Download Measurement of e/m

Measuring the charge to mass ratio (e/m) of an electron
LAST LAB! (Unless you have to make one up)
Historical background: The charge to mass ratio of an electron, e/m, was first measured by Sir J.J. Thomson
in 1897 at the Cavendish Laboratory in Cambridge, England. Thomson’s discovery that this ratio is constant
provided the best experimental evidence available at the time for the existence of electrons as particles with
definite mass and charge. In 1906, Thomson was awarded the Nobel Prize for his work. Today, you will
duplicate Thomson’s experiment.
Procedure: There are two power supplies connected to the e/m apparatus. One supply powers the “electron
gun”, which accelerates the electrons to very high speeds. The other supply provides the current to the
Helmholtz coils, creating a fairly uniform magnetic field inside the apparatus.
Part 1 (Deriving an expression for e/m):
A. First, focus on the electron gun. Make sure the current to the coils is off, and increase the voltage until you
can see the beam. It should be directed towards the right in the tube. Recall (from Chapter 21) that the amount
of energy the electron gains is proportional to the potential difference (voltage). Derive a general expression for
the speed of the electron, v, in terms of the accelerating voltage V, the charge of an electron e, and the mass of
an electron m. Call this expression “Equation 1” in your lab report.
B. In class we learned that a charged particle in a uniform magnetic field moves in a circular path. The field
created by the Helmholtz coils will be uniform and perpendicular to the velocity of the electrons, so the
magnitude of the force on an electron in the magnetic field can be written as F = evB, where e is the electron
charge, v is its speed, and B is the magnitude of the magnetic field. Use Newton’s second law to derive an
expression for the charge to mass ratio of an electron, e/m in terms of the electron’s speed v, the magnetic field
strength B, and the radius of the electron’s circular path, r. Call this expression “Equation 2” in your lab report.
C. The magnetic field strength B between a pair of Helmholtz coils is given by:
B=
Nμ 0 I
(5 / 4) 3 / 2 a
-- “Equation 3”
Where N is the number of turns in each coil, a is the radius of each coil, and I is the current in the coils.
Substitute Equation 1 and Equation 3 into Equation 2 to come up with a new expression for e/m in terms of V, a.
N, μ0, I, and r.
Questions:
1. Suppose you find that for a particular accelerating voltage V and current in the coils I, the radius of the
circular electron beam is r. What would happen to the radius of the beam if you increased the voltage by a
factor of 4, while leaving the current in the coils the same? What would happen to the radius of the beam if you
doubled the current in the coils while leaving V the same?
2. What direction should the magnetic field between the coils be in order to deflect the electron beam upward
when it first leaves the gun? What must be the direction of the current in the coils to create a magnetic field in
this direction?
3. Suppose you replaced the electron gun with a “proton gun”. How would the beam react? What could you
do to make the proton beam deflect like the electron beam?
Part 2 (Performing the experiment)
1. The equipment should already be set up for you. Turn on each power supply. Make sure the switch on the
apparatus is set to the “e/m measure” position.
IMPORTANT: There are a lot of different knobs and buttons in front of you, but you will only need to use
some of them.
-- To adjust the accelerating voltage for the electron gun: use the “500 V adjust” knob.
-- To adjust the current to the coils: use the “current adjust” knob on the e/m apparatus.
-- Do not change the 6 V AC to the heater at all.
-- The “focus” knob on the e/m apparatus can be used to change the focus of the beam.
-- Do not touch the glass bulb. It is very fragile.
2. Adjust the current to through the coils and the electron gun voltage until you get the beam to make a
complete circle. Record the value for the current and voltage in a table and measure the radius of the beam’s
path using the mirrored scale behind the e/m tube. You should record an average of rleft and rright (the radius as
measured from the center of the beam to the left edge and right edge). For the best measurement, line the beam
up with its reflection on the mirrored scale. This will ensure that you are looking straight on at the beam. Use
the equation you derived in Part 1 to calculate e/m.
3. Repeat Step 2 for seven or eight values of current and voltage. Keep the current under 2.0 A and the voltage
under 200 V. Calculate your average measured value for e/m and compare it with the accepted value (i.e.
calculate a percent difference).