Physics307L:People/Meyers/e/m ratio lab summary

Purpose
The purpose of this lab is:

1)To calculate, experimentally, the ration of charge to mass, e/m, of an electron.

2)Understand better the physics behind this principle.

Steve Koch 21:53, 13 October 2010 (EDT): Remember to include a link to your primary notebook! http://openwetware.org/wiki/User:Richard_T._Meyers/Notebook/Phys307l/E/m_Lab

Procedure
We used the online lab manual, linked [here]. When we got to the lab we realized that the equipment was already set up for us, thank you Emran and Randy.



We checked with the manual to be sure that this was the correct setup. After this and the safety quiz we began to take data. After taking points for accelerating Voltage, Constant Voltage and Constant Current we stopped.

Most of the second day of the lab was taken up with analyzing the data.

Calculations
We used the equations in the manual and the fact that $$F_B=F_c\,\!$$:

$$ B=\frac{\mu R^2NI}{(R^2+x^2)^{3/2}}$$

$$ F_c=eV=\frac{mv^2}{2}$$ and

$$ F_B=evB\,\!$$ So we got:

$$\frac{e}{m}=\frac{2}{((7.79x10^{-4})(1.42875))^2 slope}=6.747x10^8\,\!$$

and

$$\frac{e}{m}=2.741x10^{11}$$

Upon averaging the two values, one being very large and the other being very small we get:

$$\frac{e}{m}=1.374x10^{11}\,\!$$

Error
We found the accepted value to be:

$$\frac{e}{m}=1.758x10^{11} \frac{C}{kg}\,\!$$

So we compared our value and the accepted value to get a percent error:

$$ error=\frac{1.758x10^{11}-1.374x10^{11}}{1.758x10^{11}}x100=21.84%$$

21.84% error is not bad for twenty measurements.

Conclusion
We found the ratio to be:

$$\frac{e}{m}=1.374x10^{11}\frac{C}{kg}\,\!$$

and a percent error to be:

$$%error=21.84%\,\!$$

I did notice that our values for the Voltage versus radius squared had a smaller correlation than that of the Inverse Current versus the Radius. I assume that the sigmoid shape of the Constant Current graph is because of unsystematic error, parallax error, in reading the radius.

With a few more data points I am confident that we could produced a better estimation of e/m.

Thanks
1)Nathan for being my excellent lab partner and for taking down the equipment list when I had failed to.

2)Emran for setting up the lab previously and for a general outline of my report.

3)Randy also for setting up the lab previously.

Citation
1) I found the accepted value of e/m here