles, photons have no rest mass
(rest mass is the mass of a stationary
object) (no rest mass is
unique to photons, everything else has a
mass) 3. Although photons do not have mass, they
have momentum
p h / ? (p h / ? only applies to
photons, for all other objects, use p mv)
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Enter Einstein
Momentum of a photon p h /
? By substituting E hf and c f ? ,
--gt E hc/ ? --gt E pc Therefore,
the energy of a photon can be written as E
hf E hc/ ? E pc
The product of Plancks constant and the speed of
light show up so often that the AP exam will have
a value listed in the constants table
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Example Problem
A 3-milliwatt pen laser radiates at 633 nm. Find
values for the following a) Frequency of light
emitted b) energy of a single photon in joules,
c) energy of a photon in electron volts d)
momentum of a single photon.

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Example Problem
A 3-milliwatt pen laser radiates at 633 nm. Find
values for the following a) Frequency of light
emitted, b) energy of a single photon in
joules, c) energy of a photon in electron volts,
and d) momentum of a single photon
a) c f? or f c/? 3x108m/s / 633x10-9 m f
4.74x1014 Hz   b) E hf 6.63x10-34 Jsec
(4.74x1014 1/s) E 3.14x10-19 J   c) E hf
4.14x10-15 eVs (4.74x1014 1/s) E 1.96
eV d) p h/? 6.63x10-34 Jsec/ 6.33x10-9 m
or p E/c 3.14x10-19 J / 3x108m/s p
1.05x10-27 Nsec  
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The Photoelectric Effect
Late 1800s Heinrich Hertz noticed that under
the right conditions UV light could cause sparks
to fly from metal surfaces.
This
phenomenon was labeled the
photoelectric
effect.
photoelectric effect - The emission of electrons
from material as a result of light falling on it
What did not make sense about the phenomena was
that only light above a certain threshold
frequency would cause the electrons to be ejected
from the surface.  Light below that frequency,
regardless of its brightness would not knock
electrons off the surface.
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The Photoelectric Effect
Principle observations
1. Electrons are emitted only when the frequency
of light is above the threshold value, no matter
how intense the light is.
2. Using a setup similar to the one shown below,
they found that the KE of the ejected electrons
is directly proportional to the frequency of the
light hitting the metal surface.
3. It was also discovered that the current in the
circuit is proportional to the brightness of the
light hitting the metal, but only if the
threshold frequency of the metal was exceeded.
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The Photoelectric Effect
Albert Einsteins Explanation
In 1905 Albert Einstein gave a very simple
explanation of the photoelectric effect
Light is acting like particles. Each electron
can absorb a single photon. When you increase
the intensity of light more photons are created
and liberate more electrons. This explains the
liner relationship between the intensity of the
light source and the photocurrent.
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The Photoelectric Effect
Albert Einsteins Explanation
Einsteins idea incorporated Plancks quantum
hypothesis into a statement of energy
conservation The energy (hf) of the photon must
be equal to the energy needed to free the
electron plus the electron's KE KEmax hf ?
? the Work Function the energy needed to free
the electron.
hf the total energy of the photon.
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The Photoelectric Effect
Albert Einsteins Explanation
KEmax hf ?
The minimum energy (the threshold energy required
to remove an electron from the surface is easy to
calculate, set KE 0. Therefore, hfth ?
This equation is often solved to find the
threshold or cutoff frequency
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The Photoelectric Effect
Albert Einsteins Explanation
Einstein predicted that every metal should
produce a linear graph of the stopping voltage as
a function of frequency. And that all of the
graphs should have the same slope.
The equation for the line is Y mx
b Remember KEmax hf ?
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The Photoelectric Effect
Albert Einsteins Explanation
Slope h (plancks constant
) X-intercept fth (threshold frequency)
Y-intercept -? (work function)
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Compton Scattering (Verification that Photons
have momentum)
1920s Arthur Compton discovered that a photon
loses energy when it collides with an object
(electron).
The momentum was transferred, not as a wave, but
just like Billiard balls colliding with each
other. The photons were behaving like
particles. The photons obey the law of
conservation of momentum, just like a particle
with mass.
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Compton Scattering
The particle with mass gains energy and momentum
during the collision and the scattered photon
loses energy and momentum. Photons can be
scattered in any direction after the collision.
The shift in wavelength is dependant on the angle
of scattering. The bigger the angle, the greater
the loss of energy of the photon.
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Compton Scattering
Classical mechanics m1v1i m2v2i m1v1f
m2v2f
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Compton Scattering
Classical mechanics m1v1i m2v2i m1v1f
m2v2f
The set up of the problems are the same as
classical mechanics. You just have to use the
different momentum equations. Remember, if the
particles deflect at angles, you need to break
them into the X and Y components.
Momentum of a photon p h/? Momentum of an
electron p mv ?
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Compton Scattering
Fortunately, there are no Compton scattering
problems on the AP exam, only questions dealing
with the implications of Compton Scattering

Main point of Compton Scattering Compton
verified that photons obey the law of
conservation of momentum, just like a particle
with mass.
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Implications of wave/particle duality on the Atom
Einstein showed that many aspects of light can
only be predicted if we assume light is a
particle. Yet it also acts as a wave
(diffraction/interference). This is called the
Wave/Particle duality of light. It is both a wave
and a particle or something else that we can
only measure as a wave or particle.
If light can behave as a particle, can a particle
behave as a wave?
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Implications of wave/particle duality on the Atom
So far we showed that many aspects of light can
only be predicted if we assume light is a
particle. Yet it also acts as a wave
(diffraction/interference). This is called the
Wave/Particle duality of light. It is both a wave
and a particle or something else that we can
only measure as a wave or particle.
If light can behave as a particle, can a particle
behave as a wave? Yes, De Broglie generalized
Einstein's wave/particle duality of a photon.
The atom can only be fully explained if we
assume it is a wave
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Implications of wave/particle duality on the Atom
Brief history of the atom
1904 J.J. Thomson Plum Pudding Model
Based on his discovery of the (-) electron, he
hypothesized that the electrons were evenly
distributed in a positive substance. (Electrons
were the raisins, the pudding was the positive
charge)
The nucleus had not been discovered yet
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Implications of wave/particle duality on the Atom
Brief history of the atom
Ernest Rutherford Electron Orbit Model Mass is
in the Nucleus, electrons orbit 1911 Rutherford
conducted a Gold Foil Experiment, where he shot
alpha particles through a thin foil of Gold.
Almost all of the particles went straight through
the gold. However, some were deflected. Based
on this information, he concluded that the atom
was mostly empty space. Therefore, the mass of
the atom was contained mostly in a tiny nucleus,
and electrons orbited the nucleus like planets
orbiting the sun.
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Implications of wave/particle duality on the Atom
Brief history of the atom
Ernest Rutherfords model did not work!
The electrons would slowly spiral into the
nucleus every time they gave off energy.
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Implications of wave/particle duality on the Atom
Brief history of the atom
Before we go to the next model, we must
understand Spectral lines.
Spectroscopy The study of spectra which results
in diffracting light into its component colors
Spectra is thought of as the fingerprint of
matter. Each element has its own unique
spectrum.
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Implications of wave/particle duality on the Atom
Brief history of the atom
Spectroscopy plays a major role in determining
the chemical composition of substances. Most of
modern chemistry and astronomy depends on
spectroscopic analysis of materials.

MR spectroscopy of a region of the brain to
detect a tumor
Spectroscopic data of a galaxy to determine its
composition
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Implications of wave/particle duality on the Atom
Brief history of the atom

Two types of Spectra
Emission Series of light lines, each represent
a particular wavelength of light. Caused by
electrons giving off energy (dropping down an
energy level). Absorption Series of dark
lines in a spectrum, each line represents a
particular wavelength of light that is absorbed.
Caused by electrons accepting energy (moving up
an energy level).
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Implications of wave/particle duality on the Atom
Absorption spectra of the Sun
Brief history of the atom
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Implications of wave/particle duality on the Atom
Brief history of the atom

Emission and Absorption spectrum
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Implications of wave/particle duality on the Atom
Brief history of the atom

Spectroscopy
Physicists could use spectroscopy to determine
compositions, temperatures, velocities, etc of
many different object. Charts were made of the
spectra of each element. However, no one could
determine the exact cause of the spectral
lines. According to Rutherfords model,
electrons that gave off continuous energy would
spiral into the nucleus of the atom. Another
model of the atom had to be made.
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Implications of wave/particle duality on the Atom
Brief history of the atom
Neils Bohr Energy Level Model 1913 In order
to explain line Spectra, Bohr modified
Rutherford's model by saying electrons can only
have special orbits, and electrons can only jump
between these certain orbits (energy levels). In
order to jump between orbits, electrons could
only accept or give off discrete quanta of
energy (quantum leaps).
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Implications of wave/particle duality on the Atom
Brief history of the atom
Neil's Bohr Energy Level Model 1913 In order
to explain line Spectra, Bohr modified
Rutherford's model by saying electrons can only
have special orbits, and electrons can only jump
between these certain orbits (energy levels). In
order to jump between orbits, electrons could
only accept or give off discrete quanta of
energy (quantum leaps).
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Implications of wave/particle duality on the Atom
Brief history of the atom
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Implications of wave/particle duality on the Atom
Brief history of the atom
Energy levels of Bohrs model of the H atom
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Implications of wave/particle duality on the Atom
Brief history of the atom
Energy levels of Bohrs model of the H atom
Energy gt hf Ei - Ef
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Implications of wave/particle duality on the Atom
Brief history of the atom
Energy levels of Bohrs model of the H atom
When using this equation E is the energy from
Bohrs Energy level diagram. Make sure E is
converted into Joules
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Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohrs model
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Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohrs model It only works for
Hydrogen, or Ionized Helium (Helium with only 1
electron) His model does not work for any atom
with more than 1 electron
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Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohrs model It only works for
Hydrogen, or Ionized Helium (Helium with only 1
electron) His model does not work for any atom
with more than 1 electron
So why is his model important? He has the
correct concept (Energy levels). This led the
way into a more correct model of the Atom.
53
Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohrs model It only works for
Hydrogen, or Ionized Helium (Helium with only 1
electron) His model does not work for any atom
with more than 1 electron
So why is his model important? He has the
correct concept (Energy levels). This led the
way into a more correct model of the Atom.
54
Implications of wave/particle duality on the Atom
Brief history of the atom
The DeBroglie Hypothesis
In 1924 Louis DeBroglie used the concepts of
energy levels from Bohrs Incorrect atomic
model. He extended the idea of wave-particle
duality to matter, and said all matter has wave
like properties. h p? ? wavelength of a
particle His model turned the electron into a
wave. It states that a whole number of
wavelengths must fit into the orbital in order
for the orbital to be valid. (This means each
electron wave has to be in a discrete energy
level).

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Implications of wave/particle duality on the Atom
Brief history of the atom
The DeBroglie Hypothesis
h p? ? wavelength of a
particle

Not long after DeBroglies Hypothesis, Davisson
and Germer conducted an experiment to confirm the
wave nature of matter.
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Implications of wave/particle duality on the Atom
Brief history of the atom

Soon Schrodinger and Born added to DeBroglies
hypothesis. After Schrodinger and Born, the
electron wave model could predict any energy jump
of any atom on the Periodic table (s,p,d,f
orbitals)
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Implications of wave/particle duality on the Atom
Brief history of the atom

Each orbital is a different wave harmonic
where constructive interference occurs.
The electron is not in the energy cloud, it is
the energy cloud.
Soon Schrodinger and Born added to DeBroglies
hypothesis. After Schrodinger and Born, the
electron wave model could predict any energy jump
of any atom on the Periodic table (s,p,d, and f
orbitals)
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The Atom as a wave
What do atoms look like when viewed through
scanning tunneling microscopes? Waves!

Actual image from a STM. This is an Ag atom.
The constructive interference peak is the
nucleus, the diffraction pattern around the peak
are the electrons.
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The Atom as a wave
What do atoms look like when viewed through
scanning tunneling microscopes? Waves!

Actual image from a STM. This is a copper
surface with two non-copper atoms creating an
electron diffraction pattern. The electrons are
the waves. The impure atoms are the destructive
interference troughs.
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The Atom as a wave
What do atoms look like when viewed through
scanning tunneling microscopes? Waves!

Actual image from a STM. This is a ring of 48
iron atoms. The wavelike crests and Troughs are
the electrons. The constructive interference
peaks are the iron nuclei
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The Atom as a wave
What do atoms look like when viewed through
scanning tunneling microscopes? Waves!

Actual image from a STM. This is a another ring
of 8 iron atoms. The ring creates a trap for the
electrons, and sets up a standing wave pattern in
the ring. These standing waves are the
electrons.
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The Atom as a wave
What do atoms look like when viewed through
scanning tunneling microscopes? Waves!

Actual image from a STM. This is another ring
of metal atoms with two different atoms in the
centers. Again, the wave patterns are the
electrons.
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Applications of Quantum Mechanics
When physicists started thinking of the electron
(as well as P and N) as a wave/particle duality,
many breakthroughs were made and new technologies
still continue to be developed.
1. Tunneling 2. Entanglement
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Applications of Quantum Mechanics
Tunneling
An electron wave has a probability of taking up a
certain amount of space, the actual location
cant be known (uncertainty principle). If it
were near a barrier, there is a small chance it
will be on the other side of the barrier.
Electron is placed here
65
Applications of Quantum Mechanics
Tunneling
If the wave function is calculated, and there is
a probability of 5 of the electrons on the other
side of the barrier. This means, 5 of the time,
the electrons will actually be on the other side
of the barrier.
Barrier
Electron wave function
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Applications of Quantum Mechanics
Tunneling
This is an easy way to control the flow of
current in a circuit. A semiconductor uses the
quantum properties of tunneling. Semiconductors
are a vital part of almost any circuitry
Barrier
5 of the time, the electron is actually here
67
Applications of Quantum Mechanics
Tunneling
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Applications of Quantum Mechanics
Tunneling
After semiconductors were invented, the computer
revolution started. Without semiconductors, there
would be no computers and very few
other electronic devices. (Semiconductors used
in circuits include diodes, transistors, and
microchips which are made of transistors)
Standard key hole transistors
Model of the 1st transistor, built in 1947
New Surface Mount transistors are the size of a
grains of sand. Transistors integrated into
chips are currently in the size range of
nanometers, soon they will be in the size range
of atoms.
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Applications of Quantum Mechanics
Tunneling
The standard personal computer/laptop now has
approximately 150 million transistors High end
computers have approximately 1.5 billion
transistors Approximately every 18 months, the
number of transistors in a computer doubles
This microchip performs computations using
1,000s of transistors