The atom and the Bohr theory of its structure : $b an elementary presentation — John Shaqi
The atom and the Bohr theory of its structure : $b an elementary presentationHolst, Helge
Science
The atom and the Bohr theory of its structure : $b an elementary presentation
Holst, Helge
Atomic theory
Let us assume that the temperature of a mass of gas is 100° C. at a
certain altitude, and 0° C. one metre lower, _i.e._, the molecules
have different average velocities in the two places. The difference
between the velocities will gradually decrease and disappear on account
of molecular collisions. We might expect this “levelling out” process
or equilibration to proceed very rapidly because of the great velocity
of the molecules, but we must consider the fact that the molecules are
not entirely free in their movements. In reality they will travel but
very short distances before meeting other molecules, and consequently
their directions of motion will change. It is easy to understand that
the difference between the velocities of the molecules of the gas will
not disappear so quickly when the molecules move in zigzag lines with
very short straight stretches. The greater velocity in one part of the
gas will then influence the velocity in the other part only through
many intermediate steps. Gases are therefore poor conductors of heat.
When the molecular velocity of a gas and its conductivity of heat are
known, the average length of the small straight pieces of the zigzag
lines can be calculated—in other words, the length of the _mean free
path_. This length is very short; for oxygen at standard temperature
and pressure it is about one ten-thousandth of a millimetre, or 0·1 μ,
where μ is 0·001 millimetre or one _micron_.
In addition to the velocity of the molecules, the length of the mean
free path depends upon the average distance between the centres of two
neighbouring molecules (in other words, upon the number of molecules
per cubic centimetre) and upon their size. There is difficulty in
defining the size of molecules because, as a rule, each contains
at least two atoms; but it is helpful to consider the molecules,
temporarily, as elastic spheres. Even with this assumption we cannot
yet determine their dimensions from the mean free path, since there
are two unknowns, the dimensions of the molecules and their number
per cubic centimetre. Upon these two quantities depends, however,
also the volume which will contain this number of molecules, if they
are packed closely together. If we assume that we meet such a packing
when the substance is condensed in liquid form, this volume can be
calculated from a knowledge of the ratio between the volume in liquid
form and the volume of the same mass in gaseous form (at 0° C. and
atmospheric pressure). Then from this result and the length of the mean
free path the two unknowns can be determined. Although the assumptions
are imperfect, they serve to give an idea about the dimensions of
the molecules; the results found in this way are of the same order
of magnitude as those derived later by more perfect methods of an
electrical nature.
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