Strange Result of Error Calculation

  • #1

Homework Statement



We conducted an experiment on the bending of X-Rays in crystals and determined the [tex]K_{\alpha},K_{\beta}[/tex] lines of the first order and the corresponding wavelenghts of the radiation by means of the Bragg equation. We used a NaCl crystal with a d=283 pm. We determined the error of theta to be 0.3 degrees. Our two wavelenghts for the two lines were then 64 and 72 pm respectively. Inserting the respective values into the second equation given under (2) to obtain the errors, results in strange high errors, such as 100 pm.

Homework Equations



[tex]\lambda=\frac{2d \cdot \sin(\theta)}{n}[/tex]
[tex]\delta\lambda=\frac{2d \cdot \cos(\theta)}{n} \cdot d\theta[/tex]

The Attempt at a Solution


Comparison with a similar lab report (where the wavelenghts were 72 pm and the error of theta 0.2 degrees) showed that when I inserted their values, I also obtained errors of about 100 pm instead of the 1 pm they had obtained as a result. I cannot understand why using the same formula with the same variables gives numbers which deviate by a factor of 100.
 

Answers and Replies

  • #2
fzero
Science Advisor
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Have you converted [tex]\delta\theta[/tex] to radians?
 
  • #3
I now did and now I calculated the new [tex]\delta\theta=5.24~mrad[/tex]. With that I get [tex]\delta\lambda=2.9~pm[/tex]. Thanks!
 

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