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I'm currently in a modern physics class and one of our labs was an electron scattering experiment that required the use of a cathode ray tube and a target foil. We aim the electron beam through one of four quadrants on the target foil and measure the diameter of the ring diffraction pattern produced. Only 4 rings were visible, so we measure all four, change the accelerating potential for the electron beam, and repeat the measurements.

In the data analysis, it's suggested that we plot sin[.5*arctan(r/D)] vs [pi*h_bar/(a*SQRT(2meV))]. This plot should result in a linear graph with a slope that is equal to SQRT(h^2 + k^2 + l^2 ).

My issue is that I create this plot for the first ring at 3 different accelerating potentials but my slope is nowhere near a reasonable value (.66, impossible for the square root of an integer). If someone sees an issue in my method I'd really appreciate the correction, because I don't see where I've gone wrong.

Here's the data:

for n=1

V = 8kV, 9kV, 10kV

r = 1.0167cm, 0.9583cm, 0.925cm

distance from target foil to screen is 17.3355cm

The quadrant used contained an aluminum polycrystalline target with a given lattice constant a = 4.04145 Angstroms.

That should be all anyone needs to check the data. Looking it up online I found that the first miller index of Aluminum polycrystalline should be [1,1,1] which means the slope of the line should be 1.732. My slope is 0.666...

My plot for the other rings is similarly incorrect, so I'm guessing if I can figure out what's wrong with the first plot it will fix the others.

In the data analysis, it's suggested that we plot sin[.5*arctan(r/D)] vs [pi*h_bar/(a*SQRT(2meV))]. This plot should result in a linear graph with a slope that is equal to SQRT(h^2 + k^2 + l^2 ).

My issue is that I create this plot for the first ring at 3 different accelerating potentials but my slope is nowhere near a reasonable value (.66, impossible for the square root of an integer). If someone sees an issue in my method I'd really appreciate the correction, because I don't see where I've gone wrong.

Here's the data:

for n=1

V = 8kV, 9kV, 10kV

r = 1.0167cm, 0.9583cm, 0.925cm

distance from target foil to screen is 17.3355cm

The quadrant used contained an aluminum polycrystalline target with a given lattice constant a = 4.04145 Angstroms.

That should be all anyone needs to check the data. Looking it up online I found that the first miller index of Aluminum polycrystalline should be [1,1,1] which means the slope of the line should be 1.732. My slope is 0.666...

My plot for the other rings is similarly incorrect, so I'm guessing if I can figure out what's wrong with the first plot it will fix the others.

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