User:Alex G. Benedict/Notebook/Physics 307L: Junior Lab/Planck's Constant

=Planck's Constant Lab Summary=

Summary of Activities
In this lab I measured the stopping potential and time for stabilization for different frequencies of light using a photo diode, and a tube filled with Mercury gas which emitted light of known wavelengths. I measured the stopping potential using a digital multimeter attached to the photo diode, and the time for stabilization using a standard stop watch. Using the voltages and frequencies of the light I was able to determine experimentally the value of Planck's constant to a fair degree of accuracy.

The photo diode was just a material which when exposed to light of a high enough frequency began to release electrons, which generated a small current as electrons flowed off the material. These electrons had some energy which was larger than the energy they had in their bound state, and begin to collect on the anode. Eventually the anode had such a large collection of electrons that any extra electrons would have to have a huge amount of kinetic energy to overcome the potential difference between the cathode and anode, and so eventually electrons stop flowing. The voltage at the point where none of the new electrons has enough energy to overcome the potential difference is the stopping potential.

Lab Notebook
My lab notebook is located here: My Lab Notebook.

Results
The value I obtained for Planck's constant was

$$h\simeq 6.06\pm 0.38\times 10^{-34} Js$$

which is a relative error of 8%, and about 2 standard deviations from the actual value, which is not that great of a result.

and for the work function was

$$W_{measured}\simeq -1.98\pm 0.24\times 10^{-19} J$$

Where the uncertainties come from the linest function.

The largest source of error would probably be the extra light in the room from the computer monitors and hallway lights and such.

From the first part of the lab, the fact that the time it took to get back to the same potential varied based on the intensity of the light implies that there are some particles colliding with the metal, since there are more electrons being emitted per second when there are more photons colliding with the metal. The fact that the change in stopping potential with respect to the number of particles is almost nonexistent means only the energy per photon matters, and not the total energy of the beam of photons.

Improvements for Future Labs
It would be good if instead of using Mercury we used some other gas that might have more colors to measure, so that we could have more independent measurements to use.

Links
I would like to thank Andrego for her excellent derivation of how to determine h from the least squares fit of the stopping potential vs frequency, and her very detailed equipment list. User:Alexandra_S._Andrego/Notebook/Physics_307L/2009/09/14