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Quantum physics quantum theory, quantum mechanics

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Rayleigh - Jeans. Wien's radiation law. Planck's radiation law. photoelectric effect ... Rayleigh-Jeans Law (1900) r(n,T) = a n2 T (a = constant). (constant ... – PowerPoint PPT presentation

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Title: Quantum physics quantum theory, quantum mechanics


1
Quantum physics(quantum theory, quantum
mechanics)
  • Part 1

2
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

3
  • Question What do these have in common?
  • lasers
  • solar cells
  • transistors
  • computer chips
  • CCDs in digital cameras
  • superconductors
  • .........
  • Answer
  • They are all based on the quantum physics
    discovered in the 20th century.

4
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)

5
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,

6
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

7
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

8
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9
Emission spectra
10
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
  • see dark lines in continuous spectrum
  • Helium discovered by studying Sun's spectrum
  • light from continuous-spectrum source passes
    through colder rarefied gas before reaching
    observer

11
Fraunhofer spectra
12
Spectroscopic studies
13
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??)

14
  • warm bodies emit radiation

15
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

16
Studies of radiation from hollow cavity
  • 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.

17
Black-body radiation spectrum
  • Measurements of Lummer and Pringsheim (1900)
  • calculation

18
various attempts at descriptions
  • peak vs temperature ?max T C (Wiens
    displacement law), C 2.898 10-3 m K
  • total emitted power (per unit emitting
    area) P sT4 (Stefan-Boltzmann), s
    5.672 10-8 W m-2 K-4
  • 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


19
Ultraviolet catastrophe
20
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21
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 )

Eosc is the average energy of a cavity
oscillator
22
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

23
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










24
Problems
  • estimate Suns temperature
  • assume 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) ??

25
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
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