27-3 Photon Theory & Photoelectric Effect

1. 27-3 Photon Theory & Photoelectric Effect • 1905 Einstein extended the quantum theory of light by proposing a new theory • Einstein argued that when an oscillating body emits light the body’s energy must decrease in energy by an amount of nhf.

2. Then to conserve energy, the light should be emitted in packets or quanta each with an energy of • E=hf • Where f is the frequency of the emitted light • h is still Planck’s constant

3. Photons • This suggests that light is transmitted as tiny particles, photons.

4. Photoelectric Effect • When light shines on a surface, electrons are found to be emitted • This is the photoelectric effect • Happens with many materials, most easily observed on metals.

5. Both the EM (electromagnetic) wave theory and the photon theory predicts that electrons should be emitted when a light shines on the metal • The theories give different predictions in the details of the photoelectric effect. • Maximum kinetic energy (KEmax) of the emitted electrons can be measured.

6. Reverse the voltage so C is negative • Emitted electrons will be repelled by negative electrode • But if the voltage is small enough the fastest electrons will still make it to C and a current will flow • Increase the voltage until just when the current reaches zero-no electrons have sufficient KE • This is called the stopping potential or stopping voltage, V0 KEmax= eV0

7. Wave Theory • Assumes monochromatic light and the two important properties of a light wave are its intensity and its frequency (or wavelength) • When these two properties are varied the wave theory makes the following predictions

8. Increase the light intensity and the number of photoelectrons and their energy should increase • Frequency of light shouldn’t affect the KE of the photoelectrons. Only the intensity matters.

9. Photon Theory • Very different predictions • First in monochromatic light all photons have the same energy (hf). Increasing the intensity just increases the number of photons not the energy of each photon. • An ejected electron happens because of a collision with a single photon • And all energy is transferred to the electron and the photon no longer exists

10. Electrons are held in the metal by some attractive force a minimum energy, W0, is required to just get an electron out through the surface. • W0 is called the work function • If the frequency of the incoming light is so low no electrons are emitted because of the work function. hf<W0 • If hf>W0 then electrons will be ejected and energy will be conserved. • The energy above the W0 shows up as KE

11. The least tightly held electrons will be emitted with the maximum KE the • hf=KEmax + W0 • These would be just the surface electrons, most electrons require more energy to just be released so the KE will be much less

12. Predictions of the Photon Theory • Increase in intensity just produces more photons not the resulting KE • As the frequency of the light increases the maximum KE of the released electrons increases linearly • KEmax=hf-W0 • There is a minimum frequency or “cutoff” frequency below which no electrons will be ejected no matter how intense the light

13. Photon theory predictions are very different from the wave theory. • RA Millikan did careful experiments that proved Einstein’s photon theory

14. 27-4 Energy, Mass & Momentum of a Photon • Because a photon is traveling at the speed of light it is a relativistic particle • Relativistic formulas for dealing with mass, energy and momentum must be used • And after the derivations

15. 27-6 Photon Interactions; Pair Production • Four type of interactions that a photon can undergo as it passes into matter • 1. Photoelectric effect: photon is completely absorbed, electron is ejected • 2. Photon may be totally absorbed by electron, but not have enough energy to eject it; the electron moves into an excited state • 3. The photon can scatter from an atom and lose some energy (lose of frequency not speed) • 4. The photon can produce matter, an electron-positron pair. (positron has same mass as electron, but opposite charge.)