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

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## Planck's Constant Lab

Partner: Alex Andrego

SJK 02:10, 5 October 2009 (EDT)
02:10, 5 October 2009 (EDT)
Alex & Anastasia: Overall, you have an excellent primary lab notebook. Please take a look at each other's notebooks as I ended up putting comments in each of them w/o copying them to the other. I think you did a really good job with this lab, especially considering it was your first lab and I unfortunately couldn't interact with you very much. You did a great job recording and presenting your data and analysis. My main concern was the lack of description of the linear fitting procedure and where the error came from (see comments below or below on your partner's page). Otherwise, I really like the effort you put into recording what you did, including very good pictures. I'll put more comments on your summary pages.

### 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):
Our 3 Filters
1. Yellow Line
2. Green Line
3. 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 $\displaystyle E=h\nu$ where $\displaystyle \nu$ 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:
$\displaystyle E = \nu h = KE_{max} + W_0 \,\!$
where the maximum kinetic energy of the photoelectrons is $\displaystyle KE_{max} \,\!$ , independent of the light's intensity, the frequency of the incident photon is $\displaystyle \nu \,\!$ , the energy of the incident photon is $\displaystyle E \,\!$ , and the needed energy to remove them from a material is $\displaystyle W_0 \,\!$ (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:

$\displaystyle E = \nu h = KE_{max} + W_0 \,\!$

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 $\displaystyle W_0$

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

### Set Up & Procedure

Cable Connections
Final Set Up

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

In Action
SJK 01:17, 5 October 2009 (EDT)
01:17, 5 October 2009 (EDT)
Cool!
• Experiment 1
The investigation of the dependence of $\displaystyle KE_m$ 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*

key=tiP3H2NaLg-eVrZso_xVoiw width=800 height=370

}}

Analysis

SJK 01:16, 5 October 2009 (EDT)
01:16, 5 October 2009 (EDT)
Interesting color scheme...trying to scare people into accepting your data? Ha ha, well, guessing you had trouble exporting / importing an image or something? Here's an idea for next time: You can put the charts as a separate page in your embedded google spreadsheet. This will probably be easier for most charts. I could also help you on the export / import. Or maybe you actually like that color scheme, in which case, I'll recommend not liking it.
SJK 02:00, 5 October 2009 (EDT)
02:00, 5 October 2009 (EDT)
I see exponential fits on your graph for charging time versus filter percentage. Do you expect it to be an exponential relationship? What would the charging time be if you had 0% transmission? Can you think of a theoretical relationship that it should resemble? If you think about charging rate (instead of charging time), it may be more intuitive.
• 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)
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

key=tiy1HwB-2a3lx1YpZpLpDYg width=450 height=240

}}

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 SJK 01:06, 5 October 2009 (EDT)
01:06, 5 October 2009 (EDT)
I agree with you here. Is the trend in the correct direction for this to be the explanation?
• 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.) SJK 01:22, 5 October 2009 (EDT)
01:22, 5 October 2009 (EDT)
It is really good that you mention this feature of your data acquisition! We didn't get a chance to discuss this in detail (sorry--my fault for having to leave!) but the charging time is a really funky part of the lab. I understand what you mean about the measurements being quite variable. Like I said, it's really great that you wrote this down -- in case your selection of data made a huge bias in your results. Even better, (as I think you're hinting here) would be to actually record ALL of the results and then decide later (with discussion) if it's appropriate to throw them away. Or, if that's not practical, you can describe what your method was for deciding whether the measured time was "good" or not. Without this information, it would be tough for you (or anyone else) to repeat your measurements.

### Planck's Constant Measurement and Calculation

The total maximum energy of the electrons leaving the cathode is:

$\displaystyle E =h \nu= KE_{max} + W_0 \,\!$
$\displaystyle KE_{max}=\frac{1}{2}m_ev^2$

where $\displaystyle E=h\nu\,\!$ is the initial energy of the photon and $\displaystyle E=KE_{max}+W_0\,\!$ is the resulting energy containing the final kinetic energy of the electron plus the energy loss due to the electron overcoming the work function; $\displaystyle m_e\,\!$ is the rest mass of the electron and $\displaystyle v\,\!$ is its final velocity. The negative potential, $\displaystyle V_s\,\!$ , needed to stop the flow of electrons is derived by equating the potential barrier, $\displaystyle eV_s\,\!$ , to the electron's kinetic energy where $\displaystyle e\,\!$ is the charge of an electron and:

$\displaystyle eV_s=KE_{max}\,\!$

So

$\displaystyle E=eV_s+W_0=h\nu\,\!$
$\displaystyle eV_s=h\nu-W_0\,\!$
$\displaystyle V_s=\frac{h\nu-W_0}{e}\,\!$

From this equation we can see that there is a linear relation between the stopping potential $\displaystyle V_s\,\!$ and the frequency $\displaystyle \nu\,\!$ with slope $\displaystyle \frac{h}{e}\,\!$ . Using the slope from our best-fit line and the electron's charge, $\displaystyle e\,\!$ , we can approximate the value of Planck's constant:

$\displaystyle e=1.602\times {10^{-19}} C\,\!$
$\displaystyle h=me\,\!$

where $\displaystyle m\,\!$ is the slope of our line. So,

$\displaystyle m_{first order}=4 \pm 0.001\times 10^{-15} Vs\,\!$
$\displaystyle h_{measured, first order}=me=(4\pm 0.001\times 10^{-15} Vs)(1.602\times {10^{-19}} C)\,\!$
$\displaystyle \simeq 6.408\pm 0.0016\times 10^{-34} Js\,\!$
$\displaystyle m_{second order}=3\pm 0.001\times 10^{-15} Vs\,\!$
$\displaystyle h_{measured, second order}=me=(3\pm 0.001\times 10^{-15} Vs)(1.602\times {10^{-19}} C)\,\!$
$\displaystyle \simeq 4.806\pm 0.0016\times 10^{-34} Js\,\!$

Also, using the y-intercept from our graph we can find the work function, $\displaystyle W_0\,\!$ :

$\displaystyle y=mx+b\,\!$
$\displaystyle y_{intercept}=\frac{W_0}{e}\,\!$
$\displaystyle W_0=ey_{intercept}\,\!$
$\displaystyle y_{first order}=(4\pm 0.001\times 10^{-15})x-1.5483\pm 0.001\,\!$
$\displaystyle y_{intercept, first order}=-1.5483\pm 0.001\,\!$
$\displaystyle W_{0measured, first order}=(-1.5483\pm 0.001 V)(1.602\times {10^{-19}} C)\,\!$
$\displaystyle \simeq -2.48\pm 0.0016\times 10^{-19} J\,\!$
$\displaystyle y_{second order}=(3\pm 0.001\times 10^{-15})x-0.94\pm 0.001\,\!$
$\displaystyle y_{intercept, second order}=-0.94\pm 0.001\,\!$
$\displaystyle W_{0measured, second order}=(-0.94\pm 0.001 V)(1.602\times {10^{-19}} C)\,\!$
$\displaystyle \simeq -1.506\pm 0.0016\times 10^{-19} J\,\!$

### 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