D O C U M E N T 3 0 8 N O V E M B E R 1 9 2 1 1 9 3
this summer. I haven’t been able to do any reasonable work of late; but now I do
understand a little more about perturbation theory and have a vague concept of
what
Bohr[7]
is actually doing. I am also systematically pursuing my work on crys-
tals; a few papers from the summer appeared a short time ago in the Z[eitschrift]
f[ür]
Phys[ik].[8]
– I would like to know what you think of Polányi’s research on
reaction
rates;[9]
he contends that they cannot be understood without a strange kind
of energy transfer (transmission of energy quanta from one molecule to another
without there being any mechanical interaction between them, just simply, hop!,
through space). Franck and I do not believe it. Just recently
Langmuir[10]
was here;
he asserts something similar; but we still don’t believe a bit of it. Langmuir
appealed to us very much, by the way; he knows a lot about physics. Polányi’s
paper on tensile strength is also
crazy;[11]
and yet there must be something to it.
How much we would like to discuss it with you sometime! A student of mine (a
nephew of Minkowski, of the same
name[12]
) is now doing an exact theory for
streams of slow electrons (velocity under smallest h ) in gases; it sets out from the
following idea by Franck: In extreme vacuum the “space-charge law” for current is
valid as a function of voltage (I think J ~
V3/2);
if one now adds a little more gas,
back-and-forth reflections of the electrons occur, thereby the “space charge” is
raised somewhat and the J-V law is altered. Out of this alteration the electrons’ free
length of path in the gas must be calculable according to existing theory; this is of
interest because of Ramsauer’s sheer crazy assertion (in Jena) that the lengths of
path in argon electrons approach infinity as the velocity falls (slow electrons fly
freely through the
atoms!).[13]
This we would very much like to refute. My theoret-
ical idea is this: I start from the Maxwell-Boltzmann collision
equation:[14]
Normally the integral of this is taken such that to 1st approximation the left-hand
side is set equal to zero and the integral is made zero through Maxwell’s distribu-
tion function, then this second distribution to 2nd approximation is put in on the
left-hand side, etc. I, however, proceed in the opposite manner: 1st approximation,
negligence of all collisions, hence “spatial charge distribution” (one also has to set
and add the 2nd equation Fd d ); 2nd approximation
taking one collision into account, etc.
The thing seems to work very well. Minkowski wants to conduct experiments
together with Miss Sponer;[15] but they are surely very difficult.[16]
F
t
------
F
x
------
X
m
--- -------
F
+ + + + + + collision integral. =
X
x
------ – = –e =