Physics307L:People/Giannini/Electron Diffraction

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Steve Koch 20:24, 21 December 2010 (EST): Good summary and comparison w/ accepted value as far as SEMs

Purpose/Procedure

The procedure and my data can be found here. The purpose of this experiment was to measure the lattice spacing within a thin sheet of graphite and to prove the DeBroglie relationship Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda=h/p} . We proved this relationship by plotting the diameter D that we measured as a function of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 1/sqrt(V)} and determined that the relationship was linear.

Analysis and Results

I used the following equations to determine my Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle d} :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle y=R-\sqrt{R^2-\frac{D_{observed}^2}{4}}\,\!}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle tan(\theta)=\frac\frac{D_{observed}}{2}{L-y}\,\!}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle D_{corrected}=2Ltan(\theta)\,\!}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle d=\frac{2hLc}{{D}\sqrt{2eV_{accelerated}c^2}}=\frac{2hL}{{D}\sqrt{2eV_{accelerated}}}\,\!}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle d=\frac\frac{2hL}{\sqrt{2me}}{slope}\,\!}

These equations gave me:

  • Small Ring: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle d=0.267(7)nm \,\!}
  • Large ring: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle d=0.174(6)nm \,\!}

Error

As stated in my Lab Data, these values are off by ~9SEM for the first one and ~10SEM for the second one. I believe the reason that this is the case is that we may have forgotten to properly adjust our magnet before we started measuring the diameters of our rings. Another source of error is attributed to the use of the calipers. We found that the calipers would sometimes slide forward and not change to the amount shown on the ruler. As such, I tried to make sure after every adjustment that the calipers had worked properly. With these two problems I believe this accounts for most of our error, as it has shown to be precise if not accurate.

Conclusion

I found that, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle d=0.267(7)nm} for the inner ring and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle d=0.174(6)nm} for the outer ring. These measurements were within ~9SEM and ~10SEM of the accepted values, which are 0.123nm and 0.213nm.

Acknowledgments