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From Last Time…

This text discusses the concepts of energy and power in an electromagnetic wave, with a focus on the photoelectric effect and the energy of photons. It explores experimental results, Einstein's explanation, and the wavelength dependence of electron ejection.

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From Last Time…

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  1. From Last Time… Energy and power in an EM wave Polarization of an EM wave: oscillation plane of E-field Phy208 Lect. 22

  2. Maxwell’s unification: 1873 • Intimate connection between electricity and magnetism • Experimentally verified by Helmholtz and others, 1888 “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement”, Lord Kelvin, 1900 "Heavier-than-air flying machines are impossible."(1895) Phy208 Lect. 22

  3. Modern Physics • Dramatic changes in physics at turn of century. • Relativity: Completely different idea of time and space. • Quantum Mechanics: Completely different idea of matter and light. Traditional conceptions of matter and light useful, but not “fundamental” Phy208 Lect. 22

  4. Energy of light • In the classical picture of light (EM wave), we change the brightness by changing the power (energy/sec). • This is the amplitude of the electric and magnetic fields. • Classically, these can be changed by arbitrarily small amounts • Brightness, power, unrelated to frequency, wavelength Phy208 Lect. 22

  5. The photoelectric effect • A metal is a bucket holding electrons • Electrons need some energy in order to jump out of the bucket. Light can supply this energy. Energy transferred from the light to the electrons. Electron uses some of the energy to break out of bucket. Remainder appears as energy of motion (kinetic energy). A metal is a bucket of electrons. Phy208 Lect. 22

  6. Unusual experimental results • Not all kinds of light work • Red light does not eject electrons More red light doesn’t either No matter how intense the red light, no electrons ever leave the metal Until the light frequency passes a certain threshold, no electrons are ejected. Phy208 Lect. 22

  7. The experiment • Complication: When light ejects electrons, they have range of velocities • Analyze: Apply variable E-field that opposes electron motion • Stopping potential: voltage at which highest kinetic energy (Kmax) electrons turned back Phy208 Lect. 22

  8. The Data • Stopping potential depends on light frequency • Higher frequency light ejects electron with more energy • Stopping potential goes to zero at some critical frequency • For light below that frequency, no electrons are ejected. Phy208 Lect. 22

  9. Eabsorb Analyzing the data Escaped from solid Kmax • Electrons absorb fixed energy Eabsorb from light Eo Bound in solid Energy Highest KE electron Lowest KE electron SOLID Range of electron energies in solid Phy208 Lect. 22

  10. Einstein’s explanation • Einstein said that light is made up of photons, individual ‘particles’, each with energy hf. • One photon collides with one electron - knocks it out of metal. • If photon doesn’t have enough energy, cannot knock electron out. • Intensity ( = # photons / sec) doesn’t change this. Minimum frequency required to eject electron Phy208 Lect. 22

  11. Einstein’s analysis • Electron absorbs energy of one photon Slope of line =h/e Minimim frequency =Work function Phy208 Lect. 22

  12. Wavelength dependence Short wavelength: electrons ejected Long wavelength: NO electrons ejected Threshold depends on material Lo-energy photons Hi-energy photons Phy208 Lect. 22

  13. E=4hf E=3hf E=2hf E=hf Quantization and photons • 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 energytwo photons • etc • Think about light as a particle rather than wave. Phy208 Lect. 22

  14. The particle perspective • Light comes in particles called photons. • Energy of one photon is E=hf f = frequency of light • Photon is a particle, but moves at speed of light! • This is possible because it has zero mass. • Zero mass, but it does have momentum: • Photon momentum p=E/c Phy208 Lect. 22

  15. Compton scattering • Photons can transfer energy to beam of electrons. • Determined by conservation of momentum, energy. • Compton awarded 1927 Nobel prize for showing that this occurs just as two balls colliding. Arthur Compton, Jan 13, 1936 Phy208 Lect. 22

  16. Before collision After collision Compton scattering • Photon loses energy, transfers it to electron • Photon loses momentum transfers it to electron • Total energy and momentum conserved Photon energy E=hfPhoton mass = 0Photon momentum p=E/c Phy208 Lect. 22

  17. One quantum of green light • One quantum of energy for 500 nm light Quite a small energy! Quantum mechanics uses new ‘convenience unit’ for energy: 1 electron-volt = 1 eV = |charge on electron|x (1 volt) = (1.602x10-19 C)x(1 volt) 1 eV = 1.602x10-19 J In these units, E(1 photon green) = (4x10-19J)x(1 eV / 1.602x10-19 J) = 2.5 eV Phy208 Lect. 22

  18. Simple relations • Translation between wavelength and energyhas simple form in electron-volts and nano-meters Green light example: Phy208 Lect. 22

  19. Photon energy What is the energy of a photon of red light (=635 nm)? 0.5 eV 1.0 eV 2.0 eV 3.0 eV Phy208 Lect. 22

  20. 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 4x10-14 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 Phy208 Lect. 22

  21. 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 Phy208 Lect. 22

  22. Question A red and green laser both produce light at a power level of 2.5mW. Which one produces more photons/second? A. Red B. Green C. Same Red light has less energy per photon so needs more photons! Phy208 Lect. 22

  23. Nobel Trivia For which work did Einstein receive the Nobel Prize? A. Special Relativity: E=mc2 B. General Relativity: gravity bends Light C. Photoelectric Effect & Photons Phy208 Lect. 22

  24. But light is a wave Phy208 Lect. 22

  25. Neither wave nor particle • In some cases light shows properties typical of waves • Interference, diffraction • In other cases, shows properties associated with particles. • Photoelectric effect, Compton scattering • Conclusion: • Light not a wave, or a particle, but something we haven’t thought about before. • Reminds us of waves. • In some ways of particles. Phy208 Lect. 22

  26. Particle-wave duality • Light has a dual nature • Can show particle-like properties (collisions, etc) • Can show wavelike properties (interference). • It is neither particle nor wave, but some new object. • Can describe it using “particle language” or “wave language”whichever is most useful Phy208 Lect. 22

  27. Only one photon present here Photon interference? Do an interference experiment again. But turn down the intensity until only ONE photon at a time is between slits and screen ? Is there still interference? Phy208 Lect. 22

  28. Single-photon interference 1/30 sec exposure 1 sec exposure 100 sec exposure Phy208 Lect. 22

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