PHY-1620: College Physics II Lab 5: Electron Mass
Student’s name: 40 Points
Electron Mass
When a beam of electrons is introduced into a strong magnetic field, the beam’s path may become circular, with radius r. Since the magnetic force causes this circular motion,
.
The electrons achieved their velocity by being accelerated from a cathode by a voltage, V, so the following relationship holds:
.
Combining these equations,
.
For this particular apparatus, the magnetic field is supplied by a large Helmholtz coil, for which the B-field depends on the coil cu
ent and various geometric factors. Combining all these terms yields a single equation for m:
where
I = cu
ent in Helmholtz coil (A),
= radius of beam circular path (m), and
V = accelerating voltage across cathode (V).
The Experiment
The apparatus consists of a cathode electron source and a metal bar with pegs attached. This is all enclosed in a large glass tube, which contains only a small amount of gas at low pressure to make the electron beam visible. The tube, in turn, is immersed in a large magnetic field generated by a Helmholtz coil, and oriented to minimize the effect of the Earth’s natural magnetic field. When the cathode heater is turned on, electrons “boil off” and are accelerated by the voltage within the tube. The beam emerges and is bent by the magnetic field. By adjusting the beam voltage and the cu
ent in the Helmholtz coil, the beam can be made to just hit each of the pegs, which are located at known distances (see diagram below). Electron beam source
Electron beam
Peg 1
Peg 2
Peg 3
Peg 4
Peg 5
Cathode Ray Tube Assembly
The beam radius to reach each peg is:
Peg 1: XXXXXXXXXXm
Peg 2: XXXXXXXXXXm
Peg 3: XXXXXXXXXXm
Peg 4: XXXXXXXXXXm
Peg 5: XXXXXXXXXXm
Find out the mass of electron at different radius by measuring the cu
ent and voltage.
Observation 1:
R1 =
I1 =
V1 =
Find
M1 =
Observation 2:
R2 =
I2 =
V2 =
Find
M2 =
Observation 3:
R3 =
I3 =
V3 =
Find
M3 =
Average of mass (measured value) = (m1+m2+m3)/3
Using the data obtained from the CRT/Helmholtz coil apparatus, determine the mass of the electron and compare it to the accepted value of 9.109 10-31 kg.
QFT
Historically, this experiment was conducted over a decade prior to the Millikan Oil Drop Experiment. If we didn’t know the charge of the electron, then what would be the final result of this Electron Mass experiment?
Find out expression for e/m.
…………………………………………..(3)
By putting V and B expression from 2 and 3 equation find out e/m expression.
(
)
V
I
m
C
kg
2
2
27
3
2
10
844
.
4
-
´
=
qvB
F
mv
F
B
C
=
=
=
2
qV
mv
=
2
2
1
V
B
q
m
2
2
2
=