34
2.
THE MASS OF THE ELECTRON
Now, equation 2—1 may
be written in the form Heat = mv/r
or
vt/r
: He/m.
But v,;/r is equal to the angular velocity œ of
the electrons in the circles.
Then, if T is the time for an electron
to make one complete rotation,
_
27r
27r
œ—T—He/m
or
T_H6/m
(221)
It is to be noted that the angular velocity œ is independent of the
radii of the circles.
Thus the electrons travel faster in the larger
and slower in the smaller circles.
All electrons require the same
time T to complete one revolution, regardless of the size of the
circle.
When, for a given accelerating voltage, the magnetic eld is
varied until the time T for the electrons to make one rotation is
equal to the time Z for them to travel forward from the condenser
‘
plates to the screen, a distance [, all electrons Will again be on the
axis.
This condition may be detected by observing the line of
°
light on the screen. As the magnetic eld is increased from zero,
the line shortens and rotates until, at a critical eld strength H.,
it is reduced to a small spot on the screen.
With stronger elds
than HC, the electrons make more than one complete revolution
While travelling down the tube. For one revolution, equating
equations 2—20 and 2—21 to each other gives
87r2V108
e/m =
——Ëc—2—l—2—
e.m.u./g.
(2—22)
Here, V is the accelerating potential in volts, He is the critical
magnetic eld strength in oersteds and [ is the distance in centimeters indicated in gure 2—7.
This method is an extension of that used by Busch.13
Instead
of adding a transverse motion to the forward motion of the elec—
trons down the tube, however, his longitudinal magnetic eld
acted upon the perpendicular campanem‘ of the motion of a hollow
cone of electrons diverging from a cold discharge tube.
When the
electrons are focussed in the Busch method, the electron charge—
to—mass ratio is given by
_
87r2V108
2
€/m —
—_HÇZZZ
cos
[?
(2—23)
2.
THE MASS OF THE ELECTRON
Now, equation 2—1 may
be written in the form Heat = mv/r
or
vt/r
: He/m.
But v,;/r is equal to the angular velocity œ of
the electrons in the circles.
Then, if T is the time for an electron
to make one complete rotation,
_
27r
27r
œ—T—He/m
or
T_H6/m
(221)
It is to be noted that the angular velocity œ is independent of the
radii of the circles.
Thus the electrons travel faster in the larger
and slower in the smaller circles.
All electrons require the same
time T to complete one revolution, regardless of the size of the
circle.
When, for a given accelerating voltage, the magnetic eld is
varied until the time T for the electrons to make one rotation is
equal to the time Z for them to travel forward from the condenser
‘
plates to the screen, a distance [, all electrons Will again be on the
axis.
This condition may be detected by observing the line of
°
light on the screen. As the magnetic eld is increased from zero,
the line shortens and rotates until, at a critical eld strength H.,
it is reduced to a small spot on the screen.
With stronger elds
than HC, the electrons make more than one complete revolution
While travelling down the tube. For one revolution, equating
equations 2—20 and 2—21 to each other gives
87r2V108
e/m =
——Ëc—2—l—2—
e.m.u./g.
(2—22)
Here, V is the accelerating potential in volts, He is the critical
magnetic eld strength in oersteds and [ is the distance in centimeters indicated in gure 2—7.
This method is an extension of that used by Busch.13
Instead
of adding a transverse motion to the forward motion of the elec—
trons down the tube, however, his longitudinal magnetic eld
acted upon the perpendicular campanem‘ of the motion of a hollow
cone of electrons diverging from a cold discharge tube.
When the
electrons are focussed in the Busch method, the electron charge—
to—mass ratio is given by
_
87r2V108
2
€/m —
—_HÇZZZ
cos
[?
(2—23)