Download Measurement of charge to mass ratio on an electron

Measurement of charge to mass ratio on an electron
R.L.Griffith,A.Okunyan,A.Okunyan,M.R.Levi
ABSTRACT
The charge to mass ratio of an electron was studied using an electron beam tube and two
Helmholtz coils. The set up of the apparatus is included with this report. This is the same
experiment that was conducted by J.J. Thompson to measure the charge to mass ratio in the
early 20th century. A beam of electrons was accelerated through a known potential difference,
and passed through a magnetic field causing the electrons to move in a circular orbit. The
radius of curvature was calculated with placing the beam through a known distance marker
and the voltage and current were measured at those markers. The error calculations yielded
a value of 8.6 %. The errors acquired were within the allowed errors of these experiment.
Subject headings: Magnetic Force, Magnetic field, Electron
1.
Introduction
rewriting equation 4 we get
2V
e
= 2 2 2
m
G I r
When a cathode electrode is heated, it begins
to emit a large number of electrons. These electrons are then accelerated through a potential
difference V to a velocity v. A hole in the anode
allows the electrons to form a beam of electrons
who are than focused ny a Wehnelt cylinder to
which a negative voltage is applied to produce a
well defined beam. As the electrons move perpendicular to a magnetic field produced by the
Helholtz coil they are deflected by the Lorentz
force
Fl = evB
(1)
where Z is
Z=
therefore
2.
2.1.
(2)
the kinetic energy is given by
K=
mv2
= ev
2
(3)
2.2.
combining equations 2 and 3 we can find an equation for the charge to mass ratio given by
2V
e
= 2 2
m
B r
(8)
e
Z
= 2
m
G
(9)
Method
Equipment Used
Equipment
Electron beam tube
Helmholtz coils
Battery eliminator
Variac
magnetic compass
Variable power supply
Voltmeter
thus the electrons moves along a circular path of
radius r such that
mv2
evB =
r
2V
(Ir)2
(7)
Serial
n/a
n/a
n/a
n/a
n/a
n/a
Procedure
The first step is to set up the equipment as
outlined in the included diagram. Next all the
equipment is turned on and the electron beam
is then focused using the focusing voltage. The
current regulator is then adjusted to increase the
magnetic field that will cause the electron beam
to move in a circular fashion. there are four measurements taken, with the beam at different radius. The voltage is increased by increments of
50 V and four different trial are performed with
the same voltages.
(4)
The magnitude of the magnetic field is found for
the geometry of the Helmholtz coils and the field
current I by
B = GI
(5)
where G is the geometric factor for the coils given
by
G = 2.48 × 10− 4T /A(±2%)
(6)
1
3.
Results and Discussion
an error estimate was performed on this lab to
compare the experimental values obtained during this experiment and the theoretical values
obtained from the actual mass and charge of an
electron. Some possible sources of error can be
explained due to the precision of the measurements taken by the instruments used, i.e voltmeter and amp-meter. Another source of error
can be explained by the measurement of the radius of the beam, due to accuracy of the radius.
The error measurement yielded a value of 8.53
% which confirms the validity of the principles
used to conduct this experiment.
There are five calculations performed, the first
one is to find the value of Z, which is performed
using equation 8. Next the average of Z is calculated by taking the sum of all the values and
deviding by the total number of Z’s. Next the
charge to mass ratio is calculated for the experimental value by using equation 9 and is then
compared to the theoretical value that is calculated by using the theoretical values of the charge
of an electron which is 1.60×10−19 and the value
of the mass of an electron which is 9.109×10−31 .
The calculated value for the error measurements
yielded a value of 8.57 %, which is within the
range allowed due to errors introduced by taking measurements.
3.1.
Acknowledgements
The author would like to thank Roni,Alina,Arman,
and Simon for their help with this experiment.
Data and Calculations
radius Acce. voltage Current Z
V
(cm) V(V)
I(A)
(Am)2
250 V
2
247.9
3.71
9.02 × 104
3
246.8
2.43
9.29 × 104
4
246.9
1.80
9.53 × 104
5
247.7
1.53
8.47 × 104
300 V
2
301.7
4.02
9.33 × 104
3
301.3
2.71
9.12 × 104
4
301.0
2.05
8.96 × 104
5
300.6
1.68
8.52 × 104
350 V
2
350.1
4.45
8.84 × 104
3
349.7
2.87
9.43 × 104
4
348.9
2.20
9.01 × 104
5
349.3
1.82
8.44 × 104
400 V
2
401.0
4.65
9.27 × 104
3
402.0
3.12
9.18 × 104
4
402.0
2.36
9.02 × 104
5
401.0
1.95
8.35 × 104
Z average
V
8.98 × 104 (Am)
2
Experimental and theoretical values for
C
Exp.
1.60 × 1011 kg
11 C
Theo.
1.76 × 10 kg
Error
8.57 %
4.
5.
REFERENCES
Los Angeles City College Lab Manual Physics
102.
e
m
Conclusion
This lab was conducted to get a better understanding on the effects that a magnetic field
has on a charged particle. It allows us to verify the principles of electricity and magnetism.
This 2-column preprint was prepared with the AAS
LATEX macros v5.2.
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