Quantized Radiation (Particle Theory of Light) Dr. Bill Pezzaglia Part I 1 Quantum Mechanics A. Classical vs Quantum Theory B. Black Body Radiation C. Photoelectric Effect 2 Updated: 2010Apr19 D. Atomic Physics A. Classical vs Quantum Theory 1. Discussion in class. Essentially classical theory assumes: Causality (causes must precede effects, i.e. can t go backwards in time) Determinism: classical theory assumes can measure quantities to infinite precision Objectivity: classical theory assumes measurement does not affect the system Two Models: particles (things) which can be localized vs waves (fields) which are non-local. Fields mediate the forces between particles Quantum theory upsets these ideas 3 2. Is light a Wave or Particle Newton s corpuscular theory: light is a particle 1678 Huygens: light is a wave Foucault measures speed of light is slower in water (favors wave theory) 1801 Young s diffraction experiment proves it s a wave, and gives a way to measure its size Waves are very small, around 500 nm 4 3a. Electromagnetic Theory 1831 Michael Faraday proposes Electric and Magnetic Fields 1860 Maxwell shows changing electric field creates magnetic field, changing magnetic field creates electric. Derives wave solutions, with speed exactly c the speed of light. 5 3b. The Electromagnetic Spectrum 1888 Hertz produces radio waves 1895 Rontgen produces X-rays 1900 Paul Villard discovers gamma rays They are all part of the electromagnetic spectrum, of which visible light is a small piece. 6 Proposes these waves are light 1
3c Wavespeed 7 B. Black Body Radiation 8 c = f λ 1. Stephan Boltzmann Law 2. Wien s Law c = speed of light 3. Black Body Radiation f = frequency (Hertz) λ = wavelength 1a. Temperature 9 1b. Josef Stefan s Law 1879 10 1851 Lord Kelvin s temperature scale Conversion: 0 K = -273 C Experimentally shows total output of light of a hot dense (black) body is proportional to 4 th power of the temperature (in Kelvin) Temperature is a measure of average energy Power (watts)=aσt 4 σ=5.67x10-8 Watts/(m 2 -K 4 ) A=surface area 0K is absolute zero 1884 Ludwig Boltzmann (former student of Stefan) derives formula from thermodynamics. I was a guest speaker (Sept 2005) at the Josef Stefan Institute in Slovenia. 1c. Inverse Square Law 1604 Kepler proposes intensity of light drops of with square of distance (?) 11 2a. Wien s Displacement Law 1893 shows that the color of black body is inversely proportional to temperature α λ = T 12 Charles Soret measures solar flux to be about 1400 Watts/m 2 at surface of the earth. Stefan uses this to estimate temperature of sun to be 5700 K. Wien s constant α=2,898,000 nm-k So T=6000 K gives λ=483 nm 2
2b. Black Body Curve 13 2c. Color Indexing 14 Willhelm Wien gets Nobel Prize 1911 1894 coins term black body If we can measure the color of a star, we can calculate its temperature Measure magnitude of star through color filters Color Index=C.I. = B-V is measure of temperature of star. The black body emits all colors, but where it peaks is described by Wien s law Standard Filters U filter 370 nm B filter 440 nm V filter 550 nm 3a. Black Body Theory Maxwell: hot atoms vibrate, acting like small antennas, radiating electromagnetic waves Wien tries to give theory to explain shape of curve, but it fails in IR Rayleigh (1900) & Jeans (1905) have another theory, but it fails in UV, blowing up to infinite energy (the ultraviolet catastrophe ). 15 3b. Max Planck s Theory 1900 Max Planck ad-hoc proposes that vibrations are quantized, i.e. come in steps of n=1, 2, 3, rather than continuous. Energy: E=nhf n=integer quantum number f=frequency of oscillation h is Planck s Constant h=6.626x10-34 Joule-Sec 16 3c. Planck Radiation Law His theory exactly matched the experimental measurements of the black body radiation curve 17 C. Photoelectric Effect 1. Phenomena Discovered 18 2. The Experiment 3. Einstein s Photon Theory k = Boltzmann Constant (1.38 10-23 Joule/Kelvin) 3
1. Discovery of Effect 19 1b. Work Function 20 Hertz 1887 found discharge of a spark gap was greater when illuminated by light from another spark gap. Glass inserted between stopped effect (note glass absorbs uv light) 1888 Hallwachs discovers that negatively charge electroscope will discharge when UV light is shined on it, but not with visible light. No effect for positive charged electroscope. There is a certain amount of energy required to free an electron from the metal (between 2 and 3 volts) Cesium 1.9 volts Calcium 2.7 volts Magnesium 3.6 volts Use energy of light to add energy and bump off electrons. (2a) 1899 Lenard s Experimental 21 (2b) Lenard s Experimental Results 22 At a certain (negative) retarding voltage, the current stops. This tells us the electrons had (at least) energy ev 0 (2c) Findings More intense light, more current, but electrons do not have more energy (stopping voltage unchanged) Higher frequency light, electrons have higher energy (bigger stopping voltage) Below a certain threshold frequency of light, there is NO current, regardless of the intensity Even when intensity is so low that it should take an hour to give enough energy to overcome the work function of the metal, if photon is above the threshold, the effect is instantaneous. 23 (3a) The Photon 1905 Einstein proposes that its light that is quantized Proposes light is a particle, called the photon Uses idea to explain the photoelectric effect Energy of a single Photon: hc E = hf = λ 24 4
3b. Einstein 25 D. Atomic Physics 26 1905 proposed Photon concept, with quantized energy E=hf Emission is caused by ONE photon bumping off ONE electron. Photon frequency must be such that energy is above work function 1. Discrete Spectra 2. Kirchhoff s Laws 3. Model of Atom Millikan makes precise measurement of stopping voltage vs frequency and gets straight line (different for each metal), with slope (h/e) and intercept gives work function. 1a. Dark Line Spectra 27 1b. Solar spectrum 47 1802 Wollastan sees lines in solar spectra 1814 Fraunhofer Labels them A, B, C, D Later measures over 500 lines! 1c. Bright Line Spectra 29 2a. Kirchhoff s Laws 30 1857 Bunsen s burner, a clean flame with no color 1859 Kirchhoff suggest using it to study spectra of elements in flame Each element has a unique set of bright line (emission) spectra 5
2b. Gustav R Kirchhoff (1860) 31 2c. Spectral Analysis 32 His three laws: 1. A hot dense body will emit a continuous spectrum 2. A hot transparent gas will emit emission line spectrum 3. A cool transparent gas in front of a source of continuous spectrum will produce absorption spectra. The absorption lines match emission lines. Hence you can use them to identify elements in stars. 1861 Kirchhoff identifies elements in the sun from Fraunhofer lines 1868 Janssen finds a line that can t be identified during solar eclipse 1870 Lockyer & Frankland verify its an unknown element they name Helium. Helium is not discovered on the earth until 1895! 3a. Rydberg Formula 33 1885 Balmer comes up with formula that explains the Hydrogen lines ( Balmer Series ) 1888 Rydberg improves formula, where n 1 =2, n 2 ={3,4,5} 3b. Atomic Theory 1808 Dalton s theory of atoms 1897 Thomson discovers electron 1911 Rutherford s experiment implies dense core to atom (nucleus) 34 1895 Paschan Series discovered in IR, described by n 1 =3 1908 Lyman Series discovered in UV, described by n 1 =1 3c. Atomic Theory 1911 Rutherford s suggest planetary model of atom, electrons orbit nucleus But, it would be unstable! Electrons would immediately radiate and crash into nucleus. 35 3d. Niels Bohr (Nobel Prize 1922) 1913 Bohr proposes quantized orbits to atom. 36 6
3e. Emission and Absorption 37 3f. Emission & Absorption 38 3g. Spectral Series 39 References McEvoy & Zarate, Introducing Quantum Theory (Totem Books, 1996) 40 7