Download Exploration of Cathode Ray Tubes and Thomson`s Work

Exploration of Cathode Ray Tubes and Thomson’s Work
The purpose of this exploration is to become familiar with the type of cathode ray tube used by
Thomson in his famous charge-to-mass (e/m) experiment and to review the underlining physics
principles necessary to understand his experiment. As you work through this exercise, have the
applet open in a separate window. (If necessary click on the link, thomsonExp.swf). If you need
help understanding the apparatus and variables, see the Help menu for assistance before starting
this exploration.
Once you have finished this exploration, you should be able to conduct a simulation of
Thomson’s e/m experiment and complete a formal lab report. (See Simulated Exp. under the
Resources menu of the applet.)
The Cathode Ray Tube
Thomson designed many different types
of cathode ray tubes in his preliminary
work on cathode rays (See Background).
For his e/m experiment, he used a tube
similar to the one shown in Figure 1. The
cathode rays are produced at the left end
of the evacuated tube when a high
voltage is applied between the cathode
(−) and the anode (+). A thin, bluishcoloured line moves to the right between
a set of horizontal plates, shown in red in
Figure 1, and then hits the end of the
tube.
Compare Figure 1 with the schematic
diagram in the Thomson applet. In the
applet diagram:
Figure 1. Artist’s rendering of a cathode ray tube similar
to the one used by Thomson.
1. Identify the cathode and anode used to produce the cathode rays.
2. Why are there two batteries or electric power supplies shown?
3. What do you think is the purpose of the third vertical plate after the anode and before the
horizontal plates?
Effect of an Electric Field on Cathode Rays
In the applet, set the voltage at +200 V.
4. Describe the motion of the cathode ray between and after the horizontal plates.
5. State two observations that suggest cathode rays are not noticeably affected by gravity.
6. What does the motion of the cathode rays indicate about their nature?
7. What is the direction of electric field between the plates. [Check your answer by selecting
Field Directions in the Options menu.]
8. Sketch a few diagrams to show how the horizontal and vertical components for the
velocity of a cathode ray particle change when traveling between the plates? [A
gravitational analogy of a ball thrown horizontally may help.]
9. Sketch a diagram starting with a dot representing a cathode ray particle and label:
direction of the electric field, velocity of the particle and direction of the electric force.
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Exploration of Cathode Ray Tubes and Thomson’s Work
10. If the plates are separated by a distance of 1.5 cm, calculate the value of the electric field.
[Check your answer by selecting Field Values in the Options menu.]
11. How would you calculate the magnitude of the electric force?
In Thomson’s experiment, a fluorescent material was coated on the end of the tube to produce a
glowing dot where the cathode rays hit. You can see a simulation of this glow on the far right of
the applet diagram. Move the voltage slider to various settings while watching the simulated
glowing dot.
Thomson measured the deflection of the beam using a ruler etched on the end of the tube. From
measurements of this deflection, he was able to calculate the angle of deflection. In the Thomson
applet, this angle is provided by selecting Deflection Angle in the Options menu.
Effect of a Magnetic Field on Cathode Rays
Thomson also used a magnetic field to
affect the beam of cathode rays. Using
the same tube as shown in Figure 1, he
placed a pair of coils outside of the tube
and on either side of the horizontal plates
(Figure 2). When a current flows through
the coils, a uniform magnetic field is
created in the region between the
horizontal plates.
In the Thomson applet, set the voltage at
0 V and move the slider for the current to
the right. Notice the dotted circle
indicating the position of the coils, the
direction of the magnetic field between
the coils and the value of the field.
Figure 2. Artist’s rendering of a cathode ray tube with
external coils to create a magnetic field.
12. How does the magnitude of the
magnetic field change as the current changes?
13. Using the hand rule for coils, what is the direction of the current in the coil?
Move the current slider to the left (reversing the current as indicated by –I).
14. What is the direction of the magnetic field now?
15. Sketch a diagram starting with a dot representing a cathode ray particle and label:
direction of the magnetic field, velocity of the particle and direction of the magnetic
force.
16. Notice that all three vectors (field, force and velocity) are mutually perpendicular. In this
situation, what mathematical equation is used to calculate the magnitude of the magnetic
force?
17. Thomson was not able to calculate the electric force and the magnetic force even though
he knew the equations (answers to #11 and #16). What crucial information did he not
know?
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Exploration of Cathode Ray Tubes and Thomson’s Work
Effect of Simultaneous Electric and Magnetic Fields
Notice in Figures 1 and 2 that Thomson designed his apparatus so that both the electric and
magnetic fields can be present in the same region of space (between the horizontal plates). This
is a very clever design because Thomson could manipulate the voltage (and therefore the electric
field), manipulate the current (and therefore the magnetic field) or both simultaneously.
In the Thomson applet, change the voltage and the current to observe how the cathode ray
responds to simultaneous electric and magnetic fields. (Make sure Field Directions is checked in
the Options menu.) Try many different combinations of field directions and strengths.
18. What observation shows that the electric and magnetic forces are balanced (i.e., net force
is zero)?
19. Using in/out and up/down descriptors, what combinations of magnetic and electric field
directions produce opposing forces on a cathode ray particle?
20. How are these observations evidence that cathode rays are charged particles and not
electromagnetic waves?
Thomson was convinced that cathode ray particles were negatively charged, but he had no way
of determining their charge, q. However, he realized that when the cathode ray beam was not
deflected in the presence of electric and magnetic fields, the forces must be balanced.
JG
E
21. Use your answers to #11 and #16 to show that v = JG
B
Both electric and magnetic fields can be calculated and therefore the horizontal speed of the
cathode ray particles is easily obtained. All measurements have some uncertainty; therefore, it is
always a good plan to repeat the same measurement many times to average out the uncertainties.
One averaging method is to collect at least five sets of measurements and complete a best-fit line
JG
JG
graph of E versus B .
22. What shape of graph do you expect and what feature of the graph will provide the speed
of the cathode ray particles?
Using the Thomson applet, choose at least five combinations of current and voltage that produce
a cathode ray with no deflection. After each combination is obtained, click the Record Data
button. When you are finished, select Evidence in the Options menu.
23. Copy the evidence in the table and paste it into a spreadsheet program (like Excel or
Numbers). Use the features of the spreadsheet to display a graph, add a best-fit line and
display the equation of the line to obtain the slope (v).
24. Choose one trial from the evidence table. Calculate the magnitude of the electric force
and the magnetic force using the modern value of q = 1.60 × 10−19 C. Thomson assumed
that the gravitational force was insignificant (see #5). Check and evaluate this assumption
by calculating the gravitational force on a cathode ray particle using the modern mass of
9.11 × 10 −31 kg
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As you will see, the determination of the horizontal speed of cathode ray particles was crucial to
the main part of Thomson’s experiment discussed in the next section. The method used by
Thomson is not the only way to determine the speed of the cathode rays.
25. Using your knowledge of electron guns, describe how the speed could also be obtained
by measuring the accelerating potential difference between the cathode and anode.
Include appropriate equations in your answer.
Determining the Charge-to-Mass Ratio
Thomson believed that cathode rays consisted of negatively charged particles with a certain
charge (q) and mass (m), but neither of these quantities were known or able to be determined in
the late 1800s. Thomson did the next best thing and that is to determine the ratio of charge to
mass for a cathode ray particle.
A charged cathode ray particle traveling horizontally between the horizontal plates is accelerated
vertically by the electric force. The horizontal component of the velocity, vx, is not affected (see
#8).
26. The time required for the
particle to travel across the
L
plates is t = . Show that
vx
the final vertical speed of
the particle when it leaves
L
the plates is vy = ay .
vx
27. Using Newton’s second law,
show that the vertical
JG
qE
Figure 3. Diagram of electron passing through an
acceleration is ay =
.
electric field
m
28. Using the diagram above, draw
a simple vector diagram and determine the expression for the tangent of the deflection
angle, tan θ.
Recall that the horizontal speed of the cathode ray particles has already been determined and the
JG
values of L and E are also known. However, the vertical speed and acceleration are not known;
therefore, we need to eliminate both vy and ay when combining the equations.
29. Show that the equations in the previous three questions can be combined to give the
q tan θ ⋅ vx2
=
following expression:
JG .
m
LE
You are now ready to simulate one of the great experiments of the late 19th century. To get
started, select Simulated Exp. under the Resources menu.
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Significance of Thomson’s Experiment
Thomson’s work is really the story of the discovery of the electron and represents the birth of
subatomic particle physics. This is an amazing feat because it came at a time when the existence
of atoms was still doubted by some of the world’s leading physicists and the notion of a discrete
unit of charge was far from clear.
Later experiments by Millikan established the charge on the electron. This charge is now known
as the elementary charge, e. Therefore, the charge-to-mass ratio is usually symbolized by e/m.
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