Tues. Nov. 18, 2008Phy208 Lect Exam 3 is Tuesday Nov. 25 Students w / scheduled academic conflict please stay after class Tues. Nov. 18 (TODAY) to arrange alternate time. 5:30-7 pm, 2103 Ch (here) Covers: all material since exam 2. Bring: Calculator One (double-sided) 8 1/2 x 11 note sheet Exam review: Thursday, Nov. 20, in class

Tues. Nov. 18, 2008Phy208 Lect From Last Time… Photoelectric effect and light quantization

Tues. Nov. 18, 2008Phy208 Lect 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. Electron in metal absorbs one photon Can escape metal if photon energy large enough E photon >Work function E o Excess energy E photon -E o shows up as kinetic energy

Tues. Nov. 18, 2008Phy208 Lect Photon 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 by increasing the number of photons/second. Photons/second = energy/second = power

Tues. Nov. 18, 2008Phy208 Lect How 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 that could be seen was 4x Watt. How many green (500 nm, 2.5 eV) photons is this? A. 10 photons B. 100 photons C. 1,000 photons D. 10,000 photons

Tues. Nov. 18, 2008Phy208 Lect Quantization of light Possible energies for green light ( =500 nm) E=hf E=2hf E=3hf E=4hf One quantum of energy: one photon Two quanta of energy two photons etc Think about light as a particle rather than wave. Quantum mechanically, brightness can only be changed in steps, with energy differences of hf. Energy

Tues. Nov. 18, 2008Phy208 Lect 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!

Tues. Nov. 18, 2008Phy208 Lect. 23 8

Tues. Nov. 18, 2008Phy208 Lect 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

Tues. Nov. 18, 2008Phy208 Lect Difference between atoms Simplest is Hydrogen: 1 electron orbiting 1 proton Other atoms 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

Tues. Nov. 18, 2008Phy208 Lect 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! Planetary model and radiation

Tues. Nov. 18, 2008Phy208 Lect 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)

Tues. Nov. 18, 2008Phy208 Lect 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 E initial -E final Stable orbit E initial E final Photon

Tues. Nov. 18, 2008Phy208 Lect Energy levels Instead of drawing orbits, just indicate energy an electron would have if it were in that orbit. Zero energy n=1 n=2 n=3 n=4 Energy axis

Tues. Nov. 18, 2008Phy208 Lect Hydrogen atom energies Zero energy n=1 n=2 n=3 n=4 Energy Quantized energy levels: Each corresponds to different Orbit radius Velocity Particle wavefunction Energy Each described by a quantum number n

Tues. Nov. 18, 2008Phy208 Lect Emitting and absorbing light Photon is emitted when electron drops from one quantum state to another Zero energy n=1 n=2 n=3 n=4 n=1 n=2 n=3 n=4 Absorbing a photon of correct energy makes electron jump to higher quantum state. Photon absorbed hf=E 2 -E 1 Photon emitted hf=E 2 -E 1

Tues. Nov. 18, 2008Phy208 Lect 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.

Tues. Nov. 18, 2008Phy208 Lect 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? A. 827 nm B. 653 nm C. 476 nm D. 365 nm E. 243 nm Zero energy n=1 n=2 n=3 n=4 Photon emitted hf=E 2 -E 1 hf = hc/ = 1240 eV-nm/

Tues. Nov. 18, 2008Phy208 Lect Each orbit has a specific energy E n =-13.6/n 2 Photon emitted when electron jumps from high energy to low energy orbit. E i – E f = h f Photon absorption induces electron jump from low to high energy orbit. E f – E i = h f Agrees with experiment! Energy conservation for Bohr atom

Tues. Nov. 18, 2008Phy208 Lect Hydrogen emission spectrum Hydrogen is simplest atom One electron orbiting around one proton. The Balmer Series of emission lines given empirically n = 3, = nm Hydrogen n = 4, = nm n=3n=4 R H = nm -1

Tues. Nov. 18, 2008Phy208 Lect Balmer series Transitions terminate at n=2 Each energy level has energy E n =-13.6 / n 2 eV E.g. n to 2 transition Emitted photon has energy Emitted wavelength

Tues. Nov. 18, 2008Phy208 Lect Why stable orbits? Bohr argued that the stable orbits are those for which the electron’s orbital angular momentum L is quantized as Electron velocity Electron orbit radius Integer: n=1,2,3… Bohr combined this with the Coulomb force to find allowed orbital radii and energies.

Tues. Nov. 18, 2008Phy208 Lect Including more physics Circular orbit, electron is accelerating (centripetal acceleration = v 2 /r = Force/mass) Force causing this accel. is Coulomb force ke 2 /r 2 between pos. nucleus and neg. electron Also gives a condition for angular momentum.

Tues. Nov. 18, 2008Phy208 Lect Bohr model of H-atom Quantization: Orbital motion: centripetal acceleration Coulomb force / mass

Tues. Nov. 18, 2008Phy208 Lect Radius of H-atom states and Quantization Orbital motion Quantized orbital radius norbit radius 1 a o 2 4 a o 3 9 a o

Tues. Nov. 18, 2008Phy208 Lect Energy of H-atom states Total Energy = kinetic + potential Quantized energy

Tues. Nov. 18, 2008Phy208 Lect Energy quantization in a pendulum Swinging pendulum. Larger amplitude, larger energy Small energy Large energy Quantum mechanics: Not every swing amplitude is possible energy cannot change by arbitrarily small steps

Tues. Nov. 18, 2008Phy208 Lect Energy quantization Energy can have only certain discrete values Energy states are separated by  E = hf. f = frequency h = Planck’s constant= x J-s d E=mgd=(1 kg)(9.8 m/s 2 )(0.2 m) ~ 2 Joules  E min =hf=3.3x J << 2 J Quantization not noticeable Suppose the pendulum has Period = 2 sec Freq = 0.5 cycles/sec  E = hf=3.3x J for pendulum = spacing between energy levels

Tues. Nov. 18, 2008Phy208 Lect Question This quantum system has equally-spaced energy levels as shown. Which photon could possibly be absorbed by this system? E 1 =1 eV E 2 =3 eV E 3 =5 eV E 3 =7 eV A nm B. 413 nm C. 310 nm D. 248 nm