Physics307L:People/Barron/labsum~Planck

Balmer Series Lab Summary
Here is the lab manual page.

Here are my lab notes.

Partner: Justin Muehlmeyer

Introduction
Most people will immediately invoke "$$E=mc^2$$" when asked for what Einstein received his Nobel Prize. As scientists in training, we know that the Prize was instead for his work on the Photoelectric Effect, and this famous relation:

$$ E = h\nu + \omega_0 $$

...which describes the energy of an electron ejected from a material due to an atom's interaction with a photon of energy $$h\nu$$.

$$h$$ is Planck's constant, and $$\nu$$ is the frequency of the photon. $$omega_0$$ is the work function, which is a material-dependant value of energy the energized electron has to overcome in order to eject. This experiment is designed to ascertain $$h$$.

Setup

A detailed, illustrated discussion of the experimental setup can be found in Dr. Gold's manual.

Final Results
Experiment 1 - Preliminaries

This experiment is used to show the physical realities of Planck's constant and the photoelectric effect qualitatively. We take data on the stopping potential for a frequency, then see how much time the capacitor in the apparatus takes to charge to the stopping potential. Rinse and repeat for another frequency.

{|border="1" cellpadding="3" cellspacing="1" align="center"
 * align="center" style="background:#f0f0f0;"|Vstop vs. Transmission
 * align="center" style="background:#f0f0f0;"|Charge Time vs. Transmission
 * align="center" style="background:#f0f0f0;"|Charge Time vs. Transmission

The accepted values of ω0 and h do not coincide with my 68% confidence interval, but qualitatively are not far off. If one looks at my lab notes, there seems to be significant systematic error in ascertaining the correct stopping potential for either experiment. The most obvious anomaly is the ever-rising trend of voltage measurements in the 2nd-order part of experiment 2. This could result from an electronics design flaw, or perhaps have something to do with the steady rise in temperature of the Hg lamp. By the end of the experiment, the lamp was too hot to touch. It is not obvious how that would change the stopping potential reading, however. The diffraction grating would still separate the component frequencies of light into individual spectra, but the intensity of light would probably increase. An increase in stopping potential as a result of higher intensity would correspond to a classical wave theory of light, which is troubling.