Exam 3 is Thursday Dec. 3 (after Thanksgiving) 5:30-7 pm, Birge 145 Students w / scheduled academic conflict please stay after class Tues. Nov. 24 to arrange alternate time. Covers: all material since exam 2. Bring: Calculator One (double-sided) 8 1/2 x 11 note sheet Schedule: Week14HW: assigned Thur. Nov. 19, due Fri. Dec. 4 (two weeks) Last material for exam: Lecture of Tues. Nov. 24 Exam review: Tuesday, Dec. 1, in class Thurs. Nov. 19, 2009 Phy208 Lect. 23 1 Summary 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. E photon hf hc / 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 Thurs. Nov. 19, 2009 Phy208 Lect. 23 2 Photon properties of light Photon of frequency f has energy hf E photon hf hc / h 6.626 1034 J s 4.14 1015 eV s hc 1240eV nm Red light made of ONLY red photons The intensity of the beam can be increased by increasing the number of photons/second. Photons/second = energy/second = power Thurs. Nov. 19, 2009 Phy208 Lect. 23 3 Quantization of light Quantum mechanically, brightness can only be changed in steps, with energy differences of hf. Possible energies for green light (=500 nm) One quantum of energy: one photon Two quanta of energy two photons etc Think about light as a particle rather than wave. Thurs. Nov. 19, 2009 Phy208 Lect. 23 E=4hf E=3hf Energy E=2hf E=hf 4 Thompson’s model of atom J.J. Thomson’s model of atom A volume of positive charge Electrons embedded throughout the volume A change from Newton’s model of the atom as a tiny, hard, indestructible sphere This model is not correct! Thurs. Nov. 19, 2009 Phy208 Lect. 23 5 Thurs. Nov. 19, 2009 Phy208 Lect. 23 6 Resulted in new model Planetary model Based on results of thin foil experiments Positive charge is concentrated in the center of the atom, called the nucleus Electrons orbit the nucleus like planets orbit the sun Thurs. Nov. 19, 2009 Phy208 Lect. 23 7 Difference between atoms Simplest is Hydrogen: Other atoms 1 electron orbiting 1 proton number of orbiting negative electrons same as number of positive protons in nucleus Different elements have different number of orbiting electrons Helium: 2 electrons Copper: 29 electrons Uranium: 92 electrons! Organized into periodic table of elements First concentrate on hydrogen atom Thurs. Nov. 19, 2009 Phy208 Lect. 23 8 Planetary model and radiation Circular motion of orbiting electrons: electrons emit EM radiation at orbital frequency. Similar to radio waves emitted by accelerating electrons 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! Thurs. Nov. 19, 2009 Phy208 Lect. 23 9 Line 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). Hydrogen Mercury Wavelength (nm) Thurs. Nov. 19, 2009 Phy208 Lect. 23 10 The Bohr atom Retained ‘planetary’ picture with circular orbits Only certain orbits are stable Radiation emitted only when electron jumps from one stable orbit to another. Here, the emitted photon has an energy of Einitial-Efinal Einitial Photon Efinal Stable orbit Stable orbit Thurs. Nov. 19, 2009 Phy208 Lect. 23 11 Energy levels Instead of drawing orbits, just indicate energy an electron would have if it were in that orbit. Zero energy n=4 n=3 E3 13.6 eV 32 n=2 E2 13.6 eV 22 E1 13.6 eV 12 Energy axis n=1 Thurs. Nov. 19, 2009 Phy208 Lect. 23 12 Hydrogen atom energies Quantized energy levels: Each corresponds to different Orbit radius Velocity Particle wavefunction Energy Each described by a quantum number n Zero energy n=4 n=3 E3 13.6 eV 32 n=2 E2 13.6 eV 22 E1 13.6 eV 12 n=1 13.6 E n 2 eV n Thurs. Nov. 19, 2009 Energy Phy208 Lect. 23 13 Emitting and absorbing light Zero energy n=4 n=3 13.6 E 3 2 eV 3 n=2 13.6 E 2 2 eV 2 Photon emitted hf=E2-E1 n=1 E3 13.6 eV 32 n=2 E2 13.6 eV 22 E1 13.6 eV 12 Photon absorbed hf=E2-E1 E1 13.6 eV 12 Photon is emitted when electron drops fromone quantum state to another Thurs. Nov. 19, 2009 n=4 n=3 Phy208 Lect. 23 n=1 Absorbing a photon of correct energy makes electron jump to higher quantum state. 14 Hydrogen emission This says hydrogen emits only photons 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 orbiting electron. Thurs. Nov. 19, 2009 Phy208 Lect. 23 15 Hydrogen atom An electron drops from an -1.5 eV energy level to one with energy of -3.4 eV. What is the wavelength of the photon emitted? Zero energy A. 827 nm B. 653 nm C. 476 nm D. 365 nm E. 243 nm n=4 n=3 Photon emitted hf=E2-E1 n=2 hf = hc/ = 1240 eV-nm/ E3 1.5 eV E1 13.6 eV n=1 Thurs. Nov. 19, 2009 E2 3.4 eV Phy208 Lect. 23 16 Energy conservation for Bohr atom Each orbit has a specific energy En=-13.6/n2 Photon emitted when electron jumps from high energy to low energy orbit. Ei – Ef = h f Photon absorption induces electron jump from low to high energy orbit. Ef – Ei = h f Agrees with experiment Thurs. Nov. 19, 2009 Phy208 Lect. 23 17 Hydrogen emission spectrum Hydrogen is simplest atom One electron orbiting around one proton. n=4 n=3 The Balmer Series of emission lines empirically given by 1 1 RH 2 2 2 n m 1 n = 4, = 486.1 nm n = 3, = 656.3 nm Hydrogen Thurs. Nov. 19, 2009 Phy208 Lect. 23 18 Balmer series Transitions terminate at n=2 Each energy level has energy En=-13.6 / n2 eV E.g. n to 2 transition Emitted photon has energy 13.6eV 13.6eV 1 1 E photon 13.6 eV 2 2 2 2 2 n n 2 Emitted wavelength 1 hc 1240 eV nm 1 1 91.18nm E photon 13.6 eV 22 n 2 1/22 1/n 2 Thurs. Nov. 19, 2009 Phy208 Lect. 23 19 Why stable orbits? Bohr argued that the stable orbits are those for which the electron’s orbital angular momentum L is quantized as h 2 L me v r n Electron velocity Electron orbit radius Integer: n=1,2,3… Bohr combined this with the Coulomb force to find allowed orbital radii and energies. Thurs. Nov. 19, 2009 Phy208 Lect. 23 20 Including more physics Circular orbit, electron is accelerating (centripetal acceleration = v2/r = Force/mass) Force causing this accel. is Coulomb force ke2/r2 between pos. nucleus and neg. electron v2 FCoulomb = r m Also gives a condition for angular momentum. Thurs. Nov. 19, 2009 Phy208 Lect. 23 21 Bohr model of H-atom v2 e2 = FCoulomb /m k 2 /m r r Orbital motion: p mv centripetal acceleration L2 mvr mke2 r 2 Quantization: Thurs. Nov. 19, 2009 Coulomb force / mass L mvr n 2 2 Phy208 Lect. 23 2 2 22 Radius of H-atom states L2 n 2 2 and Quantization n 1 2 3 L2 mke2 r Orbital motion Quantized orbital radius orbit radius ao 4ao 9ao Thurs. Nov. 19, 2009 mke2 r 2 2 2 r n n ao 2 mke n2 2 ao Bohr radius 0.529Å Phy208 Lect. 23 23 Energy of H-atom states Total Energy = kinetic + p 2 2m e 2 k 2r potential rn n 2 ao e 2 k r ke2 1 e 2 e2 k k 2 2r r 2ao n Quantized energy Thurs. Nov. 19, 2009 Phy208 Lect. 23 En 13.6 eV n2 24