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Calculating Experimental Error

  1. Oct 5, 2014 #1
    1. The problem statement, all variables and given/known data

    I am writing a lab report for an X-ray diffraction. I have been attempting to come up with an equation for the error using formulas some people from college gave me and also some I found on wikipedia but I am quite sure I am doing it wrong. The only variable is the angle where the maximum intensities are found. I am using Bragg's law to calculate the spacing between the atoms.

    2. Relevant equations

    D = (N*wavelength)/(2*sin(x))

    As there is no error in N, wavelength, or "2", we can let that equal A.

    D = A/sin(x)

    Some equations I was given:

    Z = aX
    dZ = adX

    Z = X^a
    dZ/z = |a|dx/x

    Z = SinX
    dZ = dX CosX

    3. The attempt at a solution

    D = Z = A/sin(x) = A (sin(x))^-1 = A f(y)^-1

    I have tried loads of ways of calculating this but I keep getting silly answers. Any help, ideas or links would be really appreciated.
     
  2. jcsd
  3. Oct 5, 2014 #2

    vela

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    Take it one step at a time. You might find it helpful to introduce new variables. For example, let w=1/sin(x). Then you have ##D = Aw##, so applying your first rule, you have ##\delta D = A \delta w##. (I'm using deltas instead of d because dD looks weird.) Now your job is to find ##\delta w##. If you let ##v=\sin x##, then ##w=1/v = v^{-1}##. Using the second rule, you can find ##\delta w## in terms of ##\delta v##. Then you need to find ##\delta v## in terms of ##\delta x##, and then put it all together.
     
    Last edited: Oct 5, 2014
  4. Oct 5, 2014 #3
    Hey thanks for the reply, it is very concise and logical, I actually tried that but assumed I must have made a mistake as the value I was getting for the error seemed to large ~80%.

    The final equation I have is:

    dD = A (dx cosx)/(sinx)^2

    This equation seems to give a value for error of about 80%. x ranges from 3 to 35 and dx was 0.1. ie the beam angle ranged from 3 to 35 degree in 0.1 degree steps.
     
  5. Oct 5, 2014 #4

    vela

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    You need to use radians, not degrees. That's probably where the issue lies.
     
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