User:Johnny Joe Gonzalez/Notebook/Physics 307L/2009/09/23

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


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Safety

 * Check for exposed wires or loose connections as voltages as high as 5kV can be used.
 * Use caution when running higher currents through the electron gun as that can damage the graphite sheet.
 * The electron gun has several components made of glass, care should be taken not to break any of the glass components.

Materials
The following materials will be needed for the lab:
 * Electron gun
 * Tel2501 Universal Stand
 * Hewlett Packard 6216B power supply
 * Wavetek 85XT Multimeter
 * Carrera precision calipers
 * Rayovac industrial flashlight

Procedure

 * First connect the electron gun to the power supply, and multimeter. (Most of this was already connected so I simply double checked the connections, and that the multimeter was connected through a series circuit in order to measure current.
 * I plugged everything in and turned the system on. I checked to make sure that the leads came on and I immediately checked the current, the current was read at 1.1mA.[[Image:Electron_diffraction_green_dot.jpg|thumb|right|An Image of using the green dot to try to center the diffraction pattern in order to reduce error in measurements.]]
 * I checked to make sure the calipers were working (note that there is both a mm and inch setting. I made sure the calipers were set to mm.
 * I then raised the voltage to about 500V, and then centered the green dot on the electron gun.
 * The ring was difficult to observe at this point so after speaking with Dr. Koch, he suggested that we switch the polarity on our bias.
 * After switching the positive and negative connections on the bias the rings on the electron gun became clearer to see (not much, but it did make a difference). However, the current on the multimeter spiked up after turning down the voltage, this could be due to the way things were connected, to stay on the safe side I turned everything down while recording my data.

data

 * 1st measurement: voltage set at (4500), bias (16), Ring diameter: 41.9 inner ring: 29.9 multimeter current: .23mA
 * 2nd measurement: voltage set at(4400), bias(16), ring diameter(40.9), inner ring(26.0), multimeter current: .21mA
 * 3rd measurement: voltage set at(4300), bias(16), ring diameter(50.3), inner ring(30.9), multimeter current: .18mA
 * 4th measurement: voltage set at(4200), bias(16), ring diameter(49.21), inner ring(28.2), multimeter current: .18mA
 * 5th measurement: voltage set at(4100), bias(16), ring diameter(52.3), inner ring(31.2), multimeter current: .18
 * 6th measurement: voltage set at(4000), bias(16), ring diameter(52.4), inner ring(32.8), multimeter current: (23.0)
 * 7th measurement: voltage set at(3900), bias(16), outer ring(55.34), inner ring(32.3), multimeter current: .19mA
 * 8th measurement: voltage set at(3800), bias(16), outer ring(54.6), inner ring(33.6), multimeter current:(.19mA)
 * 9th measurement: voltage set at(3700), bias(16), outer ring(55.7), inner ring(33.8), multimeter current:(.18mA)
 * 10th measurement: voltage set at(3600), bias(16), outer ring(56.2), inner ring(NA), multimeter current:(.14mA)
 * 11th measurement: voltage set at(4300), bias(16), outer ring(50.8), inner ring(29.2), multimeter current:(14mA)
 * 12th measurement: voltage set at(4500), bias(16), outer ring(51.3), inner ring(28.5), multimeter current:(14mA)
 * Side note:(When the voltage was set to 0, the current spiked to .30mA)

procedure continued

 * I marked the current over concerns for the equipment.
 * This marks the end of the first lab day.

procedure day 2

 * I connected my experiment in the same way it was connected on day 1, the em device is switched in polarity once again to insure consistent measurements.
 * I noticed near the end of my lab last week that I may have been measuring the diffraction pattern at an angle, therefore when I make my measurements today I'll be concentrating more on eliminating bias.
 * The equipment used today will be the same equipment I used on day 1.
 * Once again out of concern for the equipment and consistency, I'll be carefully monitoring and recording current.

Data day 2

 * 1st measured potential(4.5kV)Outer ring measurement(46.10), inner ring measurement(26.6), measured current(.076mA)
 * 2nd measured potential(4.4kV)Outer ring measurement(48.01), inner ring measurement(26.34), measured current
 * 3rd measured potential(4.2kV)Outer ring measurement(49.14), inner ring measurement(26.83), measured current(.079)
 * 4th measured potential(4.0kV)Outer ring measurement(49.82), inner ring measurement(27.94), measured current(.080)
 * 5th measured potential(3.8kV)Outer ring measurement(51.96), inner ring measurement(29.19), measured current(.080)
 * 6th measured potential(3.6kV)Outer ring measurement(52.21), inner ring measurement(29.28), measured current(.081)
 * 7th measured potential(3.4kV)Outer ring measurement(53.04), inner ring measurement(31.99), measured current(.086)
 * 8th measured potential(3.2kV)Outer ring measurement(54.77), inner ring measurement(30.39), measured current(.086)
 * 9th measured potential(3.0kV)Outer ring measurement(56.05), inner ring measurement(30.81), measured current(.087)
 * 10th measured potential(2.8kV)Outer ring measurement(57.51), inner ring measurement(32.04), measured current(.089)


 * Starting at measurement #7 it became very difficult to read and measure the pattern. I tried adjusting the current and voltage from the power supply in order to help make the pattern more visible, I'm not sure whether it worked or if it was just my imagination, but I continued the measurements after the adjustments.
 * measurement 10 for the outer ring was very difficult to see, I'm not sure if I actually measured that correctly or if it was just my eyes playing tricks on me.
 * The current readings were taken from the multimeter.
 * Further more i skipped voltage this time around, going in increments of 200V after the first reading.
 * Other than the specified above I conducted the experiment exactly as I did on day 1, this time paying more attention to my own mistakes when measuring the diffraction pattern.

Data analysis
De Broglie once hypothesized the all particles have wavelike behavior. The relation he found was '''$$\lambda = h/p$$ ''' By measuring the diffraction pattern on the glass of the e/m device we are able to use the following equation: $$\frac{d=4\pi L(h/2\pi )c}{(D\sqrt{2eV{a}mc^{2}})}$$ in order to try to find the spacing inside the graphite used to diffract the electrons.

Using the above measurements I then plugged them into the equation above in order to solve for d, which is the spacing of the molecules inside the graphite. The accepted values are: 0.123nm and 0.213nm. The above equation is dependant on the measurements taken for the inner and outer rings that appear when the electrons are diffracted given a certain potential. Where $$V{a}$$ =the electric potential and D=2Ltan($$\theta )$$ , L=13cm, which is the length the electron must travel before hitting the glass tube.

Using Excel I calculated and plotted the results of my measurements. The X average of my day two results were:
 * 0.106nm for the outer lattice spacing
 * 0.190nm for the inner lattice spacing

side notes
The diffraction pattern, as explained to me by Dr. Koch, comes out in rings due to the polycrystalline nature of the graphite. This is also mentioned in Dr. Gold's lab manual. If the graphite would have been a perfect crystal, then the diffraction pattern would have looked like an array of spots instead of rings. Such experiments involving the use of bragg diffraction have lead us to applications involving crystallography.


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