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Homework Help: Errors problem

  1. Nov 10, 2004 #1
    Hi im currently trying to write up a lab report for my 3rd year lab on the scintillation counter and im struggling to convert the error i have for the gradient and intercept (using polyfit on excel) and the uncertainty i have in my x values, to the uncertainty in my energy measurements where energy=mx+c. c is the y intercept and m the gradient. The x value here is the channel number for the photo peak with an error of plus or minus 2, My gradient is 0.0037 with error 0.0002 and intercept -0.0187 with error 0.005. How do i get the error in energy from this, note the uncertainty in channel number was always 2 despite it ranging from 40 to 400. any help would be much appreciated.
     
  2. jcsd
  3. Nov 11, 2004 #2
    Any hints?
     
  4. Nov 11, 2004 #3
    Uncertainty for a general function f(a,b,c) can be calculated from

    [tex] \sigma_f^2 = \left( \frac{\partial f}{\partial a}\right)^2{\sigma_a}^2 + \left( \frac{\partial f}{\partial b}\right)^2{\sigma_b}^2 + \left( \frac{\partial f}{\partial c} \right)^2{\sigma_c}^2[/tex]

    It's easy to see how this equation would extend to a function of more variables.

    --J
     
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