Physics307L:People/Smith/Notebook: Difference between revisions

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I would probably do things slightly differently, were I to repeat this experiment. The lab manual neglected to give a procedure for calibrating the instrument, so we spent quite a while fiddling around with all the knobs. Once we finally figured out how to calibrate it, we neglected to record some very important information about the calibration procedure. The spectrometer has a fair amount of backlash and therefore is usually calibrated for taking measurements by turning the knob one way. Unfortunately, we forgot to remember which way the instrument was calibrated, so we just took twice as many measurements - some by turning the knob clockwise only, some by turning the knob counterclockwise only. It's not too hard to do that, but it takes more time.
I would probably do things slightly differently, were I to repeat this experiment. The lab manual neglected to give a procedure for calibrating the instrument, so we spent quite a while fiddling around with all the knobs. Once we finally figured out how to calibrate it, we neglected to record some very important information about the calibration procedure. The spectrometer has a fair amount of backlash and therefore is usually calibrated for taking measurements by turning the knob one way. Unfortunately, we forgot to remember which way the instrument was calibrated, so we just took twice as many measurements - some by turning the knob clockwise only, some by turning the knob counterclockwise only. It's not too hard to do that, but it takes more time.


== Lab 3: Planck's Constant ==
== [[/3 |Lab 3: Planck's Constant]] ==
=== Purpose ===
=== Purpose ===
The purpose of this lab is to experimentally measure the value of Planck's Constant by measuring the stopping voltage of known wavelengths of light.  A mercury emission lamp is used as the source of light.  The light is diffracted by a diffraction grating and is focused using a lens onto a vacuum photodiode tube.  The light knocks electrons off of a plate in the photodiode tube and they collect on another plate.  The amassed electrons on the collector plate create an electric field which will prevent further electrons from reaching the anode (their kinetic energy won't be sufficient to overcome the potential barrier).  The potential of the anode, called a stopping potential or stopping voltage, is measured using a digital multimeter.  A unity gain op-amp (an op-amp is an operational amplifier) is used to ensure there is a very high resistance for terminals for a voltmeter, in order to prevent electrons from leaving the anode ("current leaking").
The purpose of this lab is to experimentally measure the value of Planck's Constant by measuring the stopping voltage of known wavelengths of light.  A mercury emission lamp is used as the source of light.  The light is diffracted by a diffraction grating and is focused using a lens onto a vacuum photodiode tube.  The light knocks electrons off of a plate in the photodiode tube and they collect on another plate.  The amassed electrons on the collector plate create an electric field which will prevent further electrons from reaching the anode (their kinetic energy won't be sufficient to overcome the potential barrier).  The potential of the anode, called a stopping potential or stopping voltage, is measured using a digital multimeter.  A unity gain op-amp (an op-amp is an operational amplifier) is used to ensure there is a very high resistance for terminals for a voltmeter, in order to prevent electrons from leaving the anode ("current leaking").
=== Data ===
The first part of the lab was designed to demonstrate that the stopping voltages are independent of the intensity of light striking the photodiode tube.  It did demonstrate this, and we also found that it takes longer for the photodiode tube to build up enough charge to reach the stopping potential for lower intensities of light.
These data can be seen [[/3#Measurements here]].
The objective of the second part of the lab was to find the ratio of Planck's constant over the charge of the electron by looking at the slope of a linear regression of the stopping voltages vs. frequencies.  I had some trouble figuring out how to estimate the error of these data, but ended up with some acceptable answer, I think.  You can see the data [[3#Measurements_3 here]].
* My best estimate of Planck's constant based on the data we took was '''7.14817E-34 +2.03352E-36/-4.06703E-36'''.
:(To get this estimate, I took the average of the 1st and 2nd order maxima stopping potentials. The error estimate was found by doing a linear regression on the largest and smallest values of the atomic emission spectral lines' stopping potentials. I don't know whether that was a good way to do it, and it looks a little weird since my error estimate is not symmetric; the deviation to the lower end of the estimate is larger than that to the high end - in fact, it seems to be exactly twice as large! This is rather odd.)
=== Conclusions and Remarks ===
I didn't particularly enjoy the lab manual's explanation of photodiode tubes and such.  It left some questions in my mind; what was the unity gain op-amp used for?  Why did the h/e apparatus have a power supply?  I also think if I were to do this lab over, I would take more measurements of the first order maxima stopping voltages.  I wasn't very satisfied with my best estimate of the Planck's constant, and I believe that more data points would help.  I also think that there is some rather astounding systematic error sources somewhere; the relative error of my best estimate is quite low, but my mean estimate for it is almost 10% off of the accepted value.  Perhaps if the lab had been completely dark, it would have produced slightly more accurate results, I'm not sure.  I think the digital multimeter may have been slightly broken, as well, since it displayed 0.04 V when the h/e apparatus was shorted out (it should have shown 0.00 V).  Or, maybe the unity gain op-amp wasn't entirely precise; I think that the ratio of resistances on op-amp inputs is supposed to decide the gain it has - maybe the resistances weren't precisely the same, but within some tolerance acceptable to the manufacturer.


= Links to Lab Entries =
= Links to Lab Entries =

Revision as of 12:54, 10 October 2007

Lab Summaries

Lab 1: Oscilloscope Lab

Data

Reported value for fall time using AC coupling:

  • The Digital Storage Oscilloscope (DSO) has a built in function to measure "fall-time". It reported 239.6ms to 241.0ms. This was believed to be incorrect.
  • Using the cursors in the DSO interface to measure the time between the peak value and 10% of that value and using a frequency of between 2.343Hz and 2.430Hz reports a value of 58.00 ms.
    • Subsequent measurements using this method after changing the frequency on the frequency generator:
      • Frequency: 4.798Hz - 5.061Hz, fall time: 57.00ms.
      • Frequency: 7.257Hz - 7.262Hz, fall time: 55.00ms.

Note: The DSO displays these times in integer values of milliseconds. Therefore, the precision of these measurements is necessarily limited. I suspect the way the DSO rounds these numbers makes the screen display, for instance, 55.00ms for any measurement between 54.5ms and 55.5ms.

What did you learn?

I had little previous experience with oscilloscopes before this lab. I was able to familiarize myself with the the way oscilloscopes are hooked up, how they used to work (scanning CRT displays, etc), and to interact with the modern DSO we used (it has an interface similar to an ATM machine, with many useful functions able to be selected and displayed using the buttons on its face.) I also learned a bit about the concept of AC coupling, which I had never heard of before. I also wrote my first lab notebook entry in the wiki format, which was very straightforward.

What could make the lab better next year?

Well, I saw a video online of someone who interfaced an oscilloscope with a soundcard on his PC and was able to do very, very impressive things; he wrote things on the screen, had very neat patterns and effects. I don't think we should do all that, but it's an interesting concept, and it might be worth explaining how someone would be able to do all that. You can see the video here.

Lab 2: Balmer Series

Purpose

The objective of this lab is to experimentally determine the value of the Rydberg Constant by measuring the atomic emission spectral wavelengths of hydrogen and the hydrogen-like element deuterium (which is hydrogen with an extra neutron thrown in).

Data

See the data collected section of my lab notebook entry.

I used Excel to analyze the data (you can see my Excel spreadsheet here). I used our measurements of the wavelengths of the atomic emission spectra of hydrogen and of deuterium to calculate the measured Rydberg Constant (they are, believe it or not, slightly different despite the name "Rydberg Constant"). I also calculate the expected Rydberg Constant for hydrogen and deuterium by using fundamental physical constants, and compared these with our measured values. They are reported below:

Expected Rydberg Constants Avg. Measured Rydberg Constants Percent Difference
Hydrogen Clockwise 1.09677286888108E+07 [math]\displaystyle{ m^{-1} }[/math] 1.09797802016246E+07 [math]\displaystyle{ m^{-1} }[/math] -0.1099%
Counterclockwise 1.09677286888108E+07 [math]\displaystyle{ m^{-1} }[/math] 1.09583397614656E+07 [math]\displaystyle{ m^{-1} }[/math] 0.0856%
Deuterium Clockwise 1.09647449477397E+07 [math]\displaystyle{ m^{-1} }[/math] 1.09846377155094E+07 [math]\displaystyle{ m^{-1} }[/math] -0.1814%
Counterclockwise 1.09647449477397E+07 [math]\displaystyle{ m^{-1} }[/math] 1.09636035647508E+07 [math]\displaystyle{ m^{-1} }[/math] 0.0104%

And our best estimates of our measured Rydberg Constants:

Measured Rydberg Constants (in m-1)
Hydrogen Clockwise 10979780.2016246 [math]\displaystyle{ \pm }[/math] 2810.24625
Counterclockwise 10958339.7614656 [math]\displaystyle{ \pm }[/math] 3908.3275
Deuterium Clockwise 10984637.7155094 [math]\displaystyle{ \pm }[/math] 6215.96625
Counterclockwise 10963603.5647508 [math]\displaystyle{ \pm }[/math] 3312.62625

Conclusions and Remarks

I think that there was very little systematic error in this experiment, other than the uncertainty of the direction in which the instrument was calibrated (and we tried to get around that by taking measurements by repeating measurements by turning the knob one way and then the other). There was obviously some random error when measuring the wavelengths of the atomic spectra, since we didn't record the exact same number over and over. By taking five measurements for each atomic emission line, though, I think we were able to control the effects of random error on our final calculations. Because of this, we were able to measure one of the fundamental constants of atomic physics to a high degree of precision. Using an old, clunky spectrometer and getting results within 0.1% of the expected value of the Rydberg Constant for hydrogen-like elements! I think is really quite remarkable. I was very satisfied! I think it also shows the central limit theorem in action, which was kind of exciting.

I would probably do things slightly differently, were I to repeat this experiment. The lab manual neglected to give a procedure for calibrating the instrument, so we spent quite a while fiddling around with all the knobs. Once we finally figured out how to calibrate it, we neglected to record some very important information about the calibration procedure. The spectrometer has a fair amount of backlash and therefore is usually calibrated for taking measurements by turning the knob one way. Unfortunately, we forgot to remember which way the instrument was calibrated, so we just took twice as many measurements - some by turning the knob clockwise only, some by turning the knob counterclockwise only. It's not too hard to do that, but it takes more time.

Lab 3: Planck's Constant

Purpose

The purpose of this lab is to experimentally measure the value of Planck's Constant by measuring the stopping voltage of known wavelengths of light. A mercury emission lamp is used as the source of light. The light is diffracted by a diffraction grating and is focused using a lens onto a vacuum photodiode tube. The light knocks electrons off of a plate in the photodiode tube and they collect on another plate. The amassed electrons on the collector plate create an electric field which will prevent further electrons from reaching the anode (their kinetic energy won't be sufficient to overcome the potential barrier). The potential of the anode, called a stopping potential or stopping voltage, is measured using a digital multimeter. A unity gain op-amp (an op-amp is an operational amplifier) is used to ensure there is a very high resistance for terminals for a voltmeter, in order to prevent electrons from leaving the anode ("current leaking").

Data

The first part of the lab was designed to demonstrate that the stopping voltages are independent of the intensity of light striking the photodiode tube. It did demonstrate this, and we also found that it takes longer for the photodiode tube to build up enough charge to reach the stopping potential for lower intensities of light. These data can be seen /3#Measurements here.

The objective of the second part of the lab was to find the ratio of Planck's constant over the charge of the electron by looking at the slope of a linear regression of the stopping voltages vs. frequencies. I had some trouble figuring out how to estimate the error of these data, but ended up with some acceptable answer, I think. You can see the data 3#Measurements_3 here.

  • My best estimate of Planck's constant based on the data we took was 7.14817E-34 +2.03352E-36/-4.06703E-36.
(To get this estimate, I took the average of the 1st and 2nd order maxima stopping potentials. The error estimate was found by doing a linear regression on the largest and smallest values of the atomic emission spectral lines' stopping potentials. I don't know whether that was a good way to do it, and it looks a little weird since my error estimate is not symmetric; the deviation to the lower end of the estimate is larger than that to the high end - in fact, it seems to be exactly twice as large! This is rather odd.)

Conclusions and Remarks

I didn't particularly enjoy the lab manual's explanation of photodiode tubes and such. It left some questions in my mind; what was the unity gain op-amp used for? Why did the h/e apparatus have a power supply? I also think if I were to do this lab over, I would take more measurements of the first order maxima stopping voltages. I wasn't very satisfied with my best estimate of the Planck's constant, and I believe that more data points would help. I also think that there is some rather astounding systematic error sources somewhere; the relative error of my best estimate is quite low, but my mean estimate for it is almost 10% off of the accepted value. Perhaps if the lab had been completely dark, it would have produced slightly more accurate results, I'm not sure. I think the digital multimeter may have been slightly broken, as well, since it displayed 0.04 V when the h/e apparatus was shorted out (it should have shown 0.00 V). Or, maybe the unity gain op-amp wasn't entirely precise; I think that the ratio of resistances on op-amp inputs is supposed to decide the gain it has - maybe the resistances weren't precisely the same, but within some tolerance acceptable to the manufacturer.

Links to Lab Entries

Wednesday Labs