1 Introduction to modern physics: Physics of the 20 th and 21 st centuries  Lectures: lQuantum physics l Nuclear and particle physics l some condensed matter physics l Relativity – special, general l Cosmology  Lab experiments: some of the following: l Earth’s magnetic field l Geiger Müller counter, half life measurement l operational amplifier l mass of the K 0 particle l e/m of electron l Franck-Hertz experiment l Hall effect lPlanck’s constant from LED’s  Homework problems  problem solving, modeling, simulations  website

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

3 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

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

5 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, lQuantum Physics: o developed early 20 th century, in response to shortcomings of classical physics in describing certain phenomena (blackbody radiation, photoelectric effect, emission and absorption spectra…) o describes “small” objects (e.g. atoms and their constituents)

6 “Classical” vs “modern” physics

7 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, …

8 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 o quantum mechanical interference – amplitudes add o QP is intrinsically probabilistic o what you can measure is what you can know

9 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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11 Emission spectra:

12 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 Helium discovered by studying Sun's spectrum l light from continuous-spectrum source passes through colder rarefied gas before reaching observer;

13 Fraunhofer spectra

14 Spectroscopic studies

15 Kinetic theory of heat  Molecules are in constant random motion,  Average kinetic energy depends only on temperature  In thermal equilibrium, energy is equally shared between all “degrees of freedom” of the possible motions, ave. kinetic energy per degree of freedom = = ½k B T (k B = Boltzmann’s constant)  Degrees of freedom: translational motion in 3 dimensions has 3 degrees of freedom (dof);  Rotational and vibrational motion: nb. of dof depends on number of atoms and their configuration in molecule

16 0th law of thermodynamics lbetween bodies of different temperature (i.e. of different average internal thermal energy), heat will flow from the body of higher temperature to the body of lower temperature until the temperatures of the two bodies are the same; lthen the bodies are in “thermal equilibrium” ltwo bodies are in thermal equilibrium (at same temperature) if there is no heat flow between them; lcorollary: if two bodies are in thermal equilibrium with a third body, then they are in thermal equilibrium with each other. l  can use thermometer to compare temperature lnote: oobservation only shows that temperatures equalize - heat flow is hypothesis

17 temperature  Temperature: l was measured long before it was understood; lGalilei (around 1592): “device to measure degree of hotness”; inverted narrow-necked flask, warmed in hand, put upside down into liquid; liquid level indicates temperature; OK, but not calibrated. lHooke, Huygens, Boyle (1665): “fixed points” - freezing or boiling point of water; lC. Renaldini (1694): use both freezing and boiling point lModern point of view: temperature is measure of kinetic energy of random motion of molecules, atoms,.. lhttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/wiki/Temperature lhttp://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html lhttp://eo.ucar.edu/skymath/tmp2.htmlhttp://eo.ucar.edu/skymath/tmp2.html lhttp://

18 Thermal energy, heat, temperature  observation of ”Brownian motion” (1827): lsmall seeds (e.g. burlap) suspended in liquid show erratic motion (“random motion”) lhttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.htmlhttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html lhttp://  kinetic theory of heat (Boltzmann, Maxwell,...) lheat is a form of energy; linternal energy = thermal energy of material bodies is related to random motions of molecules or atoms ltemperature is a measure of this internal energy. l explanation of Brownian motion: Albert Einstein (1905): calculated speed of “diffusion” from kinetic theory of heat - found in agreement with experimental measurements l strong support for atomic picture of matter lhttp://en.wikipedia.org/wiki/Theory_of_heathttp://en.wikipedia.org/wiki/Theory_of_heat lhttp://en.wikipedia.org/wiki/Kinetic_theoryhttp://en.wikipedia.org/wiki/Kinetic_theory lhttp:// lhttp:// lhttp://galileo.phys.virginia.edu/classes/252/kinetic_theory.htmlhttp://galileo.phys.virginia.edu/classes/252/kinetic_theory.html

19 Fahrenheit, Celsius scale  Fahrenheit scale: lGabriel Daniel Fahrenheit (Danzig, ), glassblower and physicist; o reproducible thermometer using mercury (liquid throughout range) (around 1715) o 0 point: lowest temperature of winter of 1709, (using mix of water, ice, salt −17.8 °C ) o96 o = body temperature (96 divisible by 12, 8), owater freezes at 32 o F, boils at 212 o F ohttp://inventors.about.com/od/tstartinventions/a/History-Of-The-Thermometer.htmhttp://inventors.about.com/od/tstartinventions/a/History-Of-The-Thermometer.htm  Celsius scale: lAnders Celsius (Swedish astronomer, ) l0 o C = ice point (mixture of water and ice at 1 atm) l100 o C = boiling point of water at 1 atm. (1742)  relation between Fahrenheit and Celsius degrees: lT C = (5/9)(T F - 32 ), T F = (9/5)T C + 32

20 Temperature (2)  thermodynamic temperature scale l(absolute, Kelvin scale) lpressure vs temperature of gas at constant volume and volume vs temperature of gas at constant pressure extrapolate to zero at o C lthis is “absolute zero” lunit: Kelvin lSize of unit of Kelvin scale = that of Celsius scale, only shift of zero-point lThis is the temperature scale which is used in most of physics lhttp://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Kelvin lhttp://abyss.uoregon.edu/~js/glossary/temperature_scale.htmlhttp://abyss.uoregon.edu/~js/glossary/temperature_scale.html lhttp://lamar.colostate.edu/~hillger/temps.htmhttp://lamar.colostate.edu/~hillger/temps.htm

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22 Range of temperatures lUniverse 5×10 −44 s after the Big Bang: T  1.4×10 32 K lcore of hottest stars,  4  10 9 K; seems maximum now lhydrogen bomb ignites at,  4  10 7 K; linterior of Sun,  1.5  10 6 K; l plasma  10 5 K; l  10 5 K : clouds of atoms, ions, e, occasional molecule; l5800 K: surface of the Sun; 5000 K: cool spots at surface of the Sun; evidence for some molecules; l 3000 K: water steam: about 1/4 of water molecules ruptured into atoms; l 2800 K: W light bulb filament; l 2000 K: molten lava; l1520 o C: iron melts; 327 o C: lead melts; l100 o C ( K): water boils; l252 K (-21.1 o C = 5.8 o F): temp. of salt-ice saltwater mix; l234 K: mercury freezes; 194 K: dry ice freezes; l 77 K: nitrogen boils l 4 K: helium boils. l;

23 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??) lhttp://hyperphysics.phy-astr.gsu.edu/hbase/thermo/absrad.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/thermo/absrad.html lhttp://casswww.ucsd.edu/archive/public/tutorial/Planck.htmlhttp://casswww.ucsd.edu/archive/public/tutorial/Planck.html lhttp://panda.unm.edu/Courses/Finley/P262/ThermalRad/ThermalRad.htmlhttp://panda.unm.edu/Courses/Finley/P262/ThermalRad/ThermalRad.html lhttp://csep10.phys.utk.edu/astr162/lect/light/radiation.htmlhttp://csep10.phys.utk.edu/astr162/lect/light/radiation.html lhttp:// lhttp:// lhttp://ip.anndannenberg.com/IPHandouts/Heattransfernotes.pdfhttp://ip.anndannenberg.com/IPHandouts/Heattransfernotes.pdf

24  warm bodies emit radiation

25 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

26 Studies of radiation from hollow cavity  In 2 nd half of 19 th century, behavior of radiation within a heated cavity studied by many physicists, both theoretically and experimentally  Experimental findings: (f,T) T l spectral density ρ(f,T) (= energy per unit volume per unit frequency) of the heated cavity depends on the frequency f of the emitted light and the temperature T of the cavity and nothing else.

27 Thermal radiation  “Global description”, i.e without frequency dependence: lDescriptions successful, i.e. in agreement with observations  total power output of black body: Stefan-Boltzmann law: lFor an “ideal” radiator (“black body”), total emitted power (per unit emitting area), P/A P/A = σ·T 4 σ = · W m -2 K -4 (Josef Stefan, Ludwig Boltzmann 1879, 1884) lhttp://csep10.phys.utk.edu/astr162/lect/light/radiation.html  Wien’s displacement law (1893) peak vs temperature: max ·T = C, C= · m  K inverse relationship between the wavelength of the peak of the emission of a black body and its temperature when expressed as a function of wavelength lhttp://en.wikipedia.org/wiki/Wien's_displacement_law hyperphysics.phy- astr.gsu.edu/hbase/quantum/wien2.html lhttp://en.wikipedia.org/wiki/Wien's_displacement_law hyperphysics.phy- astr.gsu.edu/hbase/quantum/wien2.html l

28 Intensity vs frequency  (f, T) = af 3 exp(-bf/T) a b  Wilhelm Wien (1896)  (f, T) = af 3 exp(-bf/T), (a and b constants). lOK for high frequency but fails for low frequencies lhttp://en.wikipedia.org/wiki/Wien_approximationhttp://en.wikipedia.org/wiki/Wien_approximation / /  Rayleigh-Jeans Law (1900)  (f,T) = af 2 Ta  (f,T) = af 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, i.e. intensity grows  f 2   for f  (corresponding to limit of wavelength  0 ) lhttp://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html astr.gsu.edu/hbase/mod6.html astr.gsu.edu/hbase/mod6.htmlhttp://scienceworld.wolfram.com/physics/Rayleigh-JeansLaw.html

29 Ultraviolet catastrophe (Rayleigh-Jeans)

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31 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, hf, 2hf, 3hf, …  for a multi-state system of particles in thermal equilibrium, probability for particle to be in state with energy E, P(E) = (1/Z)e -E/kT (“Boltzmann factor” ) is the average energy of a cavity “oscillator”

32 Black-body radiation spectrum  Measurements of Lummer and Pringsheim (1900)  calculation schematisch

33 Consequences of Planck’s hypothesis  oscillator energies E = nhf, 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 = hf l average energy of oscillator = hf/(e x – 1) with x = hf/kT; for low frequencies get classical result = kT, k = 1.38 · J·K -1

34 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 ) f 2  f  if energy continuous, get equipartition, = kT  all modes have same energy  spectral density grows beyond bounds as f   If energy related to frequency and not continous (E = nhf), the “Boltzmann factor” e -E/kT leads to a suppression of high frequencies

35 Problems  estimate Sun’s surface temperature assuming: lEarth and Sun are black bodies l Stefan-Boltzmann law l Earth in energetic equilibrium (i.e. rad. power absorbed = rad. power emitted), mean temperature T = 290K lSun’s angular size  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 ) 

36 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