Introduction to modern physics: Physics of the 20th and 21st centuries

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Introduction to modern physicsPhysics of the
20th and 21st centuries

• Lectures
• Quantum physics
• Nuclear and Particle physics
• Condensed Matter physics
• Lab experiments some of the following
• Earths Magnetic Field
• Geiger Müller Counter, half life measurement
• operational amplifier
• mass of the K0 particle
• e/m of electron
• Franck-Hertz experiment
• Hall effect
• Homework problems
• website http//www.physics.fsu.edu/courses/Summer0
  9/YSP

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Quantum physics(quantum theory, quantum
mechanics)

• Part 1

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Outline

• Introduction
• Problems of classical physics
• emission and absorption spectra
• Black-body Radiation
• experimental observations
• Wiens displacement law
• Stefan Boltzmann law
• Rayleigh - Jeans
• Wiens radiation law
• Plancks radiation law
• photoelectric effect
• observation
• studies
• Einsteins explanation
• Summary

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• Question What do these have in common?
• lasers
• solar cells
• transistors
• computer chips
• CCDs in digital cameras
• Ipods
• superconductors
• .........
• Answer
• They are all based on the quantum physics
  discovered in the 20th century.

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Why Quantum Physics?

• Classical Physics
• developed in 15th to 20th century
• provides very successful description of every
  day, ordinary objects
• motion of trains, cars, bullets,.
• orbit of moon, planets
• how an engine works,..
• subfields mechanics, thermodynamics,
  electrodynamics,
• Quantum Physics
• developed early 20th century, in response to
  shortcomings of classical physics in describing
  certain phenomena (blackbody radiation,
  photoelectric effect, emission and absorption
  spectra)
• describes small objects (e.g. atoms and their
  constituents)

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Quantum Physics

• QP is weird and counterintuitive
• Those who are not shocked when they first come
  across quantum theory cannot possibly have
  understood it (Niels Bohr)
• Nobody feels perfectly comfortable with it
  (Murray Gell-Mann)
• I can safely say that nobody understands quantum
  mechanics (Richard Feynman)
• But
• QM is the most successful theory ever developed
  by humanity
• underlies our understanding of atoms,
  molecules, condensed matter, nuclei, elementary
  particles
• Crucial ingredient in understanding of stars,

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Features of QP

• Quantum physics is basically the recognition
  that there is less difference between waves and
  particles than was thought before
• key insights
• light can behave like a particle
• particles (e.g. electrons) are indistinguishable
• particles can behave like waves (or wave
  packets)
• waves gain or lose energy only in "quantized
  amounts
• detection (measurement) of a particle ? wave
  will change suddenly into a new wave
• quantum mechanical interference amplitudes add
• QP is intrinsically probabilistic
• what you can measure is what you can know

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emission spectra

• continuous spectrum
• solid, liquid, or dense gas emits continuous
  spectrum of electromagnetic radiation (thermal
  radiation)
• total intensity and frequency dependence of
  intensity change with temperature (Kirchhoff,
  Bunsen, Wien, Stefan, Boltzmann, Planck)
• line spectrum
• rarefied gas which is excited by heating, or by
  passing discharge through it, emits radiation
  consisting of discrete wavelengths (line
  spectrum)
• wavelengths of spectral lines are characteristic
  of atoms

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Emission spectra
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Absorption spectra

• first seen by Fraunhofer in light from Sun
• spectra of light from stars are absorption
  spectra (light emitted by hotter parts of star
  further inside passes through colder atmosphere
  of star)
• dark lines in absorption spectra match bright
  lines in discrete emission spectra
• Helium discovered by studying Sun's spectrum
• light from continuous-spectrum source passes
  through colder rarefied gas before reaching
  observer

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Fraunhofer spectra
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Spectroscopic studies
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Thermal radiation

• thermal radiation e.m. radiation emitted by a
  body by virtue of its temperature
• spectrum is continuous, comprising all
  wavelengths
• thermal radiation formed inside body by random
  thermal motions of its atoms and molecules,
  repeatedly absorbed and re-emitted on its way to
  surface ? original character of radiation
  obliterated ? spectrum of radiation depends only
  on temperature, not on identity of object
• amount of radiation actually emitted or absorbed
  depends on nature of surface
• good absorbers are also good emitters (why??)

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• warm bodies emit radiation

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Black-body radiation

• Black body
• perfect absorber
• ideal body which absorbs all e.m. radiation that
  strikes it, any wavelength, any intensity
• such a body would appear black ? black body
• must also be perfect emitter
• able to emit radiation of any wavelength at any
  intensity -- black-body radiation
• Hollow cavity (Hohlraum) kept at constant
  T
• hollow cavity with small hole in wall is good
  approximation to black body
• thermal equilibrium inside, radiation can escape
  through hole, looks like black-body radiation

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Studies of radiation from hollow cavity

• In 2nd half of 19th century, behavior of
  radiation within a heated cavity studied by many
  physicists, both theoretically and experimentally
• Experimental findings
• spectral density ?(n,T) ( energy per unit
  volume per unit frequency) of the heated cavity
  depends on the frequency n of the emitted light
  and the temperature T of the cavity and nothing
  else.

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various attempts at descriptions

• (Stefan-Boltzmann 1879, 1884) total
  emitted power (per unit emitting area)
• P sT4 s 5.672 10-8 W m-2 K-4
• Wiens displacement law (1893)
• peak vs temperature
• ?max T C, C 2.898 10-3 m K
• Wilhelm Wien (1896) r(n,T) a n3 e-bn
  /T, (a and b constants).
• OK for high frequency but fails for low
  frequencies.
• Rayleigh-Jeans Law (1900)
• r(n,T) a n2 T (a constant)
• (constant found to be 8pk/c3 by James Jeans,
  in 1906)
• OK for low frequencies, but ultra violet
  catastrophe at high frequencies
• 
  

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Ultraviolet catastrophe
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Plancks quantum hypothesis

• Max Planck (Oct 1900) found formula that
  reproduced the experimental results
• derivation from classical thermodynamics, but
  required assumption that oscillator energies can
  only take specific values E 0, h?, 2h?, 3h?,
  (using Boltzmann factor W(E) e-E/kT )

ltEoscgt is the average energy of a cavity
oscillator
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Black-body radiation spectrum

• Measurements of Lummer and Pringsheim (1900)

• calculation

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Consequences of Plancks hypothesis

• oscillator energies E nh?, n 0,1,
• h 6.626 10-34 Js 4.13 10-15 eVs
  now called Plancks constant
• ? oscillators energy can only change by
  discrete amounts, absorb or emit energy in small
  packets quanta Equantum h?
• average energy of oscillator ltEoscgt h?/(ex
  1) with x h?/kT for low frequencies get
  classical result ltEoscgt kT, k 1.38 10-23
  JK-1

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Frequencies in cavity radiation

• cavity radiation system of standing waves
  produced by interference of e.m. waves reflected
  between cavity walls
• many more modes per wavelength band ?? at
  high frequencies (short wavelengths) than at
  low frequencies
• for cavity of volume V, ?n (8pV/?4) ?? or
  ?n (8pV/c3) ?2 ? ?
• if energy continuous, get equipartition, ltEgt
  kT ? all modes have same energy ? spectral
  density grows beyond bounds as ???
• If energy related to frequency and not continous
  (E nh?), the Boltzmann factor e-E/kT leads
  to a suppression of high frequencies
  
  
  
  
  
  
  
  
  
  

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Problems

• estimate Suns temperature assuming
• Earth and Sun are black bodies
• Stefan-Boltzmann law
• Earth in thermal equilibrium (i.e. rad.
  power absorbed rad. power emitted) , mean
  temperature T 290K
• Suns angular size ?Sun 32
• show that for small frequencies, Plancks
  average oscillator energy yields classical
  equipartition result ltEoscgt kT
• show that for standing waves on a string, number
  of waves in band between ? and ??? is ?n
  (2L/?2) ??

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Summary

• classical physics explanation of black-body
  radiation failed
• Plancks ad-hoc assumption of energy quanta
• of energy Equantum h?, modifying Wiens
  radiation law, leads to a radiation spectrum
  which agrees with experiment.
• old generally accepted principle of natura non
  facit saltus violated
• Opens path to further developments