Very
small particles, called grains, exist in interstellar space. They are
continually bombarded by hydrogen atoms of the surrounding
interstellar gas. As a result of these collisions, the grains execute
Brownian movement in both translation and rotation. We may assume
that the grains are uniform spheres of diameter
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Solution: Click For PDF Version Data of the problem are
diameter of
each grain
density of
grains is
Therefore,
mass of a grain,
As the grains are immersed in interstellar gas at temperature 100 K, they will undergo Brownian motion because of random collisions of the hydrogen molecules of the gas. The average translational kinetic energy of a grain at temperature T will become
And, the average rotational energy of each grain, assuming that it can be considered as a rigid sphere of diameter d, will be
where the rotational inertia I is
and
(a)
We calculate
(b)
We calculate
angular speed
We have
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and density
,
and that the temperature of the gas is 100 K.
we have to find (a) the
root means square speed of the grains between collisions
and (b) the
approximate rate (
)
at which the grains are spinning.
.
is the angular speed of rotation of a grain.
of the grains using
