Charge to Mass Ratio for an Electron
Introduction
The charge-to-mass ratio (e/m) for an electron was first measured by Sir J.J. Thomson in 1897 at
the Cavendish Laboratory in Cambridge, England. His result, later recognized with the awarding
of the Nobel Prize, amounted to the discovery of the electron. It represented a fundamental
contribution to the evolving model of atom structure, which hitherto had not considered the
existence of subatomic constituent particles. Shortly after, these improvements in the atomic
model would lead to the rapid, revolutionary development of quantum and nuclear physics.
Thomsonʼs experiment was similar in principle to the one you will be doing. The principles are:
a) "Boil" electrons off a hot filament.
b) Accelerate the electrons through a known potential difference.
c) Project the electrons, which should now all be travelling at the same constant speed,
into a uniform magnetic field.
d) Knowing the electron velocity, the magnetic field strength, and the radius of the circle
of electrons travel in, the e/m ratio can be calculated.
The large glass bulb in which the electrons travel is evacuated except for some helium gas. As
the electrons hit the helium atoms, ionization, followed by recombination, will cause the emission
of blue-green light. This light will allow you to locate the path of the electron beam. The two large
copper coils outside of the bulb are called Helmholtz coils and are used to generate the uniform
magnetic field.
Theory
When a charged particle moves through a magnetic field, it experiences a force that is given by
the expression:
F = qv × B
(1)
F is the force on the charged particle
(in Newtons), q is its charge (in Coulombs), v is the
particle's velocity vector (in m/s), and B represents the magnetic field vector (in Teslas).
where
In this experiment we will observe electrons travelling through a uniform magnetic field that is
perpendicular to the velocity of the electrons. The force acting on the electrons will cause them to
move in a circular path. The uniform magnetic field will be produced using a pair of Helmholtz
coils, and the formula used to calculate the magnetic field B produced by the coils is:
B=
8μo NI
125a
(2)
where
N = 130 (the number of turns in each coil)
a = mean radius of each coil (in metres)
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I = current through each coil (in amps)
μo = 4π x 10-7 Wb A-1 m-1
The speed of the electrons, which are accelerated from rest through a potential difference V, can
be calculated from:
1 2
mv = eV
2
(3)
The magnetic force acting on these electrons will cause them to travel in a circular path of radius:
R=
mv
eB
(4)
By combining equations (3) and (4) we can show that:
1 (e / m)R 2
=
B2
2V
(5)
which we will use to find e/m, the charge-to-mass ratio for an electron.
Equipment:
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•
•
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PASCO e/m Apparatus
High Voltage Power Supply
Low Voltage Power Supply
Cables with banana plug terminations
Figure 1. Experimental apparatus (From PASCO Manual)
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Procedure and Analysis
CAUTION: High voltages are present in this lab and should be respected! Be careful not to touch
exposed metallic connections, and power off your equipment if changing connections.
1. The experimental apparatus is shown schematically in Figure 1. Note the following
inside the bulb: The accelerating anode is the silver "top hat" with the hole in it. Just to
the left of this is the cathode (filament). When there is current flowing through the
filament it will glow red and will be emitting electrons with a small (negligible) velocity.
Behind the tube (and parallel to the initial path of the electrons) is a mirrored ruler
measuring in centimeters. This ruler will allow you to measure the diameter of the
electron path.
2. Orient the Helmholtz coils so that their faces are parallel to the direction of the earth's
magnetic field (about 15° east of geographic north). This will help to minimize the effect
of the earth's magnetic field on your experiment.
3. You should take some time to familiarize yourself with the apparatus that you will be
using for this experiment. The e/m apparatus consists of a bulb filled with helium and is
surrounded by two large coils of copper wire that make up the Helmholtz coils. At the
base of the e/m apparatus are inputs for the heater filament voltage (i.e. the cathode
from which the electrons will be emitted), the electrode voltage (the voltage across
cathode and anode through which the electrons will be accelerated), and the Helmholtz
coil current. The High Voltage and Low Voltage Power Supplies are what you will be
using to power the e/m apparatus.
Figure 2. Connection diagram for power supplies (From PASCO Manual).
Before making any connections to the e/m apparatus, make sure that both power
supplies are OFF. On your High Voltage Power Supply, locate the "AC" outputs. Apply
6 volts from the output of the power supply to the heater inputs located on the base of
the e/m apparatus. Now find the High Voltage (0-500V DC) outputs on the supply and
connect these to the electrode inputs on the e/m apparatus base. Ensure the display
switch is set to measure the 500 V output. The left hand side of the Low Voltage
Power Supply is the output for the Helmholtz coil current (0-24V DC). Connect these
outputs to the Helmholtz coil inputs on the e/m apparatus base. Before turning on your
power supply double check your connections with Figure 2 below and make sure that
the voltage and current adjustment knobs on the power supply are set their lowest
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(counter clockwise) setting and that the Helmholtz coil current adjustment knob on the
base of the e/m apparatus is turned to its lowest (counter-clockwise) setting. The
toggle switch should be set to “e/m experiment”.
4. NOTE: Each of these steps should be followed closely and in the correct sequence in
order to avoid any damage to the apparatus. If you do not see what is described below
at each step, turn off the High Voltage and Low Voltage Power Supplies and either
double check your connections or ask for assistance from you lab demonstrator.
i.
Turn on the High Voltage Power Supply. The yellow knob should be set to 6 V.
In a few seconds you should see the cathode glow red-hot. Wait 30 seconds
to allow the filament to fully heat up.
ii.
Now slowly increase the electrode/anode voltage until it reaches 150 volts OR
until you see a clear strong blue-green beam emanating from the anode.
iii.
On the Low Voltage Power Supply, turn up the current knob so the supply is
not current limited (the displays should still read zero), and carefully turn up the
voltage to no greater than 9 V. Between 8-9 V is a suitable voltage.
iv.
Slowly turn up the current in the Helmholtz coils using the adjustment knob on
the e/m base. As you do so you should see the path of the electron beam
deviate from a straight line and start to bend into a circular one. The beam
should turn up and to the right. If the beam is out of focus, use the focus knob
on the e/m base to focus the beam as best you can.
Note: If the electron beam turns in the opposite direction, then the current in
the coils is going in the wrong direction. To change this, turn all the knobs on
the power supply to their lowest settings, turn off the power supply, reverse the
leads going into the Helmholtz coil inputs and then repeat the steps above
again.
5. With the electrode voltage set at 150 volts, change the radius of curvature of the
electron beam by adjusting the Helmholtz coil current. Note the current required to
make the diameter of the electron's path roughly 11.0 cm. You will need to take
measurements at the left and right side of the beam in order to record the diameter.
Record diameters every half centimeter (10.5 cm, 10.0 cm, …) down to 5.0 cm. To
observe the diameter, you will need to ensure you are measuring on the mirrored scale
perpendicular to both sides, eliminating parallax.
6. Change the electrode voltage to 300 volts and repeat the procedure above.
7. Turn down the knobs on the Power Supplies to their minimum settings in the reverse of
the order they were turned on in. Turn off the main power switch on both supplies. It is
important that the tubes be turned off when measurements are not occurring; the tubes
have a finite life.
8. Measure the mean radius, a , of the Helmholtz coils (make at least three readings on
different axes through the coils and take the average).
9. For each of your current values, calculate the magnetic field strength, B , that the
Helmholtz coils were producing. By examining equation (5) we see that if we were to
make a plot of
1 / B 2 versus R 2 for a fixed voltage, then we should get a straight line,
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and that we could extract the value for the charge-to-mass of an electron from this
slope. Do this for your two data tables (one for V = 150 volts and one for V = 300 volts)
and find your average value for e/m. Compare this with the accepted value stated in
your textbook.
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