Download Corning em ratio

Electron Charge to Mass Ratio
Sean Corning, Abdul Merhi, Tim Burnett
Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201
Abstract: In our experiment we were measuring the charge to mass ratio of the very
small and what used to be very elusive, electron. Finding the charge to mass ratio can be
important because electrons are everywhere in the universe and are a fundamental part of
the atom. To find the ratio we are introducing a beam of electrons into a magnetic field
and changing the current and finding the radius of the beam of electrons since it makes a
circle in the magnetic field. This is modeled after the J.J. Thomson experiment when he
was the first person to measured this ratio of charge and mass. This was in 1897 and there
was probably a good amount of error in his data, and with new equipment we should
hopefully be able to get less error. In the end we will found a charge to mass ratio of
1.91e11+- 6.78e9.
I. Introduction
To find the charge to mass ratio of the electron we used equations (1-5). We had the acceleration in the
magnetic field(1) as well as the force(2) and used this to find the charge and mass ratio of the election in
equation (3). However since we do not know the velocity of the electrons we substitute v in once we solve
it in equation (4) and end up with equation (5) This can now allow us to find the charge to mass ratio of the
electron. We have two unknowns of the radius and the voltage. However we can measure both the voltage
and the radius(in the experimental procedure).
𝑎𝑐 =
𝑣2
𝑟
----------------------------(1)
𝐹𝑚 = 𝑒𝑣𝐵--------------------------(2)
𝑒
𝑣
= 𝐵𝑟----------------------------(3)
𝑚
1
𝑒𝑉 = 𝑀𝑣 2 -------------------------(4)
2
𝑒
(𝑚)𝑏2 𝑟 2 = 2𝑉---------------(5)
The result gathered in our data was used using new equipment than that used in the first experiment and
should give us a new and better result for the ratio of charge to mass of the electron. As stated in the
abstract, electrons are found everywhere in the universe and finding this ratio can help us in our
understanding of the atom and how it fits into the material of the universe.
II. Experimental Setup
Figure 1- bulb that shots electrons that go in a circle around in the bulb
Our experiment required us to use the machine in figure 1which has a bulb and an electron gun that shots
electrons out and they go in a circle in the bulb. There are two coils of wire holding up the curtain that have
current run through it to produce the magnetic field, the coils have 130 turns. The wires connecting each
have a purpose and the power supplies can be seen in figure 2. One of them is the heater for the electron
gun which we kept at 6.3 volts. Another power supply is for the coils which were kept between 6-9volts.
Another power source was used to for the electron gun which we changed from 150-300 volts. This is the
power source we used to change the radius of the beam of electrons. Finally the machine had a place to
connect to that gave us the voltage difference which was used for our voltage in equation (5). One other
thing we had to be careful when using this particular machine was the parallax effect since the ruler was
behind the beam of electrons by a good amount. To combat this we used similar triangles to find the
viewed radius compared to the actual radius. We also had to be careful that we kept our eye in the same
spot so as to not change the distance away from the machine which would change the parallax effect. Once
we had our viewer up in a good spot we changed the voltage from 150-300 and recorded the voltage and
the radius the beam of electrons gave us. Once we found the voltage and the radius we could plug them into
equation (5) and given the ratio of charge and mass we were looking for.
Figure 2 our machine with the power sources and meters.
III. Results
Figure 3. This is our line to find our ratio as the slope of this line.
We created figure 3 so that the slope would give us the ratio of charge and mass of the electron. This can be
seen in equation (5) and thinking about the general equation y=mx. To find the error in the y axis we had an
error of .5 from reading off the volt meter which was accurate to the volt, and multiplied by 2 because V is
multiplied by 2, which gave us just 1 volt. Our x-axis error was harder and we had to propagate error to
find it, we used the general error propagation formula. The error in our r was somewhat tricky because we
had to use our view radius and the similar triangles to find the actual we had an error of .0005 since the
ruler measured to the mm. To find the error in B we also propagated error which came from the error in the
current and the radius of the coils. The error in current was .005 since the ammeter gave us the current to
the place of .01. Our radius error was .0015 since we thought we had a good measurement on this. Even
though our error did not change a huge amount from each point we used an instrumental weight for the line
so it would take into account points with less error since we trust those more. Our ratio of charge and mass
of the electron was given as the slope which was 1.91e11+-6.78e9. The theoretical ratio is 1.7588e11, and
comparing that to our ratio we had an error of 8.46%
IV. Discussion
Overall I think our data was decently good due to only 8.46% error, and I would expect it to be better than
or near that of the original experiment in 1897 by J.J. Thompson. One thing me and my lab partners did not
like was the parallax effect and having to keep our eye steady. If the eye was moving even a little off center
or moved forward or backward it could throw off the data, which can make it very hard to get a lot of data
since you cannot move. Since there was a parallax effect it added to our error in the final answer. However
I think we did have some nice equipment in terms of the voltage and power supplies which had small error
in them. Our final answer of 1.91e11+-6.78e9 had little error and can be trusted a good amount. One thing
though that is concerning is that we were 8.46% away from the theoretical ratio even though it seemed like
we had relatively small error in our final answer. This makes me question if we did not contribute enough
error to some things, or had another source of error we did not know about.