Understanding Photoelectric Effect in AP Physics 2

3. Plan for Today (AP Physics 2) • Turn in homework • Notes/Lecture on Photoelectric Effect

4. Background • In the late 1800s, scientists discovered that when light shines on certain metallic surfaces, electrons are emitted • This is called the photoelectric effect • Emitted electrons are photoelectrons

5. Big Idea with Set Up • If there is sufficient energy in the light, the electrons can be freed • The electrons would then go from the emitter to the collector (well, some would) • Electrons would be freed only if there is enough energy to free them

6. Energy at this level • Photons = packets of energy • Einstein extended Planck’s idea of energy quantization to electromagnetic waves • Photon is a tiny packet of light energy • Made when a quantized oscillator jumps from a higher energy state (E = nhf) to a lower state (E = (n-1)hf). • Because of conservation of energy, the decrease in energy hf must be the photon’s energy

7. Energy of a Photon • E = hf • h is Planck’s constant • F is frequency of the light

8. 1 eV = 1.60 x 10-19 J 1 keV = 1.6 x 10-16 J 1 MeV = 1.6 x 10-13 J Energy in Electron-volts Photon energies are so small that the energy is better expressed in terms of the electron-volt. One electron-volt (eV) is the energy of an electron when accelerated through a potential difference of one volt.

9. E = 2.24 eV Or Since 1 eV = 1.60 x 10-19 J Example 1:What is the energy of a photon of yellow-green light (l = 555 nm)? First we find f from wave equation: c = fl E = 3.58 x 10-19 J

10. Useful Energy Conversion Since light is often described by its wavelength in nanometers (nm) and its energy E is given in eV, a conversion formula is useful. (1 nm = 1 x 10-9 m) If lis in nm, the energy in eV is found from: Verify the answer in Example 1 . . .

11. Back to the Photoelectric Effect

12. Photoelectric Set Up • Photocell (evacuated glass tube) contains a metal plate (E) connected to the negative side of a power supply. Another plate C is connected to the positive end of the power supply. • When light shines on E (of a particular wavelength), we have a current! • The current is from photoelectrons emitted from the negative plate (emitter) and collected at the positive plate (collector)

13. Diagram of Set Up

14. Photoelectric Effect and Potential Difference • At a large potential difference, current reaches a maximum • Current increases as incident light intensity increases

15. Now what if we flip the battery • This way the collector plate is negative and the emitter plate is positive • Then the current drops to a lower value because most of the emitted photoelectrons are repelled by the collector plate • Only electrons with enough KE to overcome the repulsion reach the collector plate

16. Battery Flipped Continued • When the potential difference is more negative than Vs, no electrons reach the collector and current is 0 • This point Vs is called the stopping potential • Stopping potential is independent of radiation intensity

17. Stopping Potential

18. Maximum Kinetic Energy of Photoelectrons • KEmax = e * Stopping Potential • e is the charge of an electron

19. Problems with Classical Physics (Why the Photoelectric Effect) • No electrons emitted if light frequency is below a cutoff frequency (for a given material) • We would expect photoelectric effect at any frequency with enough intensity • Maximum KE is independent of light intensity • We would expect higher intensity means more energy means more KE in photoelectrons

20. More Problems • Max KE of photoelectrons increases with increases frequency • We wouldn’t expect there to be a relationship • Electrons emitted almost instantaneously • We would expect a bit of a delay as photoelectrons absorb energy

21. Incident light Cathode Anode A C Ammeter A + - The Photo-Electric Effect When light shines on the cathode C of a photocell, electrons are ejected from A and attracted by the positive potential due to battery. There is a certain threshold energy, called the work function W ( ), that must be overcome before any electrons can be emitted. Photons must give some of their energy here first

22. Photoelectric Effect Equation • KEmax = hf – W • Work function is the minimum energy with which an electron is bound in the metal

23. Cutoff Wavelength • Graph of frequency vs. KEmax gives us a linear relationship • X intercept (horizontal frequency axis) gives us the cutoff frequency where no photoelectrons are emitted

24. Cutoff Wavelength • Waves greater than the cutoff wavelength do not result in emission of photoelectrons

25. Incident light Cathode Anode A C Ammeter Threshold wavelength lo A + - Photo-Electric Equation The conservation of energy demands that the energy of the incoming light hc/l be equal to the work function W of the surface plus the kinetic energy ½mv2of the emitted electrons.

26. l = 600 nm A K = 1.10 x 10-19 J Or Example 2:The threshold wavelength of light for a given surface is 600 nm. What is the kinetic energy of emitted electrons if light of wavelength 450 nm shines on the metal? ; K = 2.76 eV – 2.07 eV K = 0.690 eV

27. Incident light Cathode Anode The stopping potential is that voltage Vo that just stops the emission of electrons, and thus equals their original K.E. V A + - Potentiometer Photoelectric equation: Stopping Potential A potentiometer is used to vary to the voltage V between the electrodes. Kmax = eVo

28. The slope of a line: y Slope xo x y x Slope of a Straight Line (Review) The general equation for a straight line is: y = mx + b The x-interceptxooccurs when line crosses x axis or when y = 0. The slope of the line is the rise over the run:

29. Finding h constant Stopping potential V Slope y x fo Frequency Finding Planck’s Constant, h Using the apparatus on the previous slide, we determine the stopping potential for a number of incident light frequencies, then plot a graph. Note that the x-intercept fo is the threshold frequency.

30. Stopping potential V Slope y fo x Frequency Example 3:In an experiment to determine Planck’s constant, a plot of stopping potential versus frequency is made. The slope of the curve is 4.13 x 10-15 V/Hz. What is Planck’s constant? h = e(slope) = (1.6 x 10-19C)(4.13 x 10-15 V/Hz) Experimental Planck’s h = 6.61 x 10-34 J/Hz

31. Incident light Cathode Anode A V + - Stopping potential: Vo= 0.800 V Example 4:The threshold frequency for a given surface is 1.09 x 1015 Hz. What is the stopping potential for incident light whose photon energy is 8.48 x 10-19 J? Photoelectric Equation: W = (6.63 x 10-34 Js)(1.09 x 1015 Hz) =7.20 x 10-19 J

32. Planck’s Equation: E = hf (h = 6.626 x 10-34 J s) Photon 1 eV = 1.60 x 10-19 J The Electron-volt: E = hf 1 MeV = 1.6 x 10-13 J 1 keV = 1.6 x 10-16 J Summary Apparently, light consists of tiny bundles of energy called photons, each having a well-defined quantum of energy.

33. Incident light Cathode Anode A C Ammeter Threshold wavelength lo A + - Summary (Cont.) If lis in nm, the energy in eV is found from: Wavelength in nm; Energy in eV

34. Stopping potential V Slope y fo x Frequency Summary (Cont.) Planck’s Experiment: Incident light Cathode Anode V A + - Potentiometer Kmax = eVo