Physics307L:People/McCoy/Planck

Background
For my lab over the dates November 10-23, I chose to do measure the value of Planck's constant via the use of the photoelectric effect. In the lab, I used a Pasco Scientific h/e apparatus and mercury light source to observe the photoelectric in the ejection of electrons from the metallic surface and measuring the stopping potential of the electrons. In doing so, I was able to calculate the value of Planck's constant from the slope relating the stopping potential of the electrons and the frequency of the light.

Data
For the first part of the experiment I took two different sets of data, one to try and measure the burst time, and the second to measure the charge time to reach the full potential against the intensity of the light. The data was taken to show the photon theory of light, demonstrating that the energy of the electrons is related only to the frequency of the incoming photons, which makes it viable to calculate Planck's constant as I did in the second part. The data for this is found in the first section of my raw data located here.

In the second part of the experiment, I calculated Planck's constant from a linear fit between the 3 data sets in both the first and second order spectra, then took the weighted average to find my final value. The data is found in the second section of my raw data linked above. The calculations can be found at this link. The error used in the calculations is the error in the slope and intercept given in the second line of the linest output in the excel file linked from my analysis notes.

Results
The results from experiment 1 in the lab were all qualitative and are described in the analysis section of my notes (the second linked file). To summarize those results, would be that I determined that the photoelectric effect is a phenomenon due to the particle theory of light, as the energy in light is determined by the frequency and that amount of energy is carried by each photon, that minus the work function of the metal surface, the rest of that energy goes into the freed electrons, and the intensity of the light is independent of the stopping potential for the electrons.

From Experiment #2, my final value of Planck's constant was $$h=6.524(53)\times 10^{-34}\mathrm{J}\cdot\mathrm{s}$$

Comparing this result to the accepted value of $$h=6.626\times 10^{-34}\mathrm{J}\cdot\mathrm{s}$$ demonstrates that the 95% confidence interval of my answer includes the accepted value, meaning that my answer is relatively accurate. It also means that if my answer was indeed correct, the accepted value of Planck's constant would be found in this experiment more than 5 percent of the time. For the value of the work function my final value came out to be $$\phi=1.301(22)\mathrm{eV}$$, which is significantly lower than that of any known metal. The lowest work function is that of cesium at 2.1 eV which would be more than 20 standard deviations above my approximate value. For this reason I believe that my value for the work function is significantly biased as it is far too low to be viable for any metallic element.

Causes of Error
The primary causes of error in this experiment are the timing for the demonstration of the photon theory of light, and the discharge and subsequent jump in voltage even if covered in Experiment #1, and the data sets for the second order green line. Other causes of error would be the bias of the oscilloscope and multimeter, the diffracting lens for the mercury lamp, and the filters for the apparatus.

The error caused by the timing and discharge would affect the linear fits seen in figures 1 and 2 in my calculation notes, but would not have an affect on the measurement of Planck's constant. Those errors are both random errors as the calculation of the time was done by hand, meaning there could be a shift based on human reaction time, or if I didn't notice the multimeter reach the final value. The error in the discharge is also random as it doesn't jump to a set value but when discharged it jumps to an apparently arbitrary value regardless of the amount of light entering the apparatus.

The error due to the second green line would have a dramatic affect on my calculated value as in the second order spectra, the frequencies and stopping potentials had a distinguishable linear relationship with the exception of the point for the green spectral line as that had a measured stopping potential at least .2V greater than the expected value from the linear fit. This could be a result of the green filter breaking down with respect to the second order spectrum, or a mis-alignment of the apparatus such that a higher frequency light was entering the apparatus. The transmission filter caused a small amount of error in experiment 1 as the stopping potential was not constant for all the intensities, most likely as a result of scattering decreasing the energy of each photon by a small amount. The other error that could have a significant affect on the measurement is the diffraction grating that was used to separate the mercury spectrum, as that could also have decreased the photon energy by inducing the emission of lower energy photons as they passed through, but that is relatively unlikely.

The bias in the multimeter and oscilloscope could have had a slight error that would result in all my values being slightly higher/lower than expected, mostly altering the work function as the oscilloscope and multimeter measured the voltages approximately .1 Volts different for all the data values, being the reasoning that I used the multimeter for all measurements of the potentials, as I felt that was more accurate, also the greater number of significant digits that were measured and displayed with the multimeter. This error, although it would not have any noticeable affect on the value of Planck's constant, may have been the primary reason that my value for the work function was significantly below the value of any known metal.