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henry wang
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Homework Statement
I used error propagation equation to calculate errors in x and y for each individual data. Error in y is negligible. My goal is to find the uncertainty in the gradient.
2. Homework Equations
The plotted equation is [tex]eV=h\frac{c}{2dsin(\theta)}[/tex] ,where Plank's constant, h, is the gradient, the independent variables eV and the dependent variable is theta. Also x=c/(2dsin(theta) and y=eV.
The dominant error is in the theta, and thus error in x is: [tex]\Delta x=\frac{c*cos(\theta) \Delta \theta}{2dsin^{2}(\theta)}[/tex]
c=3*10^8m, cos(theta)=1, d is about 10^-10m, sin(theta) is about 0.1 and dtheta=0.2 degrees.
This yields an extremely big error in x.
The Attempt at a Solution
My original thought was to fit lines of max and min permitted gradient using errors in x and y. However, since the error in x is so large, and the x and y-axis are in log scale, I cannot manually fit lines.
[tex]\Delta h=\frac{2eVdcos(\theta) \Delta \theta}{c}[/tex]The planks constant, h, was found to be 6.7*10-34Js, and the average uncertainty in h was found to be +-1.51^-33Js.
Is this a reasonable approach?
Update 2: After corrected dtheta from degrees to radians.
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