Planck's Constant and the Photoelectric Effect

SJK 15:10, 16 November 2008 (EST)
15:10, 16 November 2008 (EST)
Excellent summary, analysis, and lab notebook!

The photoelectric effect is important in the history of physics because it clearly displays the quantum theory of light. The photoelectric effect describes the emission of photoelectrons due to the absorption of light quanta; photons. According to Einstein's theory, each photon carries a certain amount of energy that is proportional to the frequency of light (not intensity, as in classical theory). The proportionality constant is the famous Plank constant. In this lab, we set out to find the value of this constant by measuring the stopping potential of a circuit, whose current is given by the time rate of change of photoelectron emission. In addition to measuring the planck constant, measuring the stopping potentials allows one to calculate the work function of the metal, which was also done.

Results

$h_{exp} = 7.26(14)\cdot 10^{-34} J \cdot s$

$h_{act} = 6.626\cdot 10^{-34} J \cdot s$

$W_{exp} =1.635(48)\cdot eV$

$W_{act} = 1.36(8) \cdot eV$

Conclusions

• While I believe that we gathered data well, given its linearity, our resulting planck constant and work function were clearly inconsistent with their respective accepted values. Our best measurement of the planck constant lies roughly four and a half standard deviations away from the accepted value (>99.99% confidence interval). The work function lies roughly 4 standard deviations away from the accepted value (>99.99% confidence interval).
• I believe that systematic error prevailed in this lab. While a definitive solution was not discovered, I entertain the possibilities in the discussion section of my report.
• If I had more time to explore the photon theory of light and the photoelectric effect, there is one thing that I would like to try -- I would like to build my own photoelectric effect apparatus. This way I would not have to question the accuracy of the black-box. However, I would likely introduce other uncertainties into the experiment in doing so. Either way it would be a great experience.