# User:Ryan P. Long/Notebook/Physics 307L/2009/10/19

Planck's Constant Main project page
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## Equipment

• Pasco Scientific Hg Light Source OS-9286
• Pasco Scientific h/e Apparatus AP-9368
• Fluke 111 Multimeter w/ banana cables
• National Instruments Data Acquisition Device
• Labview 8.6

## Setup

We followed the instructions in Professor Gold's Manual for experiment 2, and though we intended to follow it for experiment 1 as well, we decided to use a different method. The setup was fairly simple for this experiment. We plugged in the mercury light source and let it heat up for around 20 minutes before taking measurements, in order to ensure that the lamp was emitting at a constant intensity. Next, we plugged the voltmeter into the h/e apparatus to test the two 9 volt batteries. The batteries had to have been at a minimum level of 6 volts for the experiment to run properly (see page 3 of the Pasco Manual). Finally, before taking measurements, we focused the light from the lamp on the detector by moving the lens back and forth on the support rods until the image was as sharp as possible.

Light source and apparatus

## Data

### Experiment 1

The purpose of experiment 1 was to measure the changes caused by varying the intensity of the light incident on the detector. To measure this effect, the procedure called for using the filter with different transmission percentages for a single color and measuring the time taken for the voltage to reach its stopping potential. Since we assumed this would be similar to a capacitor charging which we knew to be an exponential function. Though the Gold manual called for the use of a simple stop watch to measure the charge time, we knew that exponentials theoretically never reach their max value, and in reality take a long time to do so. Instead of using a stopwatch, we decided to use the DAQ and Labview to plot the voltage as a function of time so we could try to fit our voltage to an exponential (and calculate a time constant for the rise time).

To collect data, we chose to use the 1st order blue color band. After centering the blue band on the detector, we held the zero button to remove any residual voltage remaining in the circuit. Then we started the data collection through labview and let it run for a while so we could get enough data for a good curve fit. The Labview code we used is attached here.

### Experiment 1 raw data

Though we intended to have multiple trials of data, we discovered in our preliminary analysis that our approach had problems with it, and therefore do not have as much data as would have been necessary. These problems will be discussed in the analysis section.

### Experiment 2

The purpose of experiment 2 was to measure the effect of different wavelengths on the stopping potential of the detector circuit and use this to measure Planck's constant. To collect our data, we positioned the h/e apparatus in front of five different colors of the spectrum produced by the mercury source: yellow, green, blue, violet, and ultraviolet. For the yellow and green lines, we used the corresponding yellow and green filters to remove any other frequency of light that might be passing through the hole. After centering the color bands on the detector, we held the zero button for a few seconds and then released it. We watched the voltage until it reached a maximum, which was then recorded in 5 trials for all 5 colors in both the 1st and second order diffracted color bands. In between measuring the first and second order lines, we readjusted the focus.

### Experiment 2 data

Note: The second order green line took considerably longer to charge than any of the other bands.

SJK 16:18, 30 October 2009 (EDT)
16:18, 30 October 2009 (EDT)

## Analysis

Experiment 1: Experiment one didn't yield promising results whatsoever. We knew that measuring the times with a stop watch would be time consuming and innacurate, so we attempted to step outside the box and use a DAQ and labview to acquire our results. We attempted to fit our data of the rise times to an exponential function, but failed to turn up significant results. Each time it was radically different, seemingly due to an inconsistent spike at the beginning of each trial.

Experiment 2: Our results from this experiment were much more successful in comparison to experiment 1. I used the raw data from above and fitted it to a line using a best fit formula incorporating the priniciple of maximum likelihood parameters, I followed Dr. Koch's Page on fitting a line The value I obtained for the first order band was:

$4.485\times 10^{-15} eVs$

or

$7.185\times 10^{-34} Js$

and for the second order band my value was:

$4.06\times 10^{-15} eV\cdot s$

or

$6.504\times 10^{-34} Js$

The accepted value from wikipedia is:

• $6.62606896(33)\cdot 10^{-34} Js$

The second order green line took a while to reach its stopping voltage, and that value was a much higher voltage than the first order voltage, we think some very faint higher frequency light may have also been hitting the detector.