Physics307L:People/Phillips/eDiffraction

Data & Results
After spending some time on the Internet and in Excel, we managed to procure some decent data:

$$d^{big}_{accepted} = 0.123 nm$$

$$d^{small}_{accepted} = 0.213 nm$$

$$d^{big}_{measured} = 0.139 \pm 0.00808 nm$$

$$d^{small}_{measured} = 0.238 \pm 0.0314 nm$$

To calculate uncertainties, we used the formula

$${\delta}d=\frac{\part d}{\part D}{\delta}D$$

where d is the lattice spacing that we are finding and D is the extrapolated diameter that we measured.

For percent error, we used the formula

$$% error=100\times\frac{|Accepted-Measured|}{Accepted}$$

with our different measured and accepted values for the lattice spacing as a result of the big ring and of the small ring.

$$% error^{big}=13.0%$$

$$% error^{small}=11.9%$$

The notebook entry for all of this is found here, and we have two Excel files that show all of our data and calculations: [[Media:Diffraction1.xls|Diffraction1.xls]] and [[Media:Diffraction2.xls|Diffraction2.xls]].

Some Conclusions
In the end, I think we did pretty well. Our values were quite close to the accepted ones and we accounted for our uncertainty by examining the differences between values measured from the outer and inner parts of the rings. There are some other sources of error, such as the variance in the length, L, of our diffraction tube, but we ignored this, as suggested by the lab manual. One thing that I noticed was that the Least Squares error, from fitting a line to our data, was minimized when using the averages for our diameter values (i.e. taking the measurements for outer and inner parts of each ring, then averaging them), which is what we guessed and is why we used this method right from the start. There could possibly be something wrong with our uncertainty calculations, since we got quite small uncertainties in our final values, but we weren't quite sure what this could be from unless we just aren't taking everything into account.

Some Comments
Something to note about this lab is just how much systematic error there is. With every diameter that we measured there would be some kind of uncertainty associated with it simply because the rings on the apparatus are quite hard to see, especially at the lower voltages (near 2.5 kV). Another thing along these lines is that we noticed how the rings fade away over some distance, leaving us somewhat unsure of when each side of each ring ended. To prevent this, a better kind of phosphorescent material could be used, or perhaps just a newer coating of the same one (how to go about re-coating the inside of a vacuum tube with a phosphorescent layer, I'm not too sure). However, in comparison to the other labs we've done this semester, this one gave us extremely nice results (if "nice" means small percent error).