L66 - Measuring the Mass of the Electron

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Physics 142

Measuring the Mass of the Electron

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L66
-

Measuring the Mass of the Electron

Exploration

1.

Discuss with your lab partner(s) what you have learned about the physics of when a
charged particle moves in a region of constant magnetic field. Write a summary of the
main points of this disc
ussion.

Invention

You have now spent a considerable amount of class and laboratory time studying
electric and magnetic fields. One remaining questions is: What good are they?! As one possible
answer to this question, you will conduct an experiment w
here you will apply these fields to
allow you to measure one of the fundamental constants of physics: the mass of a single electron
(
m
e
).

To help give you a feel for this experiment, your instructor will show you three video
sequences. The first is th
e video
e/m
-

Equipment
.

Next, watch the video
e/m
-

Electron beam
.

Discuss these questions with your group:

How can you tell there is an electron beam inside this apparatus?

Describe briefly how the electrons move.

Finally, watch the video
e/m

-

Magnetic field
.

Discuss these questions with your group:

Referring to the right
-
hand rule, discuss the effect of the magnetic field on the
electrons moving inside the glass tube.

Describe briefly the effect of increasing the strength of the magnetic

field.

Physics 142

Measuring the Mass of the Electron

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Theoretically Deriving the Experiment

Before you begin, you must plan your experimental procedure for measuring the
electron mass. To assist you in this development, answer the questions and complete the
do not turn
on any equipment

until you have completed your
derivation and recorded all relevant information in your logbook.

Electric Fields

To Get the Electrons Moving
:

2.

The cathode contained in the large glass tube is able to emit free electrons when heated.

What will happen to an electron if upon leaving the cathode, it finds itself in the presence
of an electric field? Describe this qualitatively and explain.

3.

If an electron starts from rest and passes through a potential difference

V
, then it gains
en
ergy in the amount of
e

V
. Relate this potential energy to the final kinetic energy of the
electron (that is, write an equation,
e

V=
....).

4.

From this expression (#3), how is the speed of an electron related to the potential
difference

V

that it passe
d through? That is,
electron speed

=
v
e

= ?

Magnetic Fields

To Bend the Path of the Electrons
:

Nice, uniform magnetic fields can be created by running current through large coils of
wire. The magnetic field
B
Coils

due to two identical, specially plac
ed coils is dependent on the
number of turns of wire in each coil
N
Coils
, the current
I
Coils

passing through each coil, and the
R
Coils
. This can be summarized with the equation

where

0

= 4


10
-
7

T m/A

5.

The magn
itude of the force acting on a moving electron by a magnetic field is
F = ev
e
B,
where
B

is the strength of the magnetic field. In addition, you should recall from Physics
141 that when an object moves in a circular path, its acceleration has the magnitud
e of
v
2
/R
Path
. Use Newton’s second law to relate these two quantities.

6.

Using the expressions from #5, you should find an expression for the speed of the electron
v
e

as a function of the strength of an applied magnetic field
B

and the radius of the cir
cular
path
R
Path
.

Electric and Magnetic Fields
:

7.

By combining #4 and #6, derive an expression which relates the following quantities: the
mass of an electron

m
e
, the charge of an electron
e
, the magnetic field strength applied by
the coils
B
Coils
, t
he potential difference

V
, and the radius of the circular path
R
Path
. Write

m
e

=

.

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Be careful not to confuse the speed
v
e

with the potential difference

V
!!

Be careful not to confuse the radius of the coil
R
Coil

and the r
R
Path
!!

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You have now derived the theory from which to build your own experiment for
measuring the mass of a single electron! All you need is to produce a potential difference and a
magnetic field and measure the radius of a path!

Safety Warnings!!

While completing this experiment you will be using delicate equipment. You will
also be using high values of voltage and current. Therefore it is very important that
you read the directions carefully so as to not injure yourself or d
amage the
equipment.

Do not turn on any circuit unless it has been inspected by your lab instructor.

Absolutely no drinks permitted at the lab stations during this experiment.

Magnetic fields and computers and monitors do not mix very well. Therefore,
as a
e/m

apparatus as far from the computers as possible.

Experimental Procedures Based on the Theory

Equipment
:

Apparatus containing 2 large coils, helium
-
filled vacuum tube tube, and electron
gun; DC Coil power supply; AC

Cathode heater power supply; DC High Voltage
power supply; Black cloth; Banana leads

0.

Getting Started

Before you begin, check the following settings on your e/m apparatus:

Toggle switch on the apparatus should be set to the "e/m MEASURE" position.

The coil "current adjust" knob should be turned to the "OFF" position.

Verify that all power supplies at your station are turned off and the knobs are all
turned down to 0 V and 0 A.

Schematic of the e/m Apparatus:

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Cathode
Heater Power
Supply

I.

Applying Electric Fields

In
side the helium
-
filled vacuum tube is an "electron gun," which will produce a stream
of electrons and accelerate them out into the helium gas contained in the tube once all
connections are properly made. The main parts of the electron gun are the cathode
and the
anode.

a.

The Cathode

The cathode emits electrons when it is heated by an electric current passing through it.
This is similar to the heating of the filament in a household light bulb. In this exper
iment, the
cathode just serves as a source of free electrons.

Connect the Cathode Heater AC Power
Supply as shown in the circuit diagram.

Do not turn anything on at this point.

Coils of wire

Mirrored scale

Electron gun

Helium
-
filled vacuum tube

Cathode

Anode

(positively charged with respect to
the cathode
and filament)

Deflection plates

(which are not used in this
experiment)

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When the cathode is hot it will emit electrons in all directio
ns.

b.

The Anode

The cathode is near a cylindrical anode. If this anode is charged positively with respect
to the cathode, then it attracts the electrons. Due to the potential difference

V

between the
cathode and the anode, the electrons are accelerated towards the anode. Some of these
accelerated electrons shoot through the opening in the anode and form a concentrated beam of
fast electrons.

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Accelerating
Voltage
Power Supply

Coils

Power
Supply

Keep the Cathode Heater Power Supply con

Locate the DC high voltage power supply for the anode (accelerating voltage).

Connect the DC high voltage supply to the
"electrodes", according to the diagram.
This will supply a potential difference to
accelerate the elect
rons.

Be mindful of the [+] and [
-
] designations

Do not turn anything on at this point.

II.

Applying Magnetic Fields

At your lab station are two large coils of wire. These two coils are called "Helmho
ltz
coils" because it was Helmholtz who discovered that if you orient two identical coils in just this
way, they will produce a very uniform magnetic field at the center of the two coils.

The magnetic field
B

due to the two Helmholtz coils is dependent o
n the number of
turns of wire in each coil
N
, the current
I
passing

through each of the coils, and the coils' radius
r
. This relationship can be derived using Ampere's law and can be summarized with the
equation

where

0

= 4


10
-
7

T m/A

and
N

= 130 for this experiment.

supply to the coils.

Do not turn anything on at this point.

+

-

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8.

Measure and record the diameter of your large coils and calculate the radi
us,
R
Coils
.
Convert this measurement into units of meters.

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You have now made all necessary connections to the e/m apparatus. Before you turn
anything on,
have your lab instructor inspect the circuit.

Once your circuit has passed inspection
, use the
following procedures to turn on the
various power supplies.

III.

The Experiment

Background Lights

You will need low background light levels for this experiment. Turn down the
overhead lights and be prepared to use the black cloth to block out the rema
ining light if
necessary.

Steps for Turning on the Equipment

A.

Verify that you have turned the "current adj" knob on the e/m apparatus to "off."

B.

Set the "current adjust" knob on the coils power supply to zero.

C.

Turn on the heater power supply. Gradually tu
rn up the cathode heater voltage to the

6
-
V setting (AC). You should see the cathode start to glow. Do not go higher than 6 V.

D.

Gradually turn up the accelerating voltage (DC) using the 500 V adjust knob until you
see a glowing beam leaving the electron
gun. Turn it up until this beam looks like it is
contacting the glass, and then turn it back down so it appears to go halfway to the tube's
glass.

E.

Turn on the coil power supply. Turning clockwise, set the coil current using the
e/m apparatus to the MAX setting (i.e., 10). The current
reading on the power supply should still be 0.0 A at this point.

F.

Turn the "current adjust" knob on the coils power supply so it is just a little bit off of the
minimum setting.

G.

e coil voltage to a value of 7 volts (DC). This voltage value will be
displayed on the power supply. The current reading should be low and must never go
above 2 A. If the current starts nearing 2 A, then turn down the "current adjust" knob.

H.

From here
on, you will only be adjusting two parameters during this experiment

The current passing through the coils, which you control by turning the
"current adjust" knob on the coils power supply. Do not let this current go
above 2 A at any time. You may also i
ncrease the voltage applied to the coils
to a value of 9 V, but do not go over 9 V.

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The accelerating voltage applied between the cathode and anode, which you
control by turning the "voltage adjust" knob on the accelerating voltage
power supply. Do not let

this voltage go above 300 V at any time.

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It will take a few minutes for the cathode to heat up and for you to be able to clearly see
the beam of electrons. Once all this is working, you should see an electron beam coming out of
the electron gun. Th
e potential difference gives the electron beam its kinetic energy,
. You will be able to see the electrons' path because these fast
-
moving electrons
bump into the helium gas and the collisions result in the production of light.

As

the cathode is heating, answer the following questions.

9.

(a)

Record what you observe looking at the cathode . Include a sketch of the electrons
being "boiled" off.

(b)

Make a sketch in your notebook of the beam emerging from the anode and include
the

value of the potential difference.

10.

In what direction is current flowing in the coil wire? In what direction are the electrons
moving in the coil wire? How do you know?

11.

Include a diagram in your logbook showing the direction of
B
, the directi
on of the forces
acting on the electrons, and the direction of the electron velocity. You might try changing
the coil current to see what effect it has (do not exceed 2A).

Keep these important limits in mind during the rest of this experiment…

The cat
hode heater voltage should be set at 6 V. Never exceed this value or
the filament will be burned out and destroyed.

The accelerating voltage should be in the range of 100 V
-

300 V. Do not go
above 300 V.

The coil voltage should be 7 V. Do not go above
9 V and see that the current
never goes above 2 A.

You should now be able to clearly see the electron beam emerge from the electron gun
and have its path curved by the magnetic field produced by the Helmholtz coils.

Check that the electron beam is par
allel to the Helmholtz coils. If it is not, turn the tube
until it is. Do not remove the tube from its socket! As you gently rotate the tube, the socket

passing through the coil so that the electrons appear to follow
a complete circular path, always staying below a value of 2 A and 9 V.

Once you are able to see the electron beam going in a complete circular path, then stop

following values in a data table:

Current to the Helmholtz coils

Accelerating voltage

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of the electron beam (measure to the "outside" part of the beam)

To avoid errors due to parallax, move your head to align the electron beam
with the reflection of

the beam that you can see in the mirrored scale.
Measure the radius as you see it on both sides of the scale, and then
compute an average of these two values
.

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Record data for several experimental trials. You should use different values of
I

and/or

V
and then measure the resulting value of R.
Remember,

V must be less than 300 volts and
the current I through the large coils must be less than 2 amperes at all times
. You should record
data for at least six different sets of conditions.

Keep these
important limits in mind during the rest of this experiment…

Cathode heater voltage = 6 V.

Accelerating voltage = 100 V
-

300 V. Do not go above 300 V.

Coil voltage = 6
-

9 V. Do not go above 9 V.

Coil current must be

2 A.

Data Analysis

Knowing t
he charge of an electron
e = 1.60

10
-
19

C,
determine the experimental value of
the mass of the electron,
m
e

for each of your recorded data sets.

Compute an average value of
m
e

Equipment Shutdown:

Once you are satisfied with your da
ta, turn down all voltage and current values to zero.
Turn the power off on both of the power supplies. Unplug all of the banana leads.

Summary Questions:

12.

Are all of your data equally valid? Why or why not?

13.

Find the "accepted" value for t
he mass of an electron. What is the percent difference
between your experimental value and the accepted value?

14.

How would this experiment be different if you had wanted to measure the mass of a
proton? A proton has a positive charge equal in magnitud
e to an electron, but its mass is
almost 2000 times greater than the mass of the electron.

15.

Could you use this equipment to measure the mass of a neutron (which has a neutral
charge and a mass equal to a proton)? Explain why or why not.