# Physics307L F09:People/Andrego/Planck's Constant

## PLANCK'S CONSTANT LAB SUMMARY

SJK 02:31, 5 October 2009 (EDT)
02:31, 5 October 2009 (EDT)
Very good summary, and overall very good job with this lab! Please also see notes on Anastasia's summary and both of your primary lab notebooks. The most notable thing for your next lab will be to include a statistically rigorous uncertainty on your final values (e.g., mean +/- standard error of the mean), and use this to compare with the accepted value. In addition, you will want to include more information in your data analysis section--specifically this time, information was missing that would have said how you calculated final uncertainties.

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
$\displaystyle h_{measured}\simeq 6.408\pm 0.0016\times 10^{-34} Js$
$\displaystyle W_{0 measured}\simeq -2.48\pm 0.0016\times 10^{-19} J$
$\displaystyle \frac{h}{e}\simeq4\pm 0.001\times 10^{-15} Vs$ SJK 02:22, 5 October 2009 (EDT)
02:22, 5 October 2009 (EDT)
As mentioned in your primary lab notebook, at first it was completely unclear where these uncertainties came from. Then, I think I realized where they came from (directly from your voltmeter uncertainty estimate). If so, this means you did not "propagate the uncertainty," correctly. Don't worry, though, we will go over this in lecture soon!

### 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 PercentageSJK 02:20, 5 October 2009 (EDT)
02:20, 5 October 2009 (EDT)
These discrepancies from the accepted value are good to calculate...but in the future, you will want to compare the discrepancy with your range of uncertainty...and this will provide you with a statistical basis for whether or not your measurements are consistent with the accepted value. This will become more clear as we talk about it over the next couple weeks. Also, very importantly: where do you get your accepted value? You definitely should cite the source of the accepted value, as that is very important information for the reader!

Knowing that our expected value of h is ...

$\displaystyle h_{accepted}=6.62606896(33)\times10^{-34} Js$

We can calculate our observational error...

$\displaystyle \% error=\frac{h_{accepted}-h_{measured}}{h_{accepted}}=\frac{6.62606896(33)\times10^{-34} Js-6.408\times 10^{-34} Js}{6.62606896(33)\times10^{-34} Js}\simeq 3.29 \%\,\!$

### 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)
02:27, 5 October 2009 (EDT)
I think you're talking about the issue with the 2nd order green band? If so, that's a famous mystery that I think is really fun to investigate. I'll leave it as a mystery in case you decide to return to this lab later w/ your formal report. It's definitely solvable.
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.