Quantum Mechanics: Note 2

The Photoelectric Effect Phillipp Lenard: First discovered the photoelectric effect. The photoelectric effect is an experiment where the actions of light photons are considered to be similar to particles instead of waves. When light (with a high enough frequency) shines on a piece of metal, the photons will collide with electrons in the metal and “bounce” off of them, similar to billiard balls hitting one another. Ejected Electrons Incident Light Photons

Metal

Using classical physics, scientists tried to explain this phenomenon. They compared it to water waves from a lake coming to the shore. As waves came to the beach, they moved pebbles up the beach. Large waves (high intensity) will move the pebbles a long way while small waves (low intensity) will move the pebbles a small distance. They tried to change the intensity of the light in the photoelectric effect experiment (just like changing the size of the wave), but it had NO EFFECT! The electrons were only affected by the frequency of the light, not the intensity. If water behaved the same way, this means that high frequency waves would only be able to move the pebbles, and that low frequency waves would not do anything at all. Light is clearly behaving not like a classical wave. Above this threshold frequency, light would act like a particle. A second problem occurred, only light at a certain minimum (threshold) frequency could eject electrons. Anything lower than this special frequency simply did not work. This value was unique for different types of metals. Enter Einstein Einstein used the new theories of Max Planck and assumed that incident light consists of energy quanta of magnitude E = hf. Energy photons penetrate the surface layer of the metal, where the energy of the photon is transferred to the kinetic energy of the electron. Some energy is required to “dig out” the electron, while the left over is kinetic energy:

Quantum Mechanics: Note 2 Thus, if we had an original energy of hf, and we subtract some energy needed to get the electron out of the metal (work, W), the left over will be the kinetic energy of the electron: E k = hf − W where: -Ek is kinetic energy of an electron (in Joules, J) -h is “Planck’s Constant” equal to 6.626x10-34Js -f is the frequency of the photon in Hz -W is the “work function” measured in J € *Notice how this equation resembles y = mx + b. *Note: Work functions are usually measured in electronvolts, where 1 eV = 1.6x10-19 J Eg. 1. Violet light (425 nm) is incident on a piece of sodium (W = 2.36 eV). a) How much kinetic energy will an ejected electron have? b) What is the velocity of the electron? Millikan “Not So Fast Mr. Einstein!” While working in Chicago, Millikan truly believed that light was a wave and wanted to prove Einstein wrong. He tried the photoelectric effect on different metals and found the following: All lines on the graph were _____________ and reflected Einstein’s equation perfectly. After three years, Millikan finally gave up and believed that Einstein was correct. -Where the lines intersect the x-axis, this is where Ek = 0 J. These points are the threshold frequencies (fo). -The points where the lines intersect the y-axis are the work functions (energy needed to bring the electron to the surface