User:Anastasia A. Ierides/Notebook/Physics 307L/2009/09/14

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Planck's Constant Lab
Partner: Alex Andrego

Equipment

 * Mercury (Hg) Vapor Light Source with Light Block (Model OS-9286)
 * Info: -Line Voltage Range: 108-132 VAC
 * -Power: 125 W MAX
 * -Frequency: 47-63 HZ
 * -115 Volts
 * -Accessories: Light Aperture (Model AP-9369)
 * Coupling Bar (Model AP-9369)


 * Digital Voltmeters:
 * (AMPROBE 37XR-A) with 2 connection cables (Model B-24)
 * New DVM (model FLUKE 111) (same cables)


 * Two 9 Volt Batteries (Duracell PROCELL exp. MAR 2012)
 * h/e Apparatus (Model AP-9369)
 * Stopwatch Function on Alex's Phone(Model LG Envy 2)
 * Filters (from left to right):[[Image:PCPIC1.JPG|thumb|left|Our 3 Filters]]
 * Yellow Line
 * Green Line
 * Relative Transmission

Safety
Before we begin some points of safety must be noted:
 * 1) First and foremost your safety comes first and then the equipments'
 * 2) Be careful when handling the Mercury Vapor Bulb (in case you need to)
 * 3) Check the cords and cables in use for any damage or possible electrocution points on fuses of machinery by making sure the power cords' protective grounding conductor must be connected to ground
 * 4) Make sure the areas containing and around the experiment are clear of obstacles
 * 5) When using filters do not place fingers on the filter surfaces as it will damage them and the experimental results will have errors
 * 6) Be cautious of static electricity when dealing with the h/e Apparatus as well as allowing too much light to pass through the Apparatus as we are dealing with optics
 * 7) And finally, be careful handling the equipment as it is quite expensive

Brief Description of the Photoelectric Effect and Planck's Quantum Theory

 * Any system acting as an oscillator consists of a discrete set of possible energy levels between which no value exists and the emission/absorption of radiation are transitions between energy states corresponding to quanta of energy which are emitted or absorbed with energy $$E=h\nu$$ where $$\nu$$ is the frequency of a given quantum and h is Plank's constant.
 * The photoelectric effect is the occurrence in which electrons are emitted due to the energy of quanta striking a material:
 * $$E = \nu h = KE_{max} + W_0 \,\!$$
 * where the maximum kinetic energy of the photoelectrons is $$KE_{max} \,\!$$, independent of the light's intensity, the frequency of the incident photon is $$ \nu \,\!$$, the energy of the incident photon is $$E \,\!$$, and the needed energy to remove them from a material is $$W_0 \,\!$$ (the work function).

Chapter 5: Planck's Constant Gold's Physics 307L Manual

Purpose
The purpose of this lab is to measure Planck's Constant using the Photoelectric equation:
 * $$E = \nu h = KE_{max} + W_0 \,\!$$

and an applied reverse potential V between the anode and cathode so that the photoelectric current can be stopped
 * Planck's Constant can be calculated by the relation of the kinetic energy and stopping potential which give a linear relation between the potential and the frequency whose plot allows the measurement of the constants h and $$W_0$$

For more information check pages 32-33 of Gold's Lab Manual Gold's Physics 307L Manual

Set Up & Procedure
For this lab we are using Gold's Lab Manual Gold's Physics 307L Manual


 * 1) First we tested the voltage on the two 9 V batteries inside the h/e Apparatus using the DVM and received a value of 15.97 V
 * 2) Then we plugged in and turned on the Light Block as it says that it should be turned on 20 minutes before use
 * 3) Align the aperture and light source so that the light shines directly at the center of the lens
 * 4) Connect the DVM to the OUTPUT of the h/e apparatus
 * 5) Connect the Light Block to the h/e Apparatus facing each other and check the alignment
 * 6) Turn on the apparatus and move it about the coupling bar pin so that the first order maxima show on the white reflective mask (be sure that only one color falls on the photodiode window and that there is no overlap)
 * 7) Press "Zero" button so that any accumulated charge is discharged
 * 8) The output voltage on DVM is a direct measure of the stopping potential (for our apparatus the potential read a false high and then dropped to the real stopping potential voltage)


 * Using Filters
 * The filters stop higher frequencies of light from entering the apparatus and giving a false outcome on the reading
 * Make sure the light in the room is turned as this will interfere with results as well
 * The variable transmission filter varies the intensity of incident light (100%, 80%, 60%, 40%, 20%)

Data, Tables, & Analysis

 * Experiment 1
 * The investigation of the dependence of $$KE_m$$ on the light's intensity and/or frequency.


 * Part A:Time measurement for voltage reading stabilization.
 * After completing the original procedure, record the DVM reading for the stopping voltage of 100% intensity
 * Press the "Zero" button to discharge
 * Measure time required for the voltage to return
 * Repeat for the four other intensities


 * Part B:
 * Adjust apparatus so that only one yellow line is visible on the photodiode while using the yellow filter and record the DVM voltage
 * Repeat for each color
 * Use the green filter for the green line*

Analysis


 * Experiment 2
 * Make sure everything is still aligned properly
 * For each color of the first order measure and record the DVM voltage remembering the yellow and green filters
 * Repeat for all five colors in second order as well

Analysis
 * 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
 * }



For this part we used Gold's Physics 307L Manual as well.

Notes About Our Uncertainty

 * Our light aperture was not perfectly centered on the lens/grating assembly
 * Also, the lens/grating assembly could be moved only so far on its support rods for the light to be focused onto the white reflective mask of our Apparatus so we were only able to focus it to a certain extent.


 * While measuring the stopping potential for each color's spectral line, the readings on the voltmeter during the filtration through the different transmissions varied by small amounts. Our belief is that this should not have happened because the stopping potential should not have been affected by the filtration because the intensity should not affect our results as assumed in Planck's Quantum Theory. The common collector inside the apparatus allowing small amounts of current drainage from the DVM could be the cause of theses discrepancies
 * During our lab (right before using the green filter on 100 %) our original voltmeter seemed to have ran out of battery power and we had to replace it (Model 37XR-A) with a new DVM of a different model (model FLUKE 111) which could only measure the voltage to three significant digits after the decimal place compared to our original voltmeter which could measure up to four.
 * While using the stopwatch to measure the time taken for each grating to reach the stable stopping potential we had some trouble timing it right. On average it took about two to three trials to get the correct time. (We made no note of these different trials.)

Planck's Constant Measurement and Calculation
The total maximum energy of the electrons leaving the cathode is:
 * $$E =h \nu= KE_{max} + W_0 \,\!$$
 * $$KE_{max}=\frac{1}{2}m_ev^2$$

where $$E=h\nu\,\!$$ is the initial energy of the photon and $$E=KE_{max}+W_0\,\!$$ is the resulting energy containing the final kinetic energy of the electron plus the energy loss due to the electron overcoming the work function; $$m_e\,\!$$ is the rest mass of the electron and $$v\,\!$$ is its final velocity. 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 equation we can see that there is a linear relation between the stopping potential $$V_s\,\!$$ and the frequency $$\nu\,\!$$ with slope $$\frac{h}{e}\,\!$$. Using the slope from our best-fit line and the electron's charge, $$e\,\!$$, we can approximate the value of Planck's constant:
 * $$e=1.602\times {10^{-19}} C\,\!$$
 * $$h=me\,\!$$

where $$m\,\!$$ is the slope of our line. So,
 * $$m_{first order}=4 \pm 0.001\times 10^{-15} Vs\,\!$$
 * $$h_{measured, first order}=me=(4\pm 0.001\times 10^{-15} Vs)(1.602\times {10^{-19}} C)\,\!$$
 * $$\simeq 6.408\pm 0.0016\times 10^{-34} Js\,\!$$


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

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


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


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

Planck's Constant Lab Summary
This is the link to my Planck's Constant Lab Summary: Planck's Constant Lab Summary

Acknowledgments
Please note that Alexandra S. Andrego 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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