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Introduction to modern physics:Physics of the 20th and 21st centuries • Lectures: • Quantum physics • Nuclear and Particle physics • Condensed Matter physics • Lab experiments: some of the following: • Earth’s 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/Summer10/YSP
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 law • photoelectric effect • observation • studies • Einstein’s explanation • Summary
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.
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)
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, …
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
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
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;
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??)
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
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 ρ(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.
various attempts at descriptions: • (Stefan-Boltzmann 1879, 1884): total emitted power (per unit emitting area) P = σ·T4 σ = 5.672 · 10-8 W m-2 K-4 • Wien’s 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
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 ) <Eosc> is the average energy of a cavity “oscillator”
Measurements of Lummer and Pringsheim (1900) calculation schematisch Black-body radiation spectrum
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 onlychange 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
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 = (8πV/4) or n = (8πV/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
Problems • estimate Sun’s 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 • Sun’s angular size ΔSun = 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)
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