Download Determination of e/me

Umeå University
Department of Physics
Leif Hassmyr
2007-11-27
Determination of e/me
1
Objects of the Experiment
The objects of the experiment are to give knowledge about how charged particles movement is
affected by electromagnetic fields and how this knowledge can be used to get information about
fundamental properties of the particles. Secondary the objects of the experiment are to give a
certain experience of using electrical laboratory equipment.
Aims of the Experiment
- Study of the deflection of electrons in a magnetic field into a circular orbit.
e
of the electron.
- Determination of the specific charge ε =
me
Table of Contants (Index)
Introduction
Theory
Scope of Supply, Description, Technical Data
Carrying Out the Experiment
2
2
5
6
Introduction
Joseph J. Thomson published in 1897 the discovery of the electron as a particle. In his
experiments he studied negative cathodrays, i.e. the discharge that occurs in vacuum between two
conductors at different potential. Gradually he understood that the rays were small particles that
carried a certain charge, electrons.
By studying movement of charged particles in electric fields one can obtain important
information about their properties. Thomson managed by such an experiment determine the
quotient of the electrons charge and mass.
Theory
The mass me of the electron is hard to come by experimentally. It is easier to determine the
specific charge ε of the electron:
ε=
e
me
(1)
From which the mass me can be calculated if the elementary charge e is known.
2
In this experiment the electrons are accelerated by a potential U into a homogenous magnetic
field B perpendicular to the electron velocity. The electron is then forced into a circular orbit by
the Lorentz force and the centripetal force. The situation is described by Fig.1.
Fig.1 Deflection of electrons in a magnetic field B by the Lorentz force F into a circular orbit of
a given radius r.
Step 1:
Derive a theoretical expression for the relation between the electron charge and mass as a
function of the acceleration potential U, the magnetic field B and the circular orbit radius r. Fill in
the deliberately omitted gaps in the remaining theory chapter.
Assume that the electrons are moving at a constant velocity v. The Lorentz force, acting on the
electron moving at velocity v perpendicular to a homogenous magnetic field B, is perpendicular
to both the velocity and magnetic field and has the size:
F=
(2)
For circular movement the centripetal force is:
Fcp =
(3)
In the experiment the electrons are accelerated in a vacuum tube by the potential U. By using
energy conservation the final velocity of the electrons can be determined.
v=
(4)
By combining equations (2), (3) and (4) the electron specific charge is expressed as:
ε=
(5)
The vacuum tube contains argon atoms at low pressure, which through collisions with electrons
are caused to emit light in the visible wavelength region. This makes the orbit of the electrons
indirectly visible and their orbiting radius r can be directly measured.
Direct measurement of the magnetic field with gauss meter is associated with accuracy problem.
Because of that it is interesting to find some simple method to measure the magnetic field.
3
Step 2:
Calculate the magnetic field, generated by two identical Helmholtz coils placed as in Fig.2, as a
function of the current flowing through the coils.
Fig.2 Two parallell Helmholtz coils at distance 2a
Assume that the coils have the radius R, current I, number of turns n (each coil) and are
separated by the distance equal to the radius (a=R/2). Biot-Savarts law gives the magnetic field in
the point a=R/2 on z-axis.
B(z=
R
)=
2
(6)
Near the z-axis in the plane z=a, which is the region where the electron beam is situated, the
magnetic field is nearly homogenous.
By combining equations (5) and (6) the electron specific charge is expressed as.
ε=
e
=
me
(7)
From (6) it appears that the magnetic field is proportional to the current through the Helmholtz
coils. The proportionality constant can be calculated from the radius of the coils R=200mm and
the number of turns n=154 (each coil).
4
Scope of Supply, Description, Technical Data
3
1
2
Fig.3 Apparatus used for quantitative investigations of electron beams in electrical and magnetic
fields, and for determining the specific electron charge e/me and the electron velocity.
1. Vacuum tube
Diameter: ~ 170 mm
Gas filling: argon, gas pressure: ~0,1 Pa
Cathode, upphettning:
6.3 V AC,
max +300 V DC
Anode voltage UA:
2. Holder for supporting the vacuum tube and the coils in a defined position.
3. Pair of Helmholtz coils
Number of turns:
Max current:
Resistans:
Radius:
Distance between coils:
n: 154 (each coil)
Is: 5A
2,1 Ω (each coil)
200 mm
200 mm
To avoid the earth magnetic field to influence the results, the equipment should be arranged so
that the magnetic field from the Helmholtz coils is perpendicular to the earth magnetic field (i.e.
Helmholtz field directed in east-west direction)
5
Carrying Out the Experiment
+250
a
d
-50 b
c
Fig.4 Connection plate ( End of vacuum tube )
a. Anode
b. Cathode
c. Cathode heating
d. Grid
Fig.5 Connection for Helmholtz coils.
- Connect the power supply ( PHYWE DC-Constanter) according to Fig.4. Start Powersupply.
Wait for 2-3 minutes to get a stabilized heating of the cathode.
- Set the grid voltage to 30-50V (to get a well-collimated electron beam). Set the total
acceleration voltage to 100 V and increase the total acceleration voltage in steps of 20V up to
300 V.
- Set the DC power supply of the Helmholtz coils to a current I, at which the electron beam is
deflected into a closed orbit.
6
- If the electrons do not move on a closed orbit but on a helical curve line, the magnetic field is
not completely perpendicular to the velocity of the electrons. Discuss the adjustment procedure
with your instructor. Notify that the equipment may need to be adjusted when the acceleration
voltage is changed.
- Set the DC power supply of the Helmholtz coils to a current I, at which the electron beam orbit
hits the fluorescent pin at radius r=4,0 cm or r=5,0 cm.
- Write down the acceleration voltage (UA) and the currrent (IS ) through the coils.
r=4,0 cm
UA /V
IS
r=5,0 cm
e/me
100
120
140
160
180
200
220
240
260
280
300
Fig.6 Table of measurement results
Evaluate your results.
GOOD LUCK !
7
IS
e/me