1. Wave Particle Duality Chapter 5

2. Lecture Objectives
Explain how the photoelectric effect is induced by light energy.
Indicate what is meant by the duality of light.
Discuss the wavelike properties of light that reveal its wavelike nature.
State Heisenberg’s Uncertainty Principle as it relates to atoms.
Indicate what information Schroedinger’s Wave Equation gives us about the electron.

3. The Photoelectric Effect
In 1886 and 1887, Heinrich Hertz discovered that UV light can cause electrons to be ejected from a metal surface.
According to the classical wave theory of light, the intensity of the light determines the amplitude of the wave, and so a greater light intensity should cause the electrons on the metal to oscillate more violently and to be ejected with a greater kinetic energy.
N.B. Intensity=Amplitude, so brighter light should have greater amplitude

4. The Photoelectric Effect
In contrast, the experiment showed that the kinetic energy of the ejected electrons depends on the frequency of the light.
The light intensity affects only the number of ejected electrons and not their kinetic energies.

5. Planck's Constant and the Energy of a Photon
In 1900, Max Planck asked: how does the radiation an object emits relate to its temperature?
His formula only made sense if he assumed that the energy of a vibrating molecule was quantized.
The energy would have to be proportional to the frequency of vibration, and it seemed to come in little "chunks" of the frequency multiplied by a certain constant.
This constant came to be known as Planck's constant, or h, and it has the value h=6.266 x10-32 J s.
It was an extremely radical idea to suggest that energy could only come in discrete lumps, even if the lumps were very small.
Planck actually didn't realize how revolutionary his work was at the time; he thought he was just fudging the math to come up with the "right answer," and was convinced that someone else would come up with a better explanation for his formula.

6. Einstein’s Explanation of the Photoelectric Effect
Based on Planck's work, Einstein proposed that light also delivers its energy in chunks; light would then consist of little particles, or quanta, called photons, each with an energy of Planck's constant times its frequency, E=hn.

7. Einstein’s Explanation of the Photoelectric Effect
In that case, the frequency of the light would make a difference in the photoelectric effect.
Higher-frequency photons have more energy, so they should make the electrons come flying out faster
Thus, switching to light with the same intensity but a higher frequency should increase the maximum kinetic energy of the emitted electrons.
If you leave the frequency the same but crank up the intensity, more electrons should come out (because there are more photons to hit them), but they won't come out any faster, because each individual photon still has the same energy.

8. Einstein’s Explanation of the Photoelectric Effect
And if the frequency is low enough, then none of the photons will have enough energy to knock an electron out of an atom.
So if you use really low-frequency light, you shouldn't get any electrons, no matter how high the intensity is.
If you use a high frequency, you should still knock out some electrons even if the intensity is very low.

9. Experimental Proof of Einstein’s Theory for the Photoelectric Effect
In , R.A. Millikan did a series of extremely careful experiments involving the photoelectric effect.
He found that all of his results agreed exactly with Einstein's predictions about photons, not with the wave theory.
Einstein actually won the Nobel Prize for his work on the photoelectric effect, not for his more famous theory of relativity.

10. Wave-Particle Duality of Light
Some experimental results, like Millikan’s, seem to prove beyond all possible doubt that light consists of particles
Others, like Young’s experiment, insist, just as irrefutably, that it's waves.
We can only conclude that light is somehow both a wave and a particle--or that it's something else we can't quite visualize, which appears to us as one or the other depending on how we look at it.