Physics307L:People/Rivera/Notebook/Electron Diffraction
Electron Diffraction
Procedure
"Connect the tube into the circuit shown in Fig. 3.3 but ignore VB. Both heater supply and HV are obtained from the 813 KeV power unit. The HV should be connected to the “+” and “−” HV connections to get the full voltage which is read on the top-scale of the KeV unit’s meter. Be sure the high voltage slider is at zero before switching on the unit. Switching on the unit (in back) will also switch on the heater. IMPORTANT: Switch on the heater supply (VF ), and wait one minute for the cathode temperature to stabilize before applying the HV (anode voltage VA)."(Physics 307L Lab Manual)
Also see lab notebook entries for Monday, November 19 2007.
Purpose
Diffraction patterns are evidence of the wave properties of particles such as electrons. This was first hypothesized by de Broglie in his 1924 Doctoral Dissertation. He also stated that the wavelength of the particle is given by Planck's constant divided by the particle's momentum.
"In this experiment we will investigate the difraction of electrons passing through a thin layer of graphite (carbon), which acts as a difraction grating. It was Max von Laue, who in 1912 suggested (in connection with x-ray studies) that the basic granularity of matter at the atomic level might provide a suitable grating. Bragg, using the cubic system of NaCl, first calculated the inter-atomic spacings and showed them to be of the right order for x-rays."(Physics 307L Lab Manual)
Equipment and Setup
"Our electron difraction tube, see Fig. 3.2, comprises a ‘gun’ which emits a narrow, converging beam of electrons within an evacuated clear glass bulb on the front surface of which is deposited a luminescent screen. Across the exit aperture of the gun lies a micro-mesh nickel grid, onto which a very thin layer (only a few molecular layers!) of graphite has been deposited.
The electron beam penetrates through this graphite target to become diffracted into two rings corresponding to the separation of the carbon atoms of 0.123 and 0.213 nm. The diffraction pattern appears as rings due to the polycrystalline nature of graphite. The source of the electron beam is an indirectly-heated oxide-coated cathode."(Physics 307L Lab Manual)
Data Collections
Data collection consisted of .1kV changes of the input voltage and measuring the visible rings with digital calipers. Absolute darkness is a must, but wasn't possible in my case.
| Voltage (kV) | inner circle (mm) | outer circle (mm) |
|---|---|---|
| 4.9 | 17.8 | 35.5 |
| 4.8 | 19.0 | 36.9 |
| 4.7 | 20.0 | 38.0 |
| 4.6 | 21.1 | 41.2 |
| 4.5 | 22.1 | 42.1 |
| 4.4 | 22.8 | 42.6 |
| 4.3 | 24.3 | 43.5 |
| 4.2 | 25.0 | 43.9 |
| 4.1 | 26.4 | 44.8 |
| 4.0 | 27.2 | 45.1 |
Calculations
The ultimate numbers we are looking for are the lattice spacing (d) as related to the accelerating voltage according to our data and to compare them to the known values of .123nm and .213nm. The first step in this process is to determine the extrapolated diameters. From this we can determine the lattice spacing from a plot of the extrapolated diameter versus the the inverse square root of the voltage.
Our calculations may be found on the following pages:
The final values of the lattice spacing that we found were .196nm and .207nm
Conclusions
1.) Absence of error - Digital calipers are nice but this was certainly not a very accurate measurement. The mistake was that we didn't take enough measurments. There was certainly a large amount of error associated with our eyeball method of data taking. What we should have been done is taken several measurements at each voltage. The acquired diameters could have then been averaged and error could have been recorded. Instead it would seem as though we have good numbers with no real accurate way of reporting any error. If we were to try this experiment again we could take more measurements. Also having a newer apparatus that was brighter would make it easier and quicker to take more data. As alluded to in the manual the bulb is old and as you get to higher voltages the visibility of the rings quickly goes away even if the room is almost completely dark other then the apparatus.SJK 23:31, 9 December 2007 (CST)
But you can get error from the linear fit, remember!
