Cathode Rays and the Discovery of the Electron
Andrew Chang
UC Davis COSMOS Cluster 2: Electro-Optics and Nuclear Physics
Cavendish Professor of Physics Joseph John Thomson
Professor Niels Grønbech-Jensen
Professor Diego Yankelevich
31 July, 2015
Abstract:
At the end of the 19th century, there was a huge debate about the nature of a cathode
ray. The Germans supported the view that the cathode ray was made up of waves that
disturbed the aether, while the British supported the view that the cathode ray was made up of
particles. The Germans had good reason to believe that the rays were waves. First of all, when
a radiometer was put in the path of a ray, the radiometer started to spin very quickly. Secondly,
when a ray was trying to be bent by an electric field, the ray was not affected. Joseph John
Thomson, a British physicist, used these cathode rays to settle once and for all the nature of it.
He realized first that the gas in the tube became a conductor when there was a voltage
difference between the electrodes, and that the charges are able to leak and cover the electric
plates that were supposed to generate the electric field. He then found out that the trajectory of
the rays when they were affected by both magnetic and electric fields were congruent with the
trajectory of a charged particle in a field. Thus, he set out to figure out to prove how these
cathode rays could be particles and explain how it behaves as well as its characteristics.
Introduction:
The purpose of this experiment was to provide a particulate model of the so-called
“aetherical disturbances” by the Germans and find the specific charge (m / q) of these particles.
These ‘disturbances’ first caught the eye of Michael Faraday, who had just discovered
electromagnetic induction, and realized that something interesting must have been going on in
rarefied (low pressure) gases when an electric current was passed through them and made
them and the anode glow2. Gases, obviously, are not like solids or liquids, which allow electricity
to pass via conduction. This interested Faraday very much, because this meant that there
needed to be a theory of the flow of electricity to describe the conduction of electricity in gases
that coincided with his theory of electromagnetic induction. Faraday found that this phenomenon
could be isolated in a sealed, evacuated, egg-like vessel with electrodes at the top of the
bottom2. After doing multiple experiments, Faraday discovered the factors that would change
the glow of the gas in some way. this included: “Size of the ends. Nearness of ends or wires to
glass. Size therefore of the vessel. Nature of [gas used] within. Degree of rareification.
Temperature of [gas].”2 However, Faraday realized that he did not have the suitable equipment
because he could not alter these factors to the extremes. However, in continental Europe, there
were Germans who had better equipment and were willing to do so.
Julius Plücker, a German mathematician who idolized Farday, continued Faraday’s
studies with superior equipment. He started using tubes because they were smaller and the
luminescence was brighter, and experimented extensively with them, altering every factor that
could affect the light2. He noticed three very important things. First, he noticed that it was the
leftover gas that caused the glow. Second, he noticed that each gas had a different kind of glow.
Third, he noticed that the path of the glow followed the lines of a magnetic field and that the
glow was charged2. When Plücker died, Hittorf, his assistant, continued Plücker’s studies, and
found that some sort of beam was only emitted from the cathode because when things were put
in the way, the anode stopped glowing, and thus named it the ‘cathode ray’2. When a
radiometer was put in front of the ray, it started spinning, and he thus attributed the cathode ray
(incorrectly) to a wave because he concluded that it was radiation that caused the radiometer to
spin. However, an Englishman by the name of William Crookes theorized that the ray was
actually a bunch of tiny particles, because he showed that the ray was able to move a small
paddlewheel when the paddlewheel was placed in front of the ray2. Thus, an experiment was
required to settle the dispute between the German theory of rays as waves, and the English
theory that the rays were actually particles.
This experiment assumes the particulate view and tries to find the ratio between the
mass and the charge of said particle. This can be done one of two ways. First, the charge of N
particles and the kinetic energy of the particles can be measured while they are under the
influence of an electric field, and to measure the angle of deflection. Second, the beam can be
influenced by both an electric field and a magnetic field so that the effects of each are canceled
out and thus the forces are the same1.
Materials:
- Cathode ray tube, like the one in the figure above, with phosphorescent patch at the end
- 2 coaxial cylinders with small holes in one of the ends to let the ray through, the outer cylinder
being insulated from the inner one and the inner one having a capacitance of 1.5 microfarads
- Electrometer
- 2 aluminium electric plates with a potential difference between them with a length of 5 cm
- Thermo-electric couple, which takes the heat energy from all of the kinetic energy of the
moving particles smashing into the couple and then converts it into electricity and the current
is measured
- Voltmeter
- 2 magnetic coils, each of the same size, with cross sections of a rectangle that is 5 cm by 1
-
cm
1 aluminium electrode
2 more coaxial cylinders like the first pair except with smaller holes (~1.5 mm in diameter)
2 slits to shape the ray
Air
Hydrogen
Vaporized carbonic acid
Experiment 1
Method:
1. The first 2 coaxial cylinders were inserted into the cathode ray tube, the electrometer was
connected to the inner cylinder and the thermo-electric couple was put right behind the hole
of the inner cylinder
2. An aluminium electrode was inserted at one end and the glass tube, and then the outer
cylinder was connected to the ground
3. A slit was put between the cylinders and the electrode and was connected to the ground,
and a slit next to that connected to nothing
4. A selected gas (or air) was pumped into the tube
5. The tube was evacuated over a period of several days
6. A cathode ray was shot by having an electric potential difference between the electrode and
the outer cylinder for a short period of time as to reduce the ionization and thus the
conductivity of the gas within the tube
7. The voltage measured from the thermo-electric couple was assumed to be a perfect
transmission of the kinetic energy of the particles in the rays, and the measured voltage was
multiplied by the time to get the kinetic energy of the total particles that hit the couple and
was recorded
8. The total charge of the particles that hit the cylinder was measured by the electrometer and
was recorded
9. The cylinders were taken out, another electrode was added at the other end, and the tube
was put between the two coils that generated a magnetic field of known strength and a
cathode ray was shot again
10. The radius of the path of the rays under the influence of a magnetic field was calculated by
finding CA and CE (E being the brightest point on the tube) in the diagram below
9. Steps 4-8 were repeated for different gases
10. Steps 4-9 were repeated by changing the coaxial cylinders of bigger holes to the ones with
smaller holes
Data:
When assuming that the ray is made up of charged particles, we can apply Newtonian
mechanics to the problem. When a charged particle is affected by a magnetic field that is
perpendicular to the direction the particle is traveling in, the particle will move in a circle. The
centripetal force of this circular motion is described by the following equation:
Fc = m * v2 / r
where m is the mass, v is the tangental velocity, and r is the radius of the circular motion.
However, since the particle is also under the influence of a magnetic field with a force described
by the following equation:
FB = q * v * B * sin(θ)
where q is the charge of the particle, v is the velocity of the particle, B is the strength of the
magnetic field, and θ is the angle between the direction of the magnetic field and the direction of
the particle’s velocity. Thus, an equality can be made:
m * v / q = B * r = I where I is just a shorter version of B * r.
The value of r can be calculated because the lengths of CA and CE are known, and:
2r = CE2 / AC + AC.
Also, from the collected data of the amount of charge carried by however many particles hitting
and affecting the electrometer as well as the kinetic energy, one can use the following
equations:
KE = 0.5 * m * v2 * N
Q=N*q
where N is the number of particles that hit and affected the equipment, Q is the total amount of
charge, and KE is the kinetic energy of all the particles. This means that:
Gas
KE / Q (J/C) I (mT*m)
Tube
1
Tube
2
0.5 * m * v2 / q = KE / Q.
Analysis:
From these numbers, we can do the following:
I * v / 2 = 0.5 * m * v2 / q
I * v / 2 = KE / Q
v = 2 * KE / (Q * I)
0.5 * m * (2 * KE / (Q * I) )2 / q = KE / Q
m / q = I2 * Q / 2KE.
Gas
m / e (kg/C)
v (cm/s)
Tube 1
Air
0.57 * 10-7
4 * 109
Air
0.34 * 10-7
1 * 1010
Air
0.43 * 10-7
5.4 * 109
Air
0.32 * 10-7
1.2 * 1010
Air
0.48 * 10-7
4.8 * 109
Air
0.4 * 10-7
7 * 109
Air
0.4 * 10-7
7 * 109
Hydrogen
0.35 * 10-7
6 * 109
Hydrogen
0.5 * 10-7
9.2 * 109
Carbonic acid
0.4 * 10-7
7.5 * 109
Gas
m / e (kg/C)
v (cm/s)
Carbonic acid
0.4 * 10-7
8.5 * 109
Carbonic acid
0.39 * 10-7
1.3 * 1010
Tube 2
Air
0.9 * 10-7
2.4 * 109
Air
0.7 * 10-7
3.2 * 109
Hydrogen
1.0 * 10-7
2.5 * 109
Experiment 2:
Method:
1. An aluminium electrode was inserted into one end of the tube
2. A slit connected to the ground near the electrode was inserted
3. Another slit after the grounded slit to shape the ray was inserted
4. The cathode ray was set up according to the first diagram in the materials section, including
the electric plates
5. The cathode ray was sandwiched between the magnetic coils so that if the electric plates
were in the x-z plane, the coils are in the x-y plane (according to the diagram) so that the
distance that the electric and magnetic fields affected was the same
6. The gas was pumped with a given gas, and then evacuated as much as possible
7. The length of the field was measured
8. An electric field of given strength was chosen, bending the ray, and recorded
9. The strength of the magnetic field was altered until the force applied by the magnetic field
was the same as the electric field and bended the ray by the same angle, and this was
recorded
10. Steps 8-9 were repeated for multiple strengths of the electric field
11. Steps 6-10 were repeated for multiple gases
Data:
The velocity in the y direction (assume the same coordinate system as the first experiment)
affected by electric plates put in the x-z plane is described by:
vy = E * q * l / (m * v)
where l is the length of the electric field in the x direction, E is the strength of the electric field, m
is the mass of the particle, q is the charge of the particle, and v is the initial x velocity of the
particle. Thus, we can find the angle of deflection of the particle:
Gas
θ (degrees)
B (T)
E (V)
l (cm)
θ = arctan(((E * q * l) / (m * v)) / v)
θ = arctan(E * q * l / (m * v2))
But since θ is at small angles, we can assume that
θ = E * q * l / (m * v2)
If the particle were to be instead deflected by a magnetic field made by coils in the x-z plane,
then the velocity of the particle in the y direction is:
vy = q * v * B * l / (m * v)
where B is the strength of the magnetic field and the other variables are the same. The angle of
deflection of this can also be described:
ɸ = arctan(B * q * l / (m * v))
Again, since ɸ is at small angles, we can assume that
ɸ = B * q * l / (m * v)
The velocity can be described as:
v = ɸ * B / (θ * B)
And thus the m / e value is:
m / e = B2 * θ * l / (E * ɸ2)
Since we are trying to make θ = ɸ by first shooting a ray through a magnetic field and then
through a electric field, we can replace ɸ with θ.
Analysis:
Continuing on from that last calculation,
E * q * l / (m * v2) = B * q * l / (m * v)
and thus
v=E/B
m / e = B2 * l / (E * θ)
Gas
m / q (kg/C)
v (cm/s)
Air
1.3 * 10-7
2.8 * 109
Air
1.1 * 10-7
2.8 * 109
Air
1.2 * 10-7
2.3 * 109
Hydrogen
1.5 * 10-7
2.5 * 109
Carbonic acid
1.5 * 10-7
2.2 * 109
Air
1.3 * 10-7
3.6 * 109
Air
1.1 * 10-7
2.8 * 109
Conclusion:
It is undeniable that cathode rays are made up of particles because the way they are
affected by magnetic and electric fields is exactly like how charged bodies are affected by these
fields1. It can also be concluded that the specific charges of these particles are not affected by
the type of gas used, as both the specific charge and the velocity of these particles are
generally consistent throughout both experiments1.
It is to be said that there is a significant difference between the results from Tube 1 in the
first experiment compared to the others because the holes of the smaller cylinder in Tube 1 was
too big. Because the hole was too big, charge still leaked out of the small cylinder and ionized
the gas, making it a conductor and allowing the particles (which from now on are to be called
corpuscles) to, instead of hitting the inner cylinder, be leaked to the ground and not provide a Q
value that is smaller that it is supposed to be, making the calculated specific charge smaller.
Also, because the location of point E is difficult to precisely locate, there is a 20% error in the
calculation for r, and thus B1.
This brings a a very interested question about the significance of the calculated specific
charge of these corpuscles1. It is much smaller than the specific charge of a hydrogen ion
(about 1000 times smaller) which begs the question: is it smaller in size or is it larger in charge?
Philipp Lenard’s results have shown that these particles are small because the brightness of the
path of these particles diminishes as it travels further in length, and it is also is affected by the
density of the gas the particles are traveling through and not on the gas’ chemical or physical
state. This can thus be explained by the mean free path (the distance a particle can travel
without colliding into another one): the mean free path of a corpuscle is much longer than that of
a molecule of air, meaning that the corpuscle must be much smaller than a molecule of air1.
However, the Q obtained from the first experiment as well as the fact that the charge is
comparable to ions in an electrolyte also hints at the size of the charge of this corpuscle. One
can only conclude that the smallness of the specific charge must be due to both the size of the
particle and the charge1.
The fact that the specific charge of these corpuscles is not different from substance to
substance means that corpuscles are found in all atoms, and that corpuscles must also make
up the inner workings of an atom, further advancing the present atomic model.
Works Cited:
1
"Cambridge Physics - Discovery of the Electron." Cambridge Physics - Discovery of the
Electron. Cambridge University, n.d. Web. 27 July 2015.
2
Klein, Martin J., Anne J. Kox, and Daniel M. Siegel. No Truth Except in the Details:
Essays in Honor of Martin J. Klein. Dordrecht: Kluwer Academic, 1995. Print.
3
Springford, Michael. Electron: A Centenary Volume. Cambridge: Cambridge UP, 1997.
Print.
4
Thomson, J.J. "Cathode Rays." Philosophical Magazine 1897: 1-24. Print.