Outline. Introduction Problems of classical physics emission and absorption spectra Black-body Radiation experimental observations Wien's displacement law Stefan Boltzmann law Rayleigh - Jeans Wien's radiation law Planck's radiation lawphotoelectric effect observation studies Eins
1. Quantum physics (quantum theory, quantum mechanics) Part 1:
2. Outline Introduction
Problems of classical physics
emission and absorption spectra
Wien’s displacement law
Stefan – Boltzmann law
Rayleigh - Jeans
Wien’s radiation law
Planck’s radiation law
3. Question: What do these have in common?
CCDs in digital cameras
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,
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)
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
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
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)
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
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”
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
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)
18. various attempts at descriptions: peak vs temperature: ?max ·T = C (Wien’s displacement law), C= 2.898 · 10-3 m K
total emitted power (per unit emitting area) P = s·T4 (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
21. Planck’s 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 )
22. Consequences of Planck’s hypothesis oscillator energies E = nh?, n = 0,1,…;
h = 6.626 10-34 Js = 4.13 10-15 eV·s now called Planck’s constant
? oscillator’s energy can only change by discrete amounts, absorb or emit energy in small packets – “quanta”; Equantum = h?
average energy of oscillator <Eosc> = h?/(ex – 1) with x = h?/kT; for low frequencies get classical result <Eosc> = kT, k = 1.38 · 10-23 J·K-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, <E> = 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 Sun’s temperature
assume Earth and Sun are black bodies
Earth in thermal equilibrium (i.e. rad. power absorbed = rad. power emitted) , mean temperature T = 290K
Sun’s angular size ?Sun = 32’
show that for small frequencies, Planck’s average oscillator energy yields classical equipartition result <Eosc> = 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
Planck’s ad-hoc assumption of “energy quanta”
of energy Equantum = h?, modifying Wien’s 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