Calculating Error in Energy Measurement with Scintillation Counter

[retupmoc]

Hi I am currently trying to write up a lab report for my 3rd year lab on the scintillation counter and I am 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.

 

[retupmoc]

Any hints?

 

[Justin Lazear]

Uncertainty for a general function f(a,b,c) can be calculated from

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

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

--J