Pre-%20AP%20Quantum%20Mechanics%20%20and%20the%20Atom%20Theory

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Pre- AP Quantum Mechanics and the Atom Theory

• Science Engineering Magnet High
• Mr. Puckett

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Chapter 27 - Quantum Theory

• Objectives
• Understand the spectrum emitted by a hot body and
  the basics of the theory that explains this
  spectrum.
• Define the photoelectric effect
• Define the Compton effect and explain it in terms
  of the momentum and energy of the photon.

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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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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.

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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

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Kinetic Energy of Photoelectron
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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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Photoelectric Equation
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Photoelectric Equation continued
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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 electron out of an atom
  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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Comptons Apparatus
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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
• p mv h/?, therefore ? 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 Principle Diagram

• A particle can be seen only by scattering light
  off of it. The scattering changes the electron
  momentum.

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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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Chapter 28 The Atom

• Objectives
• Explain the history of the atomic theory.
• Explain the method of discovering the electron,
  nucleus and energy levels.
• List Bohrs assumptions of atomic theory.
• Solve Bohr Model problems.

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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!

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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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The Periodic Table of Elements

• Everything we know about the Universe in One
  Chart, Robin Williams

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The Periodic Table Nomenclature

• Periods A horizontal row/energy level of
  elements.
• Groups- A vertical column of elements that share
  chemical reactive natures.
• Orbitals- Energy/ shapes of electron orbitals.
• Atomic number- the element number/ protons.
• Mass number- mass of nucleus, (protons
  neutrons).
• Metals- Left side of table that give up electrons
  and are good conductors.
• Nonmetals- right side of table that take in
  electrons and are poor conductors.

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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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The Aufbau Loading of Electrons by Energy Levels
around the Atom

• This is the chart that tells you which electron
  orbital gets the next electron. It fills from
  the bottom up (lowest energy to highest energy)
  like a glass of water.

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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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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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Electron Orbital Types S, P, D

• These are the shapes of the 3 simplest electron
  orbitals.

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P orbitals and D orbitals
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The Quantum Atom Model

• QUANTUM MECHANICAL MODEL of the atom is the most
  current theory about the makeup of atoms and
  includes both the particle and wave nature of
  electrons.
• Erwin Schrödinger developed the math equations
  for electron orbital waves and locations.

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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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Electrons around the H2O molecule An example

• Drawing electron orbitals of water makes it easy
  to understand the molecule and how it acts in a
  chemical reaction.

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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 orientation of
  an orbital around the nucleus.
• 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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Light and Atomic Spectra

• The work that led to the development of the
  quantum mechanical model came from the study of
  light and the emission of energy from atoms.
• Light consists 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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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
  (frequencies) 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. You are looking into the atom

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Photon Energy Emitted out of the Excited Level
Electrons

• When the electron absorbs the energy, it is
  promoted to the higher energy orbital.
• Nature wants the electron to go back to the
  ground state level (stability and entropy
  reasons) and give the energy back off at
  frequencies that are unique for that atom at that
  level of energy.

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Emission Spectroscopy Examples
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Orbital Energy for the Hydrogen Atom Electrons
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Frequency and Wavelength of Emitted Photons
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Atomic Absorption Spectroscopy

• In this analytical chemistry technique a white
  light is shown through a sample. When an atom
  absorbs the energy and promotes the electron up
  to a higher energy orbital, that frequency is
  seen as a dark line on the spectrum. Each
  element is unique in its absorption due to
  quantum mechanics.

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Energy Level Transitions of Electrons
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Energy Levels Chart Example

• Notice the many different pathways photon energy
  release can take back to ground state.

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Spectrum Examples
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Energy of Photon Example Problem
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Photoelectron Speed and Energy
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Lasers
Light Amplification by Stimulated Emission of
Radiation.

• 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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Common Lasers and their Wavelengths
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Laser Mechanism
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Laser Applications Holograms

• Holograms are three dimensional photography that
  uses the interference properties of light to
  record intensity and the phase of light.
• It uses a laser light and splits the beam into 2
  equal parts. One beam is directed to the object
  and the reflection is recorded on the film. The
  other beam goes directly to the photographic
  plate. The result is a complex interference
  pattern that makes the photo appear to be 3-D and
  very life-like.

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Hologram Diagram