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SECTIONAL TRANSACTIONS.—B. 365 
Prof. P. Dssys.—tInierferometric Measurements of Atomic Distances 
in Free Molecules. 
Interferometric measurements of atomic distances in single free molecules are 
possible because even a random orientation of the molecules, as it occurs in gases, 
cannot completely obliterate the intensity fluctuations in the angular distribution of 
the scattered radiation, which would have to be called self-evident in the case of a 
single molecule of definite orientation. 
Now in many cases this special interference effect has been found experimentally 
with X-rays and also with cathode rays. In the very beginning it was considered 
sufficient to register the angles for which intensity maxima or minima occurred and 
to derive the atomic distances from the comparison of the experimental result with 
a theoretical intensity curve which had been calculated assuming the atoms to act 
as scattering points. Soon it became evident that as the electrons of every atom 
are distributed over a region with dimensions comparable with the wave-length of 
the primary radiation, the interference effect of the scattered wavelets coming from 
different points of every single atom had to be taken in account. This was done by 
the introduction of an atom form factor, as it is used in discussing the intensity of 
the X-ray reflection by crystals. From an experimental point of view this presupposes 
the observation of the total intensity curve for the angular distribution. Itis certainly 
not sufficient to examine simply the photographic film obtained, which by a well-known 
physiological effect gives the impression of maxima and minima even if only slight 
fluctuations in the blackening exist. In comparing the experimental intensity curve 
with the theoretical curve obtained after the correction for the electron distribution 
in the atom, e.g. the distance Cl—Clin the CCl, molecule could be determined to 2,99 A 
with an error of +1 per cent. But even so the correspondence between the experi- 
mental and the theoretical curve is not perfect. In general the experiment gives— 
(a) More radiation for large angles than is theoretically calculated ; and 
(b) The difference in intensity between succeeding maxima and minima is less 
than predicted. 
During the last year these differences have been considered and explained. 
(a) The scattering of X-rays by an atom does not only give coherent radiation 
of the same wave-length, but also a certain amount of incoherent radiation with 
changed wave-length (Compton-Effect). The incoherent radiations fronr different 
atoms of the molecule cannot interfere. Whereas the coherent radiation sets in for 
the angle zero between the primary and the secondary ray with an intensity 
proportional to the square of the number of electrons contained in the atom and falls 
off with increasing angle, the incoherent radiation starts with the intensity zero, it 
increases with increasing angle, and ultimately can reach an intensity proportional 
only to the number of electrons. A few months ago the calculation of the angular 
distribution of the incoherent radiation was only possible starting with the knowledge 
of the density distribution for every single electron. Shortly, however, Heisenberg 
succeeded in giving a general and simple formula for this radiation, which, as in the 
case of the atom form factor for the coherent radiation, enables us to derive its angular 
distribution from one single curve valid for all atoms. 
(6) So far the atoms in the molecule had been considered as rigidly connected to 
each other. We know, however, e.g. from the evidence of specific heat measurements, 
that vibrations exist, and therefore the distances between two atoms are only constant 
in the average. It is possible to calculate the effect of the vibration on the angular 
distribution of the scattered intensity, and it is seen that it lessens the difference in 
intensity between maxima and minima. In this way the experimental intensity 
curye also gives evidence of the average amplitude of the atomic vibrations, and 
leads e.g. for CCl, to an amplitude of approximately 0-2 A, that is 6 per cent. of the 
distance CI—Cl. Moreover, we know, e.g. from experiments on the Raman-Effect of 
CCL, the frequency of the vibrations. It can be shown, by comparing their energy 
quantum with the classical value for their energy at the temperature for which the 
experiments are carried out, that a considerable part of the vibration has to be 
considered as due to zero-point energy, which even at the absolute zero-point of the 
_ temperature would still exist. 
It may be said now that the scattering curves can be explained in detail. Results 
for special molecules like CO., CS, to illustrate the effect of the differences in electronic 
density in different atoms ; CCl,, CHCl,, CHCl, CH,Cl to illustrate the distortion in 
