Download Brief history of the atom

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
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.
J.J. Thomson’s 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 ray’s 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 = 1*1011 coulombs per kilogram.
Today, the accepted value is 1.768 x1011 coulombs per kilogram
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”
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.
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.
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
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 Thompson’s charge to mass ratio, and Millikan’s charge, the mass of the electron
could then be calculated: m = 9.11x10-31 kg
The Photon
blackbody radiation
In the late 1800’s 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)
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.
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:
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.
In order to avoid the
UV catastrophe, Plank
discovered light is emitted in
Discrete energy units (quanta):
Energy of a photon:
E = hf
E: the energy
f: the frequency of light
h: a constant (Planck’s Constant) 6.63x10-34 j s
Energy of a photon:
E = hf
E: the energy
f: the frequency of light
h: a constant (Planck’s Constant) 6.63x10-34 j s
Since Planck’s 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 (1.6×10−19 C).
Therefore, one electron volt is equal to 1.6×10−19 J
h: Planck’s constant = 6.63x10-34 j s = 4.14x10-15 eV s
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
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)
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)
Enter Einstein:
Momentum of a photon:
p=h/
By substituting: E = hf and c = f  , --> E = hc/  --> E = pc
Therefore, the energy of a photon can be written as:
E = hf
E = hc/ 
E = pc
The product of Planck’s constant and the speed of light show up so
often that the AP exam will have a value listed in the constants table
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.
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
The Photoelectric Effect
Late 1800’s: 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.
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.
The Photoelectric Effect
Albert Einstein’s 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.
The Photoelectric Effect
Albert Einstein’s Explanation:
Einstein’s idea incorporated Planck’s 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 – ф
Ф: the Work Function: the energy needed to free
the electron.
hf: the total energy of the photon.
The Photoelectric Effect
Albert Einstein’s Explanation:
KEmax = hf – ф
The minimum energy (the threshold energy required to
remove an electron from the surface is easy to calculate,
set KE = 0. Therefore,
hfth = ф
This equation is often solved to find the threshold or cutoff frequency
The Photoelectric Effect
Albert Einstein’s 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 – ф
The Photoelectric Effect
Albert Einstein’s Explanation:
Slope = h
(planck’s constant )
X-intercept = fth (threshold frequency)
Y-intercept = -ф
(work function)
Compton Scattering (Verification that Photons have momentum)
1920’s: 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 photon’s obey the law of conservation of momentum, just like a particle
with mass.
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.
Compton Scattering
Classical mechanics:
m1v1i + m2v2i = m1v1f + m2v2f
Compton Scattering
Classical mechanics:
m1v1i + m2v2i = m1v1f + m2v2f
Momentum of a photon: p = h/λ
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 an electron: p = mv γ
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 photon’s obey
the law of conservation of momentum, just like a particle with mass.
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?
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…
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
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.
Implications of wave/particle duality on the Atom
Brief history of the atom
Ernest Rutherford’s model did not work!
The electrons would slowly spiral into the nucleus every time they gave
off energy.
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 it’s own unique spectrum.
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
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).
Implications of wave/particle duality on the Atom
Brief history of the atom
Absorption spectra of the Sun:
Implications of wave/particle duality on the Atom
Brief history of the atom
Emission and Absorption spectrum
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 Rutherford’s model, electrons that gave off continuous
energy would spiral into the nucleus of the atom. Another model of the
atom had to be made.
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).
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).
Implications of wave/particle duality on the Atom
Brief history of the atom
Implications of wave/particle duality on the Atom
Brief history of the atom
Energy levels of Bohr’s model of the H atom
Implications of wave/particle duality on the Atom
Brief history of the atom
Energy levels of Bohr’s model of the H atom
Energy =>
hf = Ei - Ef
Implications of wave/particle duality on the Atom
Brief history of the atom
Energy levels of Bohr’s model of the H atom
When using this equation E is the energy from
Bohr’s Energy level diagram.
Make sure E is converted into Joules
Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohr’s model:
Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohr’s 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
Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohr’s 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.
Implications of wave/particle duality on the Atom
Brief history of the atom
Problem with Bohr’s 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.
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 Bohr’s
Incorrect atomic model.
He extended the idea of wave-particle duality to matter, and said all matter
has wave like properties.
h = pλ
 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).
Implications of wave/particle duality on the Atom
Brief history of the atom
The DeBroglie Hypothesis
h = pλ
 wavelength of a particle
Not long after DeBroglie’s Hypothesis, Davisson and Germer conducted
an experiment to confirm the wave nature of matter.
Implications of wave/particle duality on the Atom
Brief history of the atom
Soon Schrodinger and Born added to DeBroglie’s 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)
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 DeBroglie’s 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)
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.
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.
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
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.
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.
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
Applications of Quantum Mechanics:
Tunneling
An electron wave has a probability of taking up a certain amount of
space, the actual location can’t 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
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 bar
Barrier
Electron wave function
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
Applications of Quantum Mechanics:
Tunneling
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.
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 1,000’s of
transistors