Physics307L F09:People/Andrego/Planck's Constant
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PLANCK'S CONSTANT LAB SUMMARY
^{SJK 02:31, 5 October 2009 (EDT)}Please note that Anastasia Ierides was my lab partner for this lab. Her version of this lab can be found here. You can also find her lab summary by following this link.
Brief Overview
- In this lab we experimentally found the value of Planck's Constant(h) and h/e. We were able to do this by using a photo diode and cathode set-up with a mercury light source to measure the stopping potential, or the energy of the photons hitting our diode through various filters. With the help of measuring the time it took for a certain percentage of our spectral light to re-stabilize at its stopping potential we were able to use the equation for the photoelectric effect and a series of graphs to determine our experimental value of h. We discovered that we could relate the frequency of our incident light to the measured stopping potential with a linear relationship. When this relationship was graphed we were able to use the slope of our best fit linear line to compute h.
- For a more thorough account of the process and proceedure for this lab please see my lab notebook or Prof. Gold's Lab Manual
- Please note that though I did repeat this experiment for incident light of the second order in our spectra, however due to the results of my graph ( the relationship between frequency and stopping potential) were not satisfactory (the slope differed by too great of an amount for accuracy in experimental values) and hence I did not include their analysis in my summary. I suspect that this lack of confidence is due to huge amounts of error in being able to measure the stopping potential of the incident light in the second order.
Data Results
- Our experiment yielded the following results
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h_{measured}\simeq 6.408\pm 0.0016\times 10^{-34} Js}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle W_{0 measured}\simeq -2.48\pm 0.0016\times 10^{-19} J}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{h}{e}\simeq4\pm 0.001\times 10^{-15} Vs} ^{SJK 02:22, 5 October 2009 (EDT)}
Error
- For ALL RECORDED accounts of error in our experiment methods and procedures please see the Notes about Our Uncertainty section in our Planck's Constant Lab Notebook.
For this lab our sources of error and uncertainty in our results can be attributed to both systematic (the focusing of the light) and random (human error during timing.. ect. )
- Calculated Error Percentage^{SJK 02:20, 5 October 2009 (EDT)}
Knowing that our expected value of h is ...
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h_{accepted}=6.62606896(33)\times10^{-34} Js}
We can calculate our observational error...
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \% error=\frac{h_{accepted}-h_{measured}}{h_{accepted}}=\frac{6.62606896(33)\times10^{-34} Js-6.408\times 10^{-34} Js}{6.62606896(33)\times10^{-34} Js}\simeq 3.29 \%\,\!}
Conclusions
- Based on our very small margin of observed error, we can conclude that our experiment was fairly successful in approximating Planck's Constant for light frequencies of the first order. There are still however some unsolved questions in our data. We were unable to understand why our green light spectra gave us very different values for stopping potentials when we varied the transmission filter. This phenomina implies that green light loses energy when filtered. We are still not sure if this is correct.^{SJK 02:27, 5 October 2009 (EDT)} We assume that our 3.29% error comes mainly from the points listed in our Lab Notebook under Notes about Our Uncertainty.
- All-in-all I found this lab to be very educational. I was able to really get a firm grip on the concepts of the photoelectric effect and the way a cathode-diode system works. I was most pleased to learn about the draining of voltage across a digital voltmeter and the way a common collector is able to correct this problem with marginal loss of voltage.