24
2.
THE MASS OF THE ELECTRON
2—3.—The Method of Lenard.—As in gure 2—3, electrons from
a
suitable source such as the hot lament F, in a vacuum, are
-
accelerated toward a positively charged metal plate P, by means
of a known potential. Let the - accelerating potential be V…
electromagnetic units. Then V… is the number of ergs of work
done upon one electro-magnetic unit of charge in moving it from
the lament to the plate
* and V…e is the corresponding work done
upon
each electron.
This appears
in the form of kinetic energy,
so that the electrons which pass through a hole in the plate have a
velocity ?) and an energy mzP/ 2. Thus
V…e :_ 108V6 = %m02,
(2—6)
where 17 is the accelerating potential in volts and 6 is measured in '
e.m.u.
The electrons, which would normally travel straight
ahead to produce a spot of light at 8 on a uorescent screen, are
bent by a magnetic eld into a circular path of radius r and reach
the screen at S'.
Lenard applied the eld over the entire path of
the electrons.
In gure 2—3, the lines of force (H per square
centimeter) are at right angles to the paper and cover the entire
region indicated by the large circle. As in the Thomson method,
the magnetic and centrifugal forces are equal, so that, again
.
'
H€U = mvZ/r.
-
(2—1)
Together with equation (2—6), this gives
'
.
2V108
v = — cm.
sec.
2—7
/
<
>
and”
“
'
_
<
27108
,
.
,
‘
'
e/m =
(2—8)
'
in which V is in volts, H is in oersteds and r _is in centimeters. In
order to determine 7 from the observed deection of the spot of
light, we note, ingure 2—3 that 72 = L2 + (r —
or
_
_
1
"
r =
(L2 + D2)/2D.
-
‘
(2—9)
'
_
*_ This assumes that every point on the lament is at the same potential and
,
that the
electrons havezero velOcit-‘ÿ as they leave the lament. Corrections for
'
dep’artures from_the ideal conditions assumed need not be made eXcept for precise
worker
when the accelerating potential, V
,
is comparatively small.