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Planck's Constant Lab: 11/10-23/2008
Experiment #1
For this portion of the lab, I was measuring the charge time for the apparatus with different transmission filters to determine if the transmission affected the charge time, the stopping potential, or both.
The results for this part were all qualitative based off the graphs.
For the first try I was measuring the burst time as seen in figure 1.
The data in this set does not look very linear, most likely because of the multiple sources of error in the triggering of the oscilloscope with the apparatus. When I drained the potential from the apparatus, it suddenly jumped when the ground switch was released, even if covered to prevent light from coming in.
Another reason for the discrepancies in the linear relationship is that pulling the cover away took an amount of time on order with the burst time, meaning that doing so could lengthen the times as that was not entirely consistent for all the measurements.
For the second set of data, I did as recommended in the lab manual measuring the amount of time required to reach full charge.
Running the experiment to full voltage showed that the different intensities of light had almost no effect on the stopping potential and only affected the charge time. This means that the energy imparted to each individual electron as a result of the photoelectric effect is independent of the intensity of the light.
Using the different spectral lines changed the value of the stopping potential for the electrons, meaning that the energy of the electrons is related to the wavelength of the light. Because the charge time was not noticeably affected by changing the wavelength, it demonstrates that the charge time is related only to the intensity of the light.
The linear relationship with a coefficient of determination greater than or approximately equal to .95 for all data sets in figure 2 demonstrates that there is a strong linear relationship between the intensity and the charge time.
This data supports the photon theory of light, as the energy of each photon is dependent only upon it's frequency, and as the data shows that the energy of each electron is dependent only upon the frequency of the light, the energy from each individual photon would be transferred into the electrons. If the wave theory of light was demonstrated here, increasing the intensity would also increase the stopping potential of the electrons, but that is shown to not happen in the experiment.
The slight difference in the stopping potential between the different intensities is most likely due to the radiation of energy by the photons as they hit the filter. Because photons can radiate energy, when they hit the less transparent filters, there is a greater chance of scattering and reflection by the electrons, which would cause a small portion of their energy to go into the scattered/reflected light.
SJK 18:05, 18 December 2008 (EST)18:05, 18 December 2008 (EST) Very nice figures (though for figure 2, I don't think a linear relationship is expected, since time is 1/rate.
Figure 1: Relationship between intensity and Voltage/Time for initial charge burst in ultraviolet light
Figure 2: Relationship between intensity and Charge time to full voltage for different colors
Experiment #2
In this portion of the experiment I calculated the value of Planck's constant and the work function of the apparatus.
The relationship between the stopping potential and the wavelength/ frequency is given by:
[math]\displaystyle{ {e}{V_{0}}={h}{f}-{\phi}={h}\frac{c}{\lambda}-{\phi} }[/math] where [math]\displaystyle{ e }[/math] is the charge of the electron, [math]\displaystyle{ V_{0} }[/math] is the stopping potential, [math]\displaystyle{ h }[/math] is Planck's constant, [math]\displaystyle{ f }[/math] is the frequency, [math]\displaystyle{ \phi }[/math] is the work function, [math]\displaystyle{ c }[/math] is the speed of light, and [math]\displaystyle{ \lambda }[/math] is the wavelength
To do the calculations, I used a least-squares regression done with the linest function in excel to generate the slope and intercept of the data for each of the three data sets taken in the first and second order of the spectrum. Those calculations can be found at the Excel standard (.xls) file located here
Doing so I got six values for h and [math]\displaystyle{ \phi }[/math], such that I could take the weighted average of all the data values, which since the weighted average is dependent on the standard deviation of the parent distribution or the number of data points, the values were all weighted equally.
For the first order of the spectra I generated values of h as 7.29E-34, 7.15E-34, and 6.93E-34 Joule*seconds and values of [math]\displaystyle{ \phi }[/math] at 2.64E-19, 2.56E-19, and 2.45E-19 Joules.
Graphs of these three data sets are seen in figures 3-5 below.
For the second order of the spectra I generated values of h as 5.93E-34, 5.91E-34, and 5.93E-34 Joule*seconds and values of [math]\displaystyle{ \phi }[/math] at 1.61E-19, 1.62E-19, and 1.61E-19 Joules.
Graphs of these three data sets are seen in figures 6-8 below.
SJK 18:07, 18 December 2008 (EST)18:07, 18 December 2008 (EST) Actually, the 2nd order measurements are quite skewed by the "green band mystery" (which is UV contamination)...thus, the weighted average is inappropriate. The 1st order measurements are statistically significantly different from accepted, due to a mystery we still have not solved.
Taking the weighted average and calculating the total error due to the slope, I came up with final answers of:
Comparing my final answer with the accepted value of Planck's Constant, [math]\displaystyle{ h=6.626\times 10^{-34}\mathrm{J}\cdot\mathrm{s} }[/math], shows that the 95% confidence interval of my answer, does include the accepted value as a 95% confidence interval of my measured value is: [math]\displaystyle{ 6.418\times 10^{-34}\mathrm{J}\cdot\mathrm{s} \lt {h} \lt 6.630\times 10^{-34}\mathrm{J}\cdot\mathrm{s} }[/math]
Figure 3: Trial 1 for first order spectra of stopping potential against frequency
Figure 4: Trial 2 for first order spectra of stopping potential against frequency
Figure 5: Trial 3 for first order spectra of stopping potential against frequency
Figure 6: Trial 1 for second order spectra of stopping potential against frequency
Figure 7: Trial 2 for second order spectra of stopping potential against frequency
Figure 8: Trial 3 for second order spectra of stopping potential against frequency
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