Physics307L:People/Gooden/Notebook/070910

Experiment 1 - The Photon Theory of Light

• This experiment is to determine Planks Constant, using the theory of the photoelectric effect

and the photon theory of light pioneered by Plank and Eistein.

Set Up

• This experiment is set up using a mercury vapor lamp and a decive called the h/e apparatus which takes advantage of the photoelectric effect. The two devices are set up opposite eachother so that light from the lamp is directed into the h/e apparatus. Inside of the apparatus light falls onto a cathod and electrons are ejected towards an anode by the photoelectic effect. Then the apparatus applies a reverse potential (stopping potential) so that the ejected electrons arrive at the anode with zero kinetic energy and the current goes to zero. The apparatus then outputs this particular voltage to a Digital Volt Meter (DVM) connected to it.
• We used the DVM to check the batterys inside the h/e apparatus were working properly by connecting to the battery output terminals on the device. Connecting the red wire to each output at a time and the black to ground we measured a correct ~9 volts per battery.

• NOTE: DVM reads incorrectly for producing a 0 potential through the h/e apparatus. It reads at a (+) .04V minimum

Experiment #1 : Photon Theory

• All measurements are using the first order spectral lines with the Variable transmission filter.

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• 1st set of data using the variable transmission filter measuring both stopping potential and times for the h/e apparatus to return to the stopping potential once all charge is discharged from it.

   Ultra-violet maxima stopping voltage readings - (NON TRANSMISSION LENS - 2.15)
   
   2.09V in 3.06 seconds at 100%
   2.09V in 4.89 seconds at 80%
   2.09V in 5.49 seconds at 60%
   2.09V in 6.99 seconds at 40%
   2.09V in 9.69 seconds at 20%

   Violet maxima stopping voltage readings - (NO TRANSMISSION LENS - 1.78)
   Previously we calculated these values:
   
   1.73V in 5.91 seconds at 100%
   1.73V in 3.83 seconds at 80%
   1.73V in 3.53 seconds at 60%
   1.73V in 4.18 seconds at 40%
   1.73V in 8.70 seconds at 20%
   They turned out to be somewhat incorrect
   NEW VALUES:
   1.74V in 3.63 seconds at 100%
   1.74V in 5.37 seconds at 80%
   1.74V in 5.58 seconds at 60%
   1.74V in 7.71 seconds at 40%
   1.74V in 14.90 seconds at 20%

   Blue maxima readings - (NO TRANSMISSION LENS - 1.57V)
   
   1.53V 4.71 seconds - new trial 1.97 100%
   1.53V 3.70 seconds - new trial 3.13 80%
   1.54V 2.70 seconds - new trial 4.03 60%
   1.54V 3.50 seconds - new trial 5.76 40%
   1.54V 6.69 seconds - new trial 6.60 20%

   Green maxima stopping voltage readings - 
   (NO TRANSMISSION LENS .91V W/O GREEN FILTER 1.05V)
   
   .91V 6.91 seconds at 100%
   .90V 8.15 seconds at 80%
   .90V 10.90 seconds at 60%
   .90V 16.99 seconds at 40%
   .90V 26.77 seconds at 20%

    Yellow maxima stopping voltage readings - 
   (NO TRANSMISSION LENS .77V W/0 YELLOW FILTER 1.11V)
   
   .76V 5.62 seconds at 100%
   .76V 6.17 seconds at 80%
   .76V 8.73 seconds at 60%
   .76V 15.03 seconds at 40%
   .76V 30.65 seconds at 20%

Experiment #2 : Planks Constant

• for this part we are suppose to once again determine the stopping potential for each color in the mercury spectrum. However we must do this for second order spectral lines also. Doing each of these two things twice to test for reproducability, and then plot all four sets of data and perform a least squares fit and determine h and Wo. Where Wo is the work function for the cathod inside the h/e apparatus.

   Ultraviolet -1st order             Ultraviolet -2nd order
      - Measurement 1: 2.12V                   - Measurement 1: 2.10V
      - Measurement 2: 2.12V                   - Measurement 2: 2.10V
   Violet -1st order                  Violet -2nd order
      - Measurement 1: 1.76V                   - Measurement 1: 1.76V
      - Measurement 2: 1.77V                   - Measurement 2: 1.76V
   Blue -1st order                    Blue -2nd order
      - Measurement 1: 1.56V                   - Measurement 1: 1.57V
      - Measurement 2: 1.55V                   - Measurement 2: 1.58V
   Yellow -1sr order                  Yellow -2nd order
      - Measurement 1: .77V                    - Measurement 1: .78V
      - Measurement 2: .76V                    - Measurement 2: .78V
   Green -1st order                   Green -2nd order
      - Measurement 1: .91V                    - Measurement 1: 1.10V
      - Measurement 2: .9V                     - Measurement 2: 1.10V

In our search for determining how to figure out the frequency order of the color spectrum we (Zane G. and I) found a wiki website: Color spectrum and for EM spectrum where we obtained most of our formulas and the actual value of Planck's constant.

[math]\displaystyle{ \lambda = \frac{c}{f} \,\! }[/math]

and

[math]\displaystyle{ E=hf \,\! }[/math]

or

[math]\displaystyle{ E=\frac{hc}{\lambda} \,\! }[/math]

Data Analysis

• In this section we will analyze the four sets of data by plotting the data and performing linear least squares fits. We will be plotting electric charge e*V where V is the measured stopping potential vs the frequency of the light.

Photoelectric Effect/Stopping Potential Relations

• From the least squares data fitting we find a result for planks constant h for each data set and the work function for the material Wo,where the first two results correspond to the 1st-order measurements 1 and 2 and then the second two results correspond with the 2nd-order measurements 1 and 2. :

  h=7.17107E-34,         Wo=2.475e-19
  h=7.24797E-34,         Wo=2.475e-19
  h=6.53185E-34,         Wo=1.9862e-19
  h=6.53787E-34.         Wo=1.9904e-19

• These are the plots of the data and the least squares lines for each data set. The plots are made as eV vs. frequency, where eV is the electron charge times the voltage. The plots are in order of data set from left to right.

Mean Value of Plank's Constant and work function

• The mean value we find for plank's constant using the four values above and the work function is

  h= 6.87219E-34           Wo=2.8003e-20

Standard Deviation of the Mean

• The standard deviation given by the formula below is the error of our measurement and we find that it is:

  [math]\displaystyle{ \sigma = 3.90785E-35  }[/math]

• The standard deviation is the error bars for our measurement assuming a gaussian distribution for the error

[math]\displaystyle{ \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}. }[/math]

Plank's Constant

• We find that plank's constant is

   h= 6.87219E-34 +/- .390785E-34