Quantum Mechanics and Modern Physics

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Quantum Mechanicsand Modern Physics

• Science Engineering Magnet High
• Mr. Puckett

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First Atomic Theory

• The notion that all matter consists of
  fundamental particles called atoms was first put
  forward by the Greek philosophers Leucippus and
  his disciple Democritus, in the 5th century BC.
• These men taught that everything is composed of
  infinitely tiny indivisible particles called
  atoms. The word atom, from the Greek, means
  "indivisible."

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First Atomic Theory continued

• The notion of atoms was rejected by other
  philosophers--most significantly Aristotle, who
  believed all matter was infinitely divisible.
• Others believed there were only four elements
  earth, air, fire, and water. These "nonatomic"
  beliefs dominated Western thought for centuries.
  Only in the early modern era did the concept of
  atoms regain acceptance. Today, however, atoms
  are known to be divisible into subatomic
  particles, such as electrons, protons, neutrons,
  and quarks1

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John Daltons Atomic Theory

• John Dalton's Atomic theory in the late 1700's
  explained the nature of chemical reactions and
  the similarity of certain elements. It
  included
• A. All elements are composed of tiny indivisible
  particles called atoms. ( Incorrect in long run)
• B. Atoms of the same element are identical.
• C. Atoms of different elements can combine with
  one another to form compounds.
• D. Chemical reactions occur when atoms are
  separated, joined or rearranged.

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JJ Thompson discovers the Electron

• The discoverer of the electron as a separate
  subatomic particle was J.J. Thompson in 1897.
  He realized that the accepted model of an
  indivisible atom did not take electrons and
  protons into account. He used a cathode ray tube
  that bent an electron beam in EM fields.
• He suggested a revised model that was compared to
  a "plum pudding atom" because it said that
  negatively charged electrons (raisins) stuck into
  a lump of positively charged protons (the dough).
  

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JJ Thompsons Cathode Ray Tube

• Thompson generated electric rays by using a
  pair of oppositely charged plates that were set
  in an evacuated tube. When this was done, a
  small glowing spot appeared at the opposite end
  of the tube. Thompson noticed that if a magnetic
  field was applied to the beam, the spot on the
  opposite side of the tube moved. This implied
  that the ray was composed of a negatively
  charged particle which responded to the magnetic
  field according to the equation F qvB ma.

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Thompsons Cathode Ray Tube

• Thompsons CRT measured the charge to mass ratio
  and gave evidence of electrons.

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Electrons from a CRT

• What Thompson had discovered were electrons,
  which were being stripped off the cathode by the
  strong voltage as shown in the diagram. Although
  he was not able to see individual electrons, the
  amount of deflection they experienced while
  traveling through the tube depended upon the
  electrons mass and charge.

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Millikans Oil Drop Experiment

• Millikan used an atomizer to create tiny drops of
  oil that were given an electric charge and
  allowed to fall between two charged plates.
• The mass of a given oil drop can be calculated by
  the rate at which it falls when the electric
  field is turned off. The electric field is then
  turned on and the drop is brought to a halt. At
  this point the electrical force on the drop and
  the gravitational force on the drop are equal
  (qEmg) and the total charge on each drop can be
  calculated.

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Millikans Oil Drop Experiment
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Determined the Elemental Charge on the Electron

• After calculating the charge on many drops,
  Millikan noticed that the charge on each drop was
  always a multiple of a common factor, 1.6x10-19C,
  which he reasoned was the fundamental electric
  charge. Although he did not know it at the time,
  he had discovered the charge of the electron.

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Ernest Rutherford Discovered the Nucleus with the
?- Gold Foil Lab

• Ernest Rutherford discovered the nucleus in 1911
  and proposed the nuclear atom in which electrons
  surround a dense nucleus.
• He thought of the rest of the atom as empty
  space. But the electrons are negatively charged
  and the nucleus (protons) are positively charged.
  

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Rutherfords Discovery of the Nucleus with the
Gold Foil Lab

• After the discovery that radioactive elements
  emitted rays of various types, physicists
  rushed out to shine beams of rays at different
  substances.
• Rutherford shone a beam of alpha particles,
  actually a beam of helium nuclei, at a thin sheet
  of gold foil. Most alpha particles behaved as
  expected, being deflected slightly or not at all.
  However, occasionally an alpha particle would be
  knocked almost backwards.

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The Dense Nucleus makes itself Known in a Big Way

• Rutherford said, This unexpected result was
  equivalent to firing an artillery shell at a
  sheet of tissue paper and having the artillery
  shell bounce back!
• These results implied that the alpha particles
  would occasionally strike a small, incredibly
  dense object Rutherford had discovered the
  nucleus!
• Note this question was asked in both 82 and 97.

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Rutherfords Gold Foil Lab
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Rutherford Experiment CloseUp
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The Bohr Atomic Model - (Solar System)

• Neils Bohr developed the next stage of the atomic
  theory in 1913 with the Bohr model.
• It proposes that the electrons are in concentric
  circular orbits around the nucleus. The model
  was patterned after our solar system with the sun
  in the center (nucleus) and the planets
  (electrons) orbiting around it.
• The energy that the orbiting provides prevents
  the electrons from falling into the nucleus

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Energy Levels of Electrons

• The ENERGY LEVEL of an electron is the region
  around the nucleus where it is most likely to be
  found.
• The different energy levels are analogous to the
  rungs of a ladder. The higher you go up the
  ladder (away from the nucleus) the higher the
  energy .
• Electrons can also climb the ladder and jump
  from one energy level to the next ( energy must
  be provided or taken away in the proper amount).

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Energy Orbitals of the Electrons

• Electron energy orbitals are the regions where
  there is the greatest chance to find them as
  clouds

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Electron Orbitals

• Electrons cannot stay between levels and will
  naturally migrate to their appropriate level.
  However, unlike the rungs of a ladder, the energy
  levels are not equally spaced.
• A QUANTUM of energy is the amount of energy
  required to move an electron from its present
  energy to the next higher level. Thus the
  energies of electrons are said to be quantized.
  The term , quantum leap, is used to describe an
  abrupt change

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The Birth of Quantum Mechanics

• It all began when Max Planck (1900) was trying
  to explain the glow of a hot glowing blackbody
  like an electric stove eye.
• A black object absorbs all wavelengths of light,
  yet glows red with high temperature. Higher temps
  yield yellow and white light. The spectrum fit an
  empirical formula when he assumed that the energy
  was not continuous, but small discrete amounts.
  These amounts were called Quanta

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Origin of the Word Quantum

• The light emitted by a glowing piece of iron, for
  instance, was actually "grainy," composed of
  minuscule light "grains" too small to be seen.
• Planck called a light "grain" a quantum, from the
  Latin word meaning "how much?"

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Temperature and Wavelength of Light

• Weins Law was the basis for the wavelength
  calculations based upon temperature for Plancks
  energy constant.
• Formula ? T 2.9 x 10-3 m.K

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Quanta comes in Specific Amounts

• Planck proposed that electrons, for some unknown
  reason, can give off light only in certain
  specific amounts of light energy--in quanta.
• Only whole quanta can be given off, never a
  fraction of a quantum.
• The energy of these quanta varies directly with
  the frequency of the light. Energetic light of
  higher frequency, such as violet or ultraviolet
  light, consists of higher-energy quanta than does
  light of lower frequency, such as red or infrared
  light.

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Plancks Constant Describes the Energy of a
Quantum

• The energy of Plancks constant is the energy
  needed to promote electrons to the next higher
  energy orbital based upon frequency. E hf
• The formula became Enhf where n is the
  whole number multiple of h (Plancks constant
  6.6 x10-34 J.s) and f is the frequency of
  light photons.

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Plancks Constant of KE vs. Frequency
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Plancks Constant Energy Level

• Planck's constant is expressed in terms of energy
  multiplied by time--a unit called action--and may
  be given in erg-seconds or joule-seconds. An erg
  is defined as the amount of energy needed to
  raise a milligram (roughly the weight of a grain
  of sand) a distance of 1 centimeter (about 1/3
  inch). This is not a great deal of energy.

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Einstein Uses Plancks Constant for the
Photoelectric Effect

• In 1905 the German-born physicist Albert Einstein
  used Planck's quantum theory to explain the
  photoelectric effect, in which charged particles
  such as electrons are emitted from certain
  materials when light (electromagnetic radiation)
  strikes the materials - mostly metals.
• This is the topic of Einsteins Nobel Prize- not
  Relativity.

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Plancks Threshold Electron Ejection
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Einstein Explained Plancks Constant with the PE
of the Photoelectric Effect

• Albert Einstein said that the electrons around an
  atom were trapped in a potential energy well.
  If an electron was to escape the well it would
  have to be struck by a single photon of light
  which would have enough energy to kick the
  electron out of the well.  
• Chemists call this the ionization constant the
  amount of energy needed to remove electrons.
• This question was asked on the AP test in 1997.

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The KE of Electrons with Escape Velocity from the
Atom

• Photons with a frequency of fo have just
  enough energy to accomplish this. Photons with
  higher frequencies not only have enough energy
  for the electron to escape, but have extra energy
  to give the electron additional kinetic energy,
  KEmax in the diagram.

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Work Function Exciting the Electrons Up

• The Energy required to take the electron from the
  one level and promote it to a higher level is
  found with the Work Function W?E hfo
  where h is Plancks constant and fo is the
  threshold frequency to promote the electron.
• The KE of an ejected electron is the quantum
  energy the work function. KE hf hfo .
  The difference is the amount of energy for the
  kinetic energy ½ mv2.

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Photon Energy Problem
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Photon Speed and Energy
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Photoelectric Effect Diagram

• In this lab the light shines on the metal and has
  enough energy that it knocks electrons off the
  metal into a detector that causes a current
  through the circuit.

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Einstein proposes Quanta Energy Levels of
Electrons

• Einstein also proposed that electrons, besides
  emitting electromagnetic radiation in quanta,
  also absorb it in quanta.
• Einstein's work demonstrated that electromagnetic
  radiation has the characteristics of both a
  wave--because the fields of which it is composed
  rise and fall in strength--and a
  particle--because the energy is contained in
  separate "packets." These packets were later
  called PHOTONS.

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Comptons Scattering Effect

• This experiment was similar to the Rutherfords
  experiment except that the beam was composed of
  particles of light, called photons. In this case
  a photon stuck an atom, knocked an electron off
  the target, and was then deflected. The only way
  a photon can knock an atom out of an electron
  is if the photon had momentum. This suggested
  that photons were particles.
• However, the scattered photon did not seem to
  change speed during the collision, but rather
  changed their frequency.

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Comptons Scattering Effect

• This suggested that photons were actually waves
  that travel at the speed of light, changing
  frequency as energy is lost.
• Comptons conclusion? Photons can act as both
  waves and as particles depending on the
  situation. This question was asked in 1982.

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Michelson Morley Determined the Speed of Light

• Michelson and Morley first proposed the
  experiment to find the speed of the Earth through
  the ether that filled the universe.
• A single beam of light was split into two paths
  and then rejoined at an observation scope. If
  the Earth was traveling to the right through the
  Ether Wind the light traveling at right angles
  to the wind would be blown off course and
  require more time to reach the telescope.

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Michelson Morley Experiment Continued

• By allowing the two beams to interfere with each
  other, sight differences in the speed of the two
  beams could be calculated. By measuring the
  difference in the speed of the two beams, the
  speed of the Earth through the Ether could be
  worked out.
• It turned out that no matter how the experiment
  was set up, the speed of light in both directions
  remained constant. Thus no Ether.
•  Note Although this question was asked in both
  1982 and 1987, relativity is no longer on the AP

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Michelson-Morley Experiment

• The Michelson- Morley Interferometer was used to
  measure the speed of light and measure the
  Ether. It never found the ether, but did
  establish 2.99 x 10 8 m/s as the speed of light.

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Nuclear Reactions

• It was originally thought that the fundamental
  particle of matter was the atom and that atoms
  could neither be created nor destroyed.
• The discovery that atoms were made up of protons,
  neutrons, and electrons suggested the possibility
  that one type of atom could be transformed into
  another type of atom by adding or subtracting
  these fundamental particles.
• The reactions are either FUSION or FISSION.

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Nuclear Fusion in the SUN !

• This happens every day as hydrogen isotopes are
  transformed into helium in the sun.
• In this type of equation, atoms are written in
  the form where X is the atomic symbol, Z is the
  atomic number of the atom (basically the number
  of protons an atom contains) and A is the mass
  number of the atom (the total number of protons
  and neutrons in the atom). AZX Example 21H is
  deuterium (heavy hydrogen)

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Nuclear Fusion Formula

• Fusion is the nuclear reaction that combines the
  hydrogen isotopes into helium and releases huge
  amounts of energy as in the sun and stars.
• The equation is 21H 31H ? 42 He 10n E

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Nuclear Fission Reaction

• Fission is the process of breaking down the
  nucleus by physical bombardment with neutrons of
  other decaying radioactive atoms.
• This is the type of reaction that is used in
  modern nuclear reactors and was the first Atomic
  Bomb mechanism.

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Nuclear Fission Reaction

• As the first nucleus decays it gives off 3
  neutrons that strike other atoms and cause them
  to decay in a cascading reaction.

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Nuclear Power Reactor

• A nuclear reactor is a complex heat exchanger
  with a steam driven generator.

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The Infamous E mc2

• Under normal conditions, the total number of
  fundamental particles in an atomic reaction
  remains constant. The exception usually occurs
  in particle accelerators, black holes, and other
  unpleasant environments where there is enough
  excess energy to create new matter according to
  the Einsteins equation Emc2.
• An electron and a proton can also combine to form
  a neutron, which usually occurs only under very
  high pressures.

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Mass and Energy are Equivalent

• Atoms form because it requires less energy for
  two protons and two neutrons to exist as a He
  atom than as separate particles.
• Since Einstein showed that mass and energy are
  equivalent (Emc2) we can directly measure the
  energy content of atoms by measuring their mass.

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The Loss of Mass in Fusion gives ENERGY !!

• Since He consists of two protons and two
  neutrons, we can estimate the mass of a He atom
  as 2(mn1.008665 au) 2(mp1.007825 au)
  4.032980 au
• However, the measured mass of the He atom is
  only 4.002603 au, a difference of 0.0030377 au.
  

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Energy Release from Fusion

• This mass deficit may seem small, but if we use
  Einsteins formula to convert this mass into
  energy we get Emc2
• E (0.00303)(6.66x10-27 kg)(3x108m/s)2
  4.5 x10-13 Joules.
• This does not seem like a lot of energy, but
  remember this is for just one atom. The process
  of making a mole of He atoms releases 2.7x1011 J

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Radioactive Decay The Three Products

• The weak nuclear force in nature is responsible
  for Radioactive Decay the spontaneous splitting
  of radioactive isotopes gradually into more
  stable elements and energy release.
• There are three decay products the Alpha
  particle, Beta particle and the Gamma Ray.

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Decay Particles from Fission

• The Alpha particle (??) is the nucleus of the
  Helium atom. When it is given off the atomic
  number reduces by 2 and mass number by 4 and
  changes to a new element.
• The Beta particle (?) is a high speed electron
  from a neutron and leaving a proton that
  increases the atomic number by 1.
• The Gamma Ray (?) is an energy ray without mass.

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Alpha Particle Decay

• Example When Uranium-238 decays by an alpha
  decay the result is a helium nucleus and a
  thorium-234 atom. Notice that as in any
  chemical equation, the summation of the mass
  before and after the reaction adds up.
• 23892 U ? 42He 23490Th

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Beta Particle Emission

• The beta particle is actually a high speed
  electron. It originates from the decay of a
  neutron (0) in the nucleus into a proton(1) and
  an electron(-1). This causes a change of 1 to
  the atomic number and a ZERO change to the Mass
  number. Remember the electron is 1/1830 the mass
  of a proton.
• Example If an carbon-14 decays into a
  nitrogen-14 the formula looks like
• 146C ? 147N e- a neutrino

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Gamma Emission

• The gamma emission is a photon of very high
  energy. The decay of a nucleus by emissions of a
  gamma ? ray is much like emission of photons by
  excited atoms. Except this time it is an excited
  nucleus with a lot more energy. Since it is only
  energy, there is NO CHANGE in mass or charge.
  Gammas are deadly ionizing radiation. Neutron
  bombs work from this mechanism.
• AZ N ? AZ N ?

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Radioactive Half Life

• The half-life of a radioactive material is the
  amount of time it takes for ½ of the mass of a
  radioactive isotope sample to decay spontaneously
  into new material. Two versions of the formula
  are ?N - ?N ?t and N Noe-?t where ? is
  the decay constant and N is the number of
  radioactive nuclei. The shortcut formula is T ½
  0.693/ ?
• Half-lives can range from a fraction of a second
  to billions of years. Carbon-14 has a ½ life of
  5370 years while U-238 has a 2.3 billion year
  half life.

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Erwin Schrodingers Wave Equations for Electron
Orbitals

• Erwin Schrodinger took the atomic model another
  step in 1926, when he used the new quantum theory
  to write and solve an equation describing the
  location and energy level of an electron.
• The most modern description of the position of
  the electrons is the Quantum Mechanical Model.
  It is not a description of an exact pathway of
  the electron but is concerned with the likelihood
  of finding an electron in a certain position.
  The mathematical probability is artistically
  portrayed as a blurry cloud of negative charge.

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The Quantum Atom Model

• QUANTUM MECHANICAL MODEL of the atom designates
  the energy levels of electron and are designated
  by 4 numbers to describe the energy level,
  orbital and sub-orbital and the spin property.

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Quantum Mechanics of Atomic Orbitals

• ATOMIC ORBITALS are regions in space where there
  is a high probability of finding an electron.
  There are a maximum of two electrons per orbital.
  They will fill the atomic orbitals in a specific
  filling pattern.
• Quantum Mechanics is an accounting system to map
  out the electrons of an atom.

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Quantum Numbers of Hydrogen

• The Principle Quantum number is an integer value
  of the energy orbital.
• The Orbital quantum number is the orbital type
  s, p, d, f
• The Magnetic quantum number is the direction of
  the angular momentum.
• The Spin quantum number is the direction of
  electron rotation ½ or - ½ that gives rise
  to the magnetic properties within the structural
  domain.

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Quantum Numbers for Electrons
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Atomic Orbital Shapes

• Different atomic orbitals are denoted by letters.
  
• S - orbitals are spherical clouds.
• P-orbitals give pear or dumbbell-shaped clouds.
  The shapes of d-orbitals and f-orbitals are more
  complex than what we will study this year.
• Just as the clouds in the sky that you see,
  these clouds of probability are not sharp edged.
  They just gradually disappear.

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Light and Atomic Spectra

• The work that led to the development of the
  quantum mechanical model came from the study of
  light.
• Light is considered to consist of
  electromagnetic waves that travel in a vacuum at
  the speed of 3 x 108 meters per second.
  
• Spectroscopy is the study of the light emitted by
  the electrons when they undergo quantum leaps.

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Wave Nature of Matter

• The properties of light had been debated and
  researched for years. The photoelectric effect,
  Compton effect and others predict particle
  nature. Youngs double slit and Comptons
  experiments showed the wave nature.
• In 1923 Louis de Broglie proposed that all matter
  (not just photons) had wave properties.

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De Broglie Wavelength of Matter

• De Broglie proposed that the wavelength of a
  material particle would related to its momentum
  with the equation
• ? h/mv

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• deBroglie wavelength problem

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Heisenberg Uncertainty Principle

• In 1927 Walter Heisenberg developed the
  uncertainty principle that explains why we cannot
  measure the position and momentum of an object
  (electrons) precisely at the same time.
• We can measure either property accurately, but
  not both due to the nature of matter / wave
  duality.
• Another form of the same idea relates energy and
  time. If we measure the position of a photon,
  then ?x ? ? and ?t ?x/c so ?t ?/c

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Heisenberg Uncertainty Example

• An analogy of the uncertainty in measurement
  concept is this picture that you cannot measure
  the location of cars due to speed.

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Heisenberg Uncertainty Principle
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Heisenberg Uncertainty Problem
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Position Uncertainty of Electron
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Wavelength of an Electron
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Photoelectron Speed and Energy
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Atomic Spectroscopy

• Atomic Spectroscopy is the analytical measurement
  of the quantum energy level jumps of different
  electron energy states.
• It is a spectral analysis of the colors that an
  atom gives off (or takes in) when it changes
  energy levels.
• It involves either Emission spectroscopy or
  Absorption spectroscopy.

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Atomic Emission Spectroscopy

• In this technique, the atoms are heated up to the
  point that the thermal energy promotes the
  electron up to an excited energy level and then
  measures the color (wavelength) of light that is
  given off when the electron collapses back into
  the ground state.

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Energy Level Transitions of Electrons
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Spectrum Examples
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Energy of Photon Example Problem
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Wavelength Problem in Spectroscopy
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Lasers

• A laser is a device that can produce a very
  narrow intense beam of monochromatic coherent
  light.
• Coherent means that across any cross section of
  the beam, all parts would have the same phase.
• It uses stimulated emission to stay in phase An
  excited electron is stuck by a photon of the
  same energy gives off a double photon.

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Laser Stimulated Emission

• When a photon of light at the same frequency hits
  an excited electron The electron produces
  coherent E M

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AP Problems on Quantum Mechanics and Modern
Physics

• Historical Physics Atomic Physics
• 1982 7 1996 5
• 1997 6 1999 4
• Atomic Energy Levels Photoelectric Effect
• 1992 4 1980 3
• 1995 4 1988 6