.
5—4.
EQUATION
107
of the lament surface, Â is a constant for a given lament, _6 is the
'
base of the Naperian system of logarithms
2.718.
.), T is
the absolute temperature of the lament (= 273 +° C.), @ is the
work function of the lament metalin ergs per electron and le is
Boltzmann’s constant (= R/N =__ 8.315 X,107/6.064 X 1023 =
'
1.371 X 10*16 ergs per degree).
;
‘
'
Theexponenti'al form of equation 5—3 has been tested and
found to be correct over an exceedingly wide range of temperatures.
It is shown graphically in gure 5—5 by the heavy line 01%.
In case the plate voltage is not suiciently
-
A
great to withdraw all emitted electrons from
_
the vicinity of the lament, curves OV result.
'
These space charge limitedcurrents Will be
‘
‘
'
discussed in the next Chapter. Richardson’s
.“
equation deals only with the total or emission
0
T-TeTs_
Î
current to the plate.
,.
FIG- 5—5Plate €ur—
Richardson was the rst to dérive this
rent
tem_
'
law.
He considered the free electr0ns inthe
'.
metal to be suiciently sepaÏrated
other and suici€ntly
small that they could be treated as though they formed a perfect
gas. The Well known kinetic theory laws for a perfect gas passing
through a constrairiing boundarysurface into a complete vacuum
were used. The Fermi—Dirac distribution law had not been dis'
Covered at this time]andñRichdsçÿn
the customary .
_
‘
.Maxwellian law
was applicable to
the electron
.
gas.
the two
laws lies
interpretati0ri of the—constants % and çà. _We have’
_
mthephotoelectricchapterthatd>1s
not the total
_
potential ; barr1eratthe
as _;FRichædàon
“the
"
derenoebetweenthwanthemnerenergÿ of the» électrons—«
_R) Î
.
:‘(5—4)
'
Planksœnstant<6$Sx1@*7ergsecns>Thevalufthe
…
degreessuaredmagreementmthexpementalvaïuesFOI“