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Calculating Experimental Error of Braggs Equation

  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

    BvU

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    Science Advisor
    Homework Helper
    Gold Member

    Hello Lemenks, and welcome to PF :)

    I don't see an attempt at solution under 3, only a repeat of D=A/sin(x).

    From your account, I think what you are asking is: What is the error in D = A/sin(x), given the error in x. Correct ?

    Your relevant equations are some examples of error propagation in functions of a single variable. Generally: ##df = {df\over dx} dx##, which in error analysis is extended to finite differences: ##\Delta f = {df\over dx} \Delta x##.
    Do you know how to find the derivative of 1/sin(x) ?

    And I am interested in the way you determine ##\Delta x## too. Is it really just a simple reading off of a single angle ?
     
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