- #1

henry wang

- 30

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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.

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2. Homework Equations

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.

**Update:**Therefore I rearranged the above equation to isolate h, calculated the uncertainties in h for each data points and took its average.

[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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