1Tues. Nov. 18, 2008 Phy208 Lect. 231Exam 3 is Tuesday Nov. 25Students w / scheduled academic conflict please stay after classTues. Nov. 18 (TODAY) to arrange alternate time.5:30-7 pm, 2103 Ch (here)Covers: all material since exam 2.Bring: CalculatorOne (double-sided) 8 1/2 x 11 note sheetExam review: Thursday, Nov. 20, in classTues. Nov. 18, 2008 Phy208 Lect. 232From Last Time…Photoelectric effectand light quantizationTues. Nov. 18, 2008 Phy208 Lect. 233Summary of Photoelectric effect Light comes in photons - particles of light h=Planck’s constant Red photon is low frequency, low energy. (Ultra)violet is high frequency, high energy. Electron in metal absorbs one photon Can escape metal if photon energy large enough Ephoton>Work function Eo Excess energy Ephoton-Eo shows up as kinetic energy! Ephoton= hf = hc /"Tues. Nov. 18, 2008 Phy208 Lect. 234Photon properties of light Photon of frequency f has energy hf Red light made of ONLY red photons The intensity of the beam can be increased byincreasing the number of photons/second. Photons/second = energy/second = power! Ephoton= hf = hc /"! h = 6.626 "10#34J $ s = 4.14 "10#15eV $ s! hc = 1240eV " nmTues. Nov. 18, 2008 Phy208 Lect. 235How many photons can you see?In a test of eye sensitivity, experimenters used 1 milli-second(0.001 s) flashes of green light. The lowest power light thatcould be seen was 4x10-14 Watt.How many green (500 nm, 2.5 eV) photons is this?A. 10 photonsB. 100 photonsC. 1,000 photonsD. 10,000 photons! 4 "10#14J /s( )0.001s( )= 4 "10#17J4 "10#17J( )1eV /1.6 "10#19J( )= 250eV250eV( )1photon /2.5eV( )= 100 photonsTues. Nov. 18, 2008 Phy208 Lect. 236Quantization of light Possible energies for green light (λ=500 nm)E=hfE=2hfE=3hfE=4hf One quantum of energy:one photon Two quanta of energytwo photons etc Think about light as aparticle rather than wave.Quantum mechanically, brightness can only bechanged in steps, with energy differences of hf.Energy2Tues. Nov. 18, 2008 Phy208 Lect. 237Thompson’s model of atom J.J. Thomson’s model of atom A volume of positive charge Electrons embedded throughoutthe volume A change from Newton’s modelof the atom as a tiny, hard,indestructible sphere This model is not correct!Tues. Nov. 18, 2008 Phy208 Lect. 238Tues. Nov. 18, 2008 Phy208 Lect. 239Resulted in new model Planetary model Based on results of thinfoil experiments Positive charge isconcentrated in thecenter of the atom,called the nucleus Electrons orbit thenucleus like planets orbitthe sunTues. Nov. 18, 2008 Phy208 Lect. 2310Difference between atoms Simplest is Hydrogen: 1 electron orbiting 1 proton Other atoms number of orbiting negative electrons same as number ofpositive protons in nucleus Different elements have different number oforbiting electrons Helium: 2 electrons Copper: 29 electrons Uranium: 92 electrons! Organized into periodic table of elementsFirst concentrate on hydrogen atomTues. Nov. 18, 2008 Phy208 Lect. 2311 Circular motion of orbiting electrons: electrons emit EM radiation at orbital frequency. Similar to radio waves emitted by acceleratingelectrons in a antenna. In an atom, emitted EM wave carries away energy Electron predicted to continually lose energy. The electron would eventually spiral into the nucleus However most atoms are stable!Planetary model and radiationTues. Nov. 18, 2008 Phy208 Lect. 2312Line spectra from atoms Atoms do emit radiation,but only at certain discrete frequencies. Emission pattern unique to different atoms Spectrum is an atomic ‘fingerprint’,used to identify atoms (e.g. in space).HydrogenMercuryWavelength (nm)3Tues. Nov. 18, 2008 Phy208 Lect. 2313The Bohr atom Retained ‘planetary’ picturewith circular orbits Only certain orbits are stable Radiation emitted only whenelectron jumps from onestable orbit to another. Here, the emitted photon hasan energy ofEinitial-EfinalStable orbitStable orbitEinitialEfinalPhotonTues. Nov. 18, 2008 Phy208 Lect. 2314Energy levels Instead of drawing orbits, just indicate energy anelectron would have if it were in that orbit.Zero energyn=1n=2n=3n=4! E1= "13.612 eV! E2= "13.622 eV! E3= "13.632 eVEnergy axisTues. Nov. 18, 2008 Phy208 Lect. 2315Hydrogen atom energiesZero energyn=1n=2n=3n=4! E1= "13.612 eV! E2= "13.622 eV! E3= "13.632 eVEnergy! En= "13.6n2 eV Quantized energy levels: Each corresponds todifferent Orbit radius Velocity Particle wavefunction Energy Each described by aquantum number nTues. Nov. 18, 2008 Phy208 Lect. 2316Emitting and absorbing lightPhoton is emitted when electrondrops from one quantumstate to anotherZero energyn=1n=2n=3n=4! E1= "13.612 eV! E2= "13.622 eV! E3= "13.632 eVn=1n=2n=3n=4! E1= "13.612 eV! E2= "13.622 eV! E3= "13.632 eVAbsorbing a photon of correctenergy makes electron jumpto higher quantum state.Photonabsorbed hf=E2-E1Photonemittedhf=E2-E1Tues. Nov. 18, 2008 Phy208 Lect. 2317Hydrogen emission This says hydrogen emits onlyphotons of a particular wavelength, frequency Photon energy = hf,so this means a particular energy. Conservation of energy: Energy carried away by photon is lost by the orbitingelectron.Tues. Nov. 18, 2008 Phy208 Lect. 2318Hydrogen atomAn electron drops from an -1.5 eV energy level to one withenergy of -3.4 eV. What is the wavelength of the photonemitted?A. 827 nmB. 653 nmC. 476 nmD. 365 nmE. 243 nmZero energyn=1n=2n=3n=4! E1= "13.6 eV! E2= "3.4 eV! E3= "1.5 eVPhotonemittedhf=E2-E1hf = hc/λ = 1240 eV-nm/ λ4Tues. Nov. 18, 2008 Phy208 Lect. 2319 Each orbit has a specific energyEn=-13.6/n2 Photon emitted when electronjumps from high energy to lowenergy orbit.Ei – Ef = h f Photon absorption induceselectron jump fromlow to high energy orbit.Ef – Ei = h f Agrees with experiment!Energy conservation for Bohr atomTues. Nov. 18, 2008 Phy208 Lect. 2320Hydrogen emission spectrum Hydrogen is simplest atom One electron orbiting around oneproton. The Balmer Series of emissionlines given empiricallyn = 3, λ = 656.3 nmHydrogenn = 4, λ = 486.1 nmn=3n=4! 1"m= RH122#1n2$ % & ' ( ) RH=0.01097nm-1Tues. Nov. 18, 2008 Phy208 Lect. 2321Balmer series Transitions terminate at n=2 Each energy level has energyEn=-13.6 / n2 eV E.g. n to 2 transition Emitted photon has energy Emitted wavelength! Ephoton= "13.6eVn2# $ % & ' ( " "13.6eV22# $ % & ' (
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