198
THEORY OF
LIGHT
PRODUCTION
energy
is
needed
for the
photoelectric
diffusion, i.e.,
the smaller the
photoelectric
sensitivity
of
the metal.
So
far
we
have
considered
the
facts without
making
assumptions about
the
nature of photoelectric
diffusion.
However,
the
hypothesis
of
light
quanta
also yields
a
quantitative relationship between
the Volta effect
and
photo
electric diffusion.
Thus, to
move a
negative elementary quantum (charge
e)
from
the metal into the
gas,
it
has to be
supplied
with
at
least
an energy
Ve.
Then,
a
light
species
will
be
able
to
remove
negative
electricity
from
the metal
only when
the
"light
quantum"
of
that
light
species
has at
least the
value
Ve.
We
thus obtain
Ve ^ ^
ßv
or
v
ijßv
,
where
A
denotes the
charge
of
one
grammolecule
of
a
univalent ion.
If
we now
assume
that
some
of the
absorbing
electrons
are
able
to
leave
the
metal
as soon as
the
energy
of
the light
quanta exceeds
Ve1

which
is
a
very
plausible
assumption

we
obtain
v.«ß"
,
where
v
denotes the lowest
photoelectrically
effective
frequency.
Thus,
if
v1
and
v2 are
the lowest light
frequencies
acting
on
the
metals
M1
and
M2,
the
following equation
will hold for the Volta
potential
difference
V12
of the
two
metals:
12 V1v

or,
if
V12
is
measured
in
volts:
V^
=
4.2
x
10"15(^2 ~
•
1The
thermal
energy
of
electrons is
disregarded.