User:Alexandra S. Andrego/Notebook/Physics 307L/2009/09/14

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Planck's Constant
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 * style="background-color: #F2F2F2" align="center"|  |Main project page


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Purpose

 * The purpose of this lab is to measure Planck's Constant(h/e) using properties of the Photoelectric Effect.
 * Planck's Constant can be calculated through the use of the following photoelectric equation:
 * $$E=h\nu=KE_{max}+W_0\,\!$$ this equation can be found in Prof. Gold's Manual on pages 32-33
 * We can plot the relationship between the potential and the frequency of our spectral lines to find experimental values for h and WO in this equation.

Materials



 * Mercury Vapor Light Source and Light Block(Model OS-9286)
 * Voltage Range: 108-132 VAC
 * Power: 125 W MAX
 * Frequency: 47-63 HZ
 * 115 Volts
 * Light Aperture (Model AP-9369)
 * Coupling Bar (Model AP-9369)
 * Digital Voltmeter (Model 37XR-A)and/or (model FLUKE 111)
 * 2 Connection Cables (Model 8-24)
 * Stopwatch Function on Alex's Phone(Model LG Envy 2)
 * Two 9 Volt Batteries
 * Duracell-Procell
 * h/e Apparatus (Model AP-9369)
 * 3 Filters
 * Relative Transmission
 * Yellow Line
 * Green Line

Safety

 * Some points about safety that should be considered before beginning this lab are...
 * Proper handling of the mercury bulb(The light box minimizes this danger)
 * Check for any damage on all cables and machinery
 * Avoid touching the surfaces of the filters
 * Basic safety procedures used in working with electrical equipment (Such as proper grounding of the equipment)
 * Be cautious of static electricity when dealing with the h/e Apparatus
 * Turn on our mercury bulb 20 minutes before use and avoid toggling the power.
 * Because we are dealing with optical equipment be cautious of allowing too much light into our apparatus

Set Up

 * To see the Lab guidelines visit Prof. Gold's Lab Manual

To begin the experiment the following preliminary steps were taken

 * Tested the voltage of the 2 9 volt batteries located in the h/e Apparatus
 * our Digital Voltmeter gave us a reading of 15.97 Volts
 * Hooked up our digital voltmeter to the h/e apparatus
 * Turned on our light source and allowed it to warm up for the required 20 minutes
 * Placed the h/e Apparatus directly in front of the light source and lined up the beam of light with the face plate
 * Focused the beam on the face plate by sliding the light aperture on its mounting rods.
 * Turned the h/e Apparatus on and lined up the first colored maxima of the grating on the slot of the face plate.
 * "Zero" out our h/e apparatus by using the "Zero" button. This discharges any accumulated charge on our apparatus.
 * By using the filters and the spectral lines, measure the potential on the apparatus created by the light.
 * Be sure to use a stopwatch to time how long it takes for the potential to re-stabilize for each trial.
 * Calculate the value of h/e (Planck's Constant)

Measurements and Data

 * Experiment 1
 * We had to experimentally find the stopping potential for each colored spectral line for each grade of the relative transmission filter (100%,80%,60%,40%,20%).
 * We then had to measure the fall time for each grade of the relative transmission filter for each spectral color line. This was carried out by using a stopwatch to measure the time it took for the h/e apparatus to fall back to the stopping potential.
 * The data can be seen in the table below.


 * Experiment 2
 * We had to find the stopping potential for each colored spectral line(using only the green and yellow filters for their corresponding spectraal lines)
 * We repeated this process for the second order spectral lines as well.
 * The data can be seen in the table below.




 * In order to do our final analysis and calculations for this lab we need to know the known wave lengths and frequencies for our different colors of light. We obtained the following chart and information from Professor Gold's Manual (page 38)


 * {| border="1"

!Color !Frequency (Hz) !Wavelength (nm)
 * Yellow
 * 5.18672E+14
 * 578
 * Green
 * 5.48996E+14
 * 546.074
 * Blue
 * 6.87858E+14
 * 435.835
 * UV 1(or Violet)
 * 7.40858E+14
 * 404.656
 * }
 * UV 1(or Violet)
 * 7.40858E+14
 * 404.656
 * }

Calculations and Analysis

 * Passing different amounts of the same colored light through our variable transmission filter elongates the amount of time it takes for the capacitor in our h/e apparatus to reach the stopping potential. This is because our variable transmission filter decreases the number of photons hitting our photo diode per second. The diode still needs the same amount of transferred energy from the photons to reach the specific stopping potential, so when using the filters we are only slowing the process.


 * This can be seen in the following graph...




 * We can now use the rest of our data to plot the stopping potential versus the frequency of our light to help us in calculating our value of h/e. We can make this plot for both our first order spectral lines, and our second order spectral lines.


 * These plots can be seen in the following graph...




 * As you can see in the graph above we have given each plot a best fit linear line and allowed our excel program to calculate and demonstrate the equations for both of those lines. We will use this information in our actual calculation of h/e below.

Finding a Value for h/e

 * The total maximum energy of the electrons leaving the cathode in our experiment can be calculated using the following:
 * $$E =h \nu= KE_{max} + W_0 \,\!$$
 * $$KE_{max}=\frac{1}{2}m_ev^2$$
 * where $$E=h\nu\,\!$$ is the initial energy of the photon
 * and $$E=KE_{max}+W_0\,\!$$ is the resulting energy (the final kinetic energy of the electron plus the energy loss due to the overcoming the work function)
 * $$m_e\,\!$$ is the rest mass of the electron and $$v\,\!$$ is the final velocity of the electron
 * The negative potential, $$ V_s\,\!$$, needed to stop the flow of electrons is derived by equating the potential barrier, $$ :eV_s\,\!$$, to the electron's kinetic energy where $$e\,\!$$ is the charge of an electron and
 * $$eV_s=KE_{max}\,\!$$
 * So...
 * $$E=eV_s+W_0=h\nu\,\!$$
 * $$eV_s=h\nu-W_0\,\!$$
 * $$V_s=\frac{h\nu-W_0}{e}\,\!$$
 * From this we can see that there is a linear relation between the stopping potential $$V_s\,\!$$ and the frequency $$\nu\,\!$$
 * We can find the slope of this equation to be $$\frac{h}{e}\,\!$$.
 * Using the slope from our best-fit line and the electron's charge, $$e\,\!$$, we can approximate the value of Planck's constant to be
 * $$e=1.602\times {10^{-19}} C\,\!$$
 * $$h=me\,\!$$
 * where $$m\,\!$$ is the slope of our line.
 * So...


 * $$m_{first order}=4 \pm 0.001\times 10^{-15} Vs\,\!$$
 * $$h_{measured, first order}=me=(4\pm 0.001\times 10^{-15} Vs)(1.602\times {10^{-19}} C)\,\!$$
 * $$\simeq 6.408\pm 0.0016\times 10^{-34} Js\,\!$$


 * $$m_{second order}=3\pm 0.001\times 10^{-15} Vs\,\!$$
 * $$h_{measured, second order}=me=(3\pm 0.001\times 10^{-15} Vs)(1.602\times {10^{-19}} C)\,\!$$
 * $$\simeq 4.806\pm 0.0016\times 10^{-34} Js\,\!$$


 * By using the y-intercept from our graph we can find the work function $$W_0\,\!$$ for our equation
 * $$y=mx+b\,\!$$
 * $$y_{intercept}=\frac{W_0}{e}\,\!$$
 * $$W_0=ey_{intercept}\,\!$$


 * $$y_{first order}=(4\pm 0.001\times 10^{-15})x-1.5483\pm 0.001\,\!$$
 * $$y_{intercept, first order}=-1.5483\pm 0.001\,\!$$
 * $$W_{0measured, first order}=(-1.5483\pm 0.001 V)(1.602\times {10^{-19}} C)\,\!$$
 * $$\simeq -2.48\pm 0.0016\times 10^{-19} J\,\!$$


 * $$y_{second order}=(3\pm 0.001\times 10^{-15})x-0.94\pm 0.001\,\!$$
 * $$y_{intercept, second order}=-0.94\pm 0.001\,\!$$
 * $$W_{0measured, second order}=(-0.94\pm 0.001 V)(1.602\times {10^{-19}} C)\,\!$$
 * $$\simeq -1.506\pm 0.0016\times 10^{-19} J\,\!$$

Notes about Our Uncertainty

 * We were unable to fully focus the light from our light aperture onto the face plate of the h/e apparatus because the support bars were not long enough on the light aperture.
 * When we were measuring our stopping potential for each color on the spectral line we noticed that our values varied by a small but not an insignificant amount for each grading of the relative transmission filter. We believe that this should not be varying and that the stopping potential should be the same for all gradings because the filter should not affect the stopping potential for the spectral color. These inconsistencies could be due to the way we measure our voltage. The use of a common collector still allows for a small amount of current drainage from the digital volt meter. This could cause or small discrepancies in the measured stopping potential for each spectral color.
 * Due to the fact that our original digital voltmeter(Model 37XR-A) died on us we had to switch over to a new voltmeter(model FLUKE 111). We were unable to find one of the same model(Model 37XR-A) that was not dead, so we had to use a different make(model FLUKE 111). The new digital voltmeter did not read voltages to the the ten-thousandths place. This will effect our analysis later.
 * NOTE:This exchange of voltmeters took place during experiment one using the green filter on 100%.
 * Using a stopwatch to measure the time for stabilization was a huge source of inconsistency in our experiment. It took two or three trials of trying to time the stabilization before we were able to determine an effective stopping point(or value for our stopping potential). Perhaps it would have been a lot easier and more effective to have measured the time it would have taken for our voltmeter to read a certain percentage of our measured stopping potential (refer back to our Oscilloscope Lab to see an example of this method).

Summary
If you wish to see my informal summary of this lab follow this link

Acknowledgments
Please note that Anastasia Ierides was my lab partner for this lab. Her version of this lab can be found here Prof. Gold's Lab Manual Kyle Martin's Planck's Constant Lab Notebook Google Docs Common Collector Wikipedia Page


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