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

2 Outline  Introduction  Problems of classical physics  emission and absorption spectra  Black-body Radiation l experimental observations l Wien’s displacement law l Stefan – Boltzmann law l Rayleigh - Jeans l Wien’s radiation law l Planck’s radiation law  photoelectric effect l observation l studies l Einstein’s explanation  Summary

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

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

5 Quantum Physics  QP is “weird and counterintuitive” o“Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niels Bohr) o “Nobody feels perfectly comfortable with it “ (Murray Gell-Mann) o“I can safely say that nobody understands quantum mechanics” (Richard Feynman)  But: oQM is the most successful theory ever developed by humanity o underlies our understanding of atoms, molecules, condensed matter, nuclei, elementary particles oCrucial 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: o light can behave like a particle o particles (e.g. electrons) are indistinguishable o particles can behave like waves (or wave packets) o waves gain or lose energy only in "quantized amounts“ o detection (measurement) of a particle  wave will change suddenly into a new wave oquantum mechanical interference – amplitudes add o QP is intrinsically probabilistic owhat you can measure is what you can know

7 emission spectra  continuous spectrum osolid, liquid, or dense gas emits continuous spectrum of electromagnetic radiation (“thermal radiation”); ototal intensity and frequency dependence of intensity change with temperature (Kirchhoff, Bunsen, Wien, Stefan, Boltzmann, Planck)  line spectrum orarefied gas which is “excited” by heating, or by passing discharge through it, emits radiation consisting of discrete wavelengths (“line spectrum”) o wavelengths of spectral lines are characteristic of atoms

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9 Emission spectra:

10 Absorption spectra l first seen by Fraunhofer in light from Sun; l spectra of light from stars are absorption spectra (light emitted by hotter parts of star further inside passes through colder “atmosphere” of star) l dark lines in absorption spectra match bright lines in discrete emission spectra l see dark lines in continuous spectrum l Helium discovered by studying Sun's spectrum l 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” l perfect absorber o ideal body which absorbs all e.m. radiation that strikes it, any wavelength, any intensity o such a body would appear black  “black body” l must also be perfect emitter oable to emit radiation of any wavelength at any intensity -- “black-body radiation”  “Hollow cavity” (“Hohlraum”) kept at constant T o hollow cavity with small hole in wall is good approximation to black body othermal 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: (,T) T spectral density ρ(,T) (= energy per unit volume per unit frequency) of the heated cavity depends on the frequency 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 schematisch

18 various attempts at descriptions:  peak vs temperature: max ·T = C (Wien’s displacement law), C= · m K  total emitted power (per unit emitting area) P = σ·T 4 (Stefan-Boltzmann), σ = · W m -2 K -4  (,T) = a 3 e -b  /T a b  Wilhelm Wien (1896)  (,T) = a 3 e -b  /T, (a and b constants). lOK for high frequency but fails for low frequencies.  (,T) = a 2 Ta  Rayleigh-Jeans Law (1900)  (,T) = a 2 T (a = constant). 8  k/c 3 (constant found to be = 8  k/c 3 by James Jeans, in 1906) lOK for low frequencies, but “ultra – violet catastrophe” at high frequencies

19 Ultraviolet catastrophe

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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 ) E osc is the average energy of a cavity “oscillator”

22 Consequences of Planck’s hypothesis  oscillator energies E = nh, n = 0,1,…; l h = Js = eV·s now called Planck’s constant l  oscillator’s energy can only change by discrete amounts, absorb or emit energy in small packets – “quanta”; E quantum = h l average energy of oscillator = h /(e x – 1) with x = h /kT; for low frequencies get classical result = kT, k = 1.38 · 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 lfor cavity of volume V,  n = (8πV/ 4 )  or  n = (8πV/c 3 ) 2   if energy continuous, get equipartition, = 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 l assume Earth and Sun are black bodies l Stefan-Boltzmann law l Earth in thermal equilibrium (i.e. rad. power absorbed = rad. power emitted), mean temperature T = 290K lSun’s angular size θ Sun = 32’  show that for small frequencies, Planck’s average oscillator energy yields classical equipartition result = 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 E quantum = 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