Wave / Particle Duality

1. Wave / Particle Duality PART I • Electrons as discreteParticles. • Measurement of e (oil-drop expt.) and e/m (e-beam expt.). • Photonsas discrete Particles. • Blackbody Radiation:Temp. Relations & Spectral Distribution. • Photoelectric Effect: Photon “kicks out” Electron. • Compton Effect: Photon “scatters” off Electron. PART II • Wave Behavior: Diffraction and Interference. • PhotonsasWaves:l = hc / E • X-rayDiffraction (Bragg’s Law) • ElectronsasWaves: l = h / p = hc / pc • Low-Energy Electron Diffraction (LEED)

2. Electrons: Quantized Charged Particles • In the late 1800’s, scientists discovered that electricity was composed of discrete or quantized particles (electrons) that had a measurable charge. • Found defined amounts of charge in electrolysis experiments, whereF (or Farad) = NA e. • OneFarad (96,500 C) always decomposes one mole (NA) of monovalent ions. • Found chargee using Millikan oil-drop experiment. • Found charge to mass ratio e/m using electron beams in cathode ray tubes.

3. Electrons: Millikan’s Oil-drop Expt. • Millikan measured quantized charge values for oil droplets, proving that charge consisted of quantized electrons. • Formula for charge q usedterminal velocity of droplet’s fall between uncharged plates (v1) and duringrise(v2) between charged plates. Charged oil droplets Charged Plates Scope to measure droplet terminal velocity.

4. Electron Beam e/m :Motion in E and B Fields Circular Motion of electron in B field:  Larger e/mgives smaller r, orlarger deflection. Electron (left hand) Proton (right hand)

5. Electron Beam e/m: Cathode Ray Tube (CRT) • Tube used toproduce an electron beam, deflect it with electric/magnetic fields, and thenmeasure e/m ratio. • Found in TV, computer monitor, oscilloscope, etc. J.J. Thomson Charged Plates (deflect e-beam) Deflection  e/m (+) charge Cathode (hot filament produces electrons) (–) charge Slits (collimate beam) Fluorescent Screen(view e-beam)

6. Ionized Beam q/m: Mass Spectrometer Mass spectrometer measures q/m for unknown elements. 1. Ions accelerated by E field. Ion path curved by B field. 2. 2. 1.

7. Photons: Quantized Energy Particle • Light comes in discrete energy “packets” called photons. Energy of Single Photon Rest mass From Relativity: For a Photon (m = 0): Momentum of Single Photon

8. Photons: Electromagnetic Spectrum 400 nm Gamma Rays X-Rays Ultraviolet Visible Spectrum Visible Frequency Wavelength Infrared Microwave Short Radio Waves TV and FM Radio AM Radio Long Radio Waves 700 nm

9. Photoelectric Effect: “Particle Behavior” of Photon PHOTON IN ELECTRON OUT • Photoelectric effect experiment shows quantum natureof light, or existence of energy packets called photons. • Theory by Einstein and experiments by Millikan. • A single photon can eject a single electron from a material only if it has the minimum energy necessary (or work function f). • For example, if 1 eV is necessary to remove an electron from a metal surface, then only a 1 eV (or higher energy) photon can eject the electron.

10. Photoelectric Effect: “Particle Behavior” of Photon PHOTON IN ELECTRON OUT • Electron ejection occurs instantaneously, indicating that photons cannot be “added up.” • If 1 eV is necessary to remove an electron from a metal surface, then two 0.5 eV photons cannot add together to eject the electron. • Extra energy from the photon is converted to kinetic energy of the outgoing electron. • For example above, a 2 eV photon would eject an electron having 1 eV kinetic energy.

11. Photoelectric Effect: Apparatus • Electrons collected as “photoelectric” currentat anode. • Photocurrent becomes zero when retarding voltage VR equals stopping voltageVstop, i.e. eVstop = Ke • Photons hit metalcathodeand eject electrons with work function f. • Electrons travel from cathode to anode against retarding voltage VR(measures kinetic energy Ke of electrons). Cathode Anode Light

12. Photoelectric Effect: Equations • Total photon energy =e– ejection energy + e– kinetic energy. • where hc/l= photon energy, f = work function, and eVstop = stopping energy. • Special Case: No kinetic energy (Vo = 0). • Minimum energy to eject electron.

13. Photoelectric Effect: IV Curve Dependence Intensity I dependence Vstop= Constant f1 > f2 > f3 Frequency fdependence f1 f2 f3 Vstop f

14. Photoelectric Effect: Vstop vs. Frequency hfmin Slope = h = Planck’s constant -f

15. Photoelectric Effect: Threshold Energy Problem If the work function for a metal is f = 2.0 eV, then find the threshold energy Et and wavelengthlt for the photoelectric effect. Also, find the stopping potential Voif the wavelength of the incident light equals 2t and t /2. At threshold, Ek = eVo = 0 and the photoelectric equation reduces to: For 2t, the incoming light has twice the threshold wavelength (or half the threshold energy) and therefore does not have sufficient energy to eject an electron. Therefore, the stopping potential Vo is meaninglessbecause there are no photoelectrons to stop! For t/2, the incoming light has half the threshold wavelength (or twice the threshold energy) and can therefore eject an electron with the following stopping potential:

16. Compton Scattering: “Particle-like” Behavior of Photon • An incoming photon (E1) can inelastically scatter from an electron and lose energy, resulting in an outgoing photon (E2) with lower energy (E2 < E1). • The resulting energy loss (or change in wavelength Dl) can be calculated from the scattering angleq. Incoming X-ray Scattered X-ray Scattering Crystal Angle measured

17. Compton Scattering: Schematic PHOTON INPHOTON OUT(inelastic)