The Origins of the Quantum Theory

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The Origins of the Quantum Theory
Planck (1900)
E h f
Bohr (1911)
Einstein (1905)
Emax
Slope h
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Announcements

• Schedule
• Today The beginnings of Quantum Mechanics
• Hobson Chapter 13
• Next Time Atomic physics
• Hobson Chapter 14
• Report/Essay
• Short description due TODAY
• Full report due Monday, December 6 three weeks
• Homework 9 due Wednesday

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Timeline - Modern Physics
Einstein
Bohr
Michelson
Rutherford
Nuclear Energy Released
Thomson
Neutron Stars discovered
De Broglie Schrodinger Heisenberg
Planck
Curie
2000
1950
1900
Expansion of Universe discovered
Laser Invented
Special Relativity
Start ofQuantum Mechanics
Transistor Invented
All the Quarks discovered
Quantum Mechanics
General Relativity

• Modern Physics was a sudden revolution starting
  around 1900, and ending ????
• See Timeline description of lives of various
  scientists on WWW pages.

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General Comment

• Quote from the famous modern physicist, Richard
  Feynman
• If we were able to pass along only one bit of
  scientific knowledge to future generations, what
  would be the most important one piece of
  information to choose?
• Feynmans answer That matter is made of atoms
• What could this mean? How could this fact be so
  important?

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The Appeal of Atomism

• It is natural to try to explain the vast
  diversities that we see in terms of the
  arrangements and interactions of a small number
  of fundamental building blocks atoms!
• Atomism in Ancient Greece
• Democritus There are only atoms and the void.
  Apparent qualities are result of shape,
  arrangement, and position of atoms. Atoms remain
  unaltered.Gave us the name atom -
  indivisible

• Explains the basic properties of matter
• Changes but is never created nor destroyed (in
  our ordinary experience)
• Solid Atoms linked together
• Liquid Atoms flowing around each other
• Gas expands to fill any container because the
  atoms are in motion

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The Periodic Table

• Question Do the properties of atoms (elements)
  indicate that there are more than 100 different
  flavors of these fundamental pieces?
• Or do the properties indicate a pattern of
  substructure??

Atomic of protons
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Are Atoms Indivisible?

• X-rays discovered in 1895 by Roentgen - World
  Wide sensation!
• Unknown ray produced from electric discharge that
  penetrates matter!
• J.J. Thomson discovers the electron in 1897.
• Henri Becquerel (1896) tries to produce X-rays
  from natural sources.
• Finds radiation (less penetrating than X-rays)
  given off from ore containing Uranium.

• Marie Curie (1897) discovers immense radiation
  energy from element she named Radium.
• Surprising? Yes!
• If the radiation comes from the atom, it could
  indicate that an atom had been transformed into
  another kind of atom!
• If atoms are not immutable, then it makes sense
  to ask what are atoms made of?

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Atomic Models

• Conclusion Atoms contain electrons. Questions
  How are they arranged? Since atoms are
  neutral, where is the positive charge?
• Two models
• Plum pudding Electrons are embedded in
  continuum of positive electricity like plums in a
  pudding.
• Planetary model Electrons orbit a small
  nucleus of positive charge like planets orbit the
  Sun.

Electrons
Or
Positive Charge
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Atomic Models

• How to distinguish between these models?
• Ernest Rutherford had discovered that certain
  rays given off by radioactive material were ?
  rays - positive particles (ions) with the mass
  He atom.
• Used to study the atoms itself! Observe how ?
  particles (Helium ions) scatter from a Gold foil.
  

Au
Count the number of times an ? particle scatters
through an angle ?, for different angles ?.
?
?
v

• What do you expect?
• Plum Pudding only small deflections since ?
  particles much heavier than electrons.
• Planetary can occasionally get large
  deflections if most of the mass of the atom
  resides in the nucleus.

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Scattering Experiments
probe
For plum pudding expect only small angle
scattering.
probe
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Scattering Experiments
probe
For plum pudding expect only small angle
scattering.
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The Problem of the atom

• Experiments supported the picture that an atom is
  composed of light electrons around a heavy
  nucleus
• Problem if the electrons orbit the nucleus,
  classical physics predicts they should emit
  electromagnetic waves and loose energy. If this
  happens, the electrons will spiral into the
  nucleus!
• The atom would not be stable!
• What is the solution to this problem?

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Blackbody Radiation

• The true beginnings of the quantum theory lie in
  a strange place the frequency spectrum emitted
  by a solid when it is heated (blackbody
  radiation).
• Experimental measurements the frequency
  spectrum was well determined.. a continuous
  spectrum with a shape that depended only on the
  temperature (light bulb, )
• Theoretical prediction Classical kinetic theory
  predicts the energy radiated to increase as the
  square of the frequency (Completely Wrong! -
  ultraviolet catastrophe).

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Plancks Solution

• Max Planck (1901) In order to describe the data
  Planck made the bold assumption that light is
  emitted in packets or quanta, each with energy E
  h f, where f is the frequency of the light.
• Some texts use the notation n for frequency.
• The factor h is now called Plancks constant, h
  6.626 (10-27) erg-sec.

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E h f

• The two most important formulas in modern physics
  E mc2 (Einstein special relativity -
  1905) E h f (Planck quantum mechanics -
  1901)
• Planck initially called his theory an act of
  desperation.
• I knew that the problem is of fundamental
  significance for physics I knew the formula
  that reproduces the energy distribution in the
  normal spectrum a theoretical interpretation had
  to be found , no matter how high.
• Leads to the consequence that light comes only in
  certain packets or quanta
• A complete break with classical physics where all
  physical quantities are always continuous

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Photoelectric Effect

• Einstein took Plancks hypothesis seriously
• in order to explain the photoelectric effect.
• Effect Shining light on a metal can liberate
  electrons from its surface.
• Experimental facts
• Easy for UV light (high frequency) hard
• for red light (low freq).
• Energy of the electrons depends on frequency of
  light
• Increasing intensity of light increases number of
  electrons emitted, but not the energy of each
  electron

• Cant be explained by wave behavior of light.
• If light is generated in quantized units,
  Einstein reasoned it would also arrive with
  quantized amounts of energy

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Photoelectric Effect The Theory

• Einsteins explanation Suppose the energy in the
  light is concentrated in particle-like objects
  (now we call them photons) whose energy depend on
  the frequency of the light according to Plancks
  equation E h?.
• Prediction Maximum energy of electrons liberated
  energy of photon - binding energy of electron.
  
  Emax hf - hf0
• Experiment done accurately by Millikan in 1916

Frequency f
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Light is Quantized!

• We referred to light as a wave.
• We did experiments to show that light behaves
  like a wave.
• Recall
• Waves continuously transmit energy, they do not
  transmit matter.
• Blackbody radiation and the photoelectric effect
  indicate that the energy transmitted by light
  comes in packets!!
• Light doesnt behave like a wave.
• The energy light carries is quantized, which
  means it comes in tiny bursts. The amount of
  energy per burst is determined by the frequency
  and Plancks constant h
• Ehf
• Light can behave like a particle. Any chance a
  particle can behave like a wave?

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The Two-Slit Experiment

• We will first examine an experiment which Richard
  Feynman says contains all of the mystery of
  quantum mechanics.
• The general layout of the experiment consists of
  a source, two-slits, and a detector as shown
  below

x
source
detector
slits
The idea is to investigate three different
sources (a classical particle (bullets), a
classical wave (water), and a quantum object
(electron or photon)). We will study the spatial
distribution (x) of the objects which arrive at
the detector after passing through the slits.
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Classical Particles

• Classical particles are emitted at the source and
  arrive at the detector only if they pass through
  one of the slits.
• Key features
• particles arrive in lumps. ie the energy
  deposited at the detector is not continuous, but
  discrete. The number of particles arriving per
  second can be counted.
• The number which arrive per second at a
  particular point (x) with both slits open (N12)
  is just the sum of the number which arrive per
  second when only the top slit is opened (N1) and
  the number which arrive per second when only the
  bottom slit is opened (N2).

only bottom slit open
only top slit open
Both slits open
N
N
x
x
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Classical Waves

• Classical waves are emitted at the source and
  arrive at the detector only if they pass through
  the slits.
• Key features
• detector measures the energy carried by the
  waves. eg for water waves, the energy at the
  detector is proportional to the square of the
  height of the wave there. The energy is measured
  continuously.
• The energy of the wave at a particular point (x)
  with both slits open (I12) is NOT just the sum of
  the energy of the wave when only the top slit is
  opened (I1) and the energy of the wave when only
  the bottom slit is opened (I2). An interference
  pattern is seen, formed by the superposition of
  the piece of the wave which passes through the
  top slit with the piece of the wave which passes
  through the bottom slit.

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Quantum Mechanics

• Particles act like waves!
• Experiment shows that particles (like electrons)
  also act like waves!

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The de Broglie Wavelength

• Big question How can we quantify deBroglies
  hypothesis that matter can sometimes be viewed as
  waves? What is the wavelength of an electron?
• de Broglies idea define wavelength of electron
  so that same formula works for light also, when
  expressed in terms of momentum!
• What is momentum of photon? This is known from
  relativity
• p E / c (plausible since E mc2 and p
  mc ? E pc)
• How is momentum of photon related to its
  wavelength?
• from photoelectric effect E hf ? pc hf
• change frequency to wavelength c ??f ? c/f
  ??

p ?? h
?? h / p
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Summary

• Near the turn of the 20th century, a second
  revolution was in the works.
• Experiments were probing very small distance
  scales, learning about electrons, atoms, nuclei
  
• Max Planck (1900) had the idea that blackbody
  radiation could be explained if light was emitted
  in quanta with Ehf
• Einstein (1905) reasoned that this would also
  explain the photoelectric effect (light transfers
  quanta of energy to emitted electrons)
• Light can behave like a particle!
• deBroglie (1923) proposed that matter could
  behave as a wave
• Scattering experiments showed this to be true!
• The quantum theory is born.
• Nature is not continuous as Newton thought.
• It is discrete. Energy comes in packets.
• This explains how atoms behave as wellnext time.