that the root mean square variation in the outgoing angle satisfies
where p is the magnitude of the total momentum (set by the initial
kinetic energy of the ball), 
, 
is the uncertainty in the impact parameter and 
is the
uncertainty in the component of the momentum in the same direction,
the direction perpendicular to the ideal incoming direction.
Hints: You may assume that and are
uncorrelated random variables and that 
, so that for
instance 
.
the minimum uncertainty 
consistent
with the HUP. Taking a typical value of 
to be R/2,
the numerical magnitude of this uncertainty in
terms of physical parameters given in the problem.
Figure 2: Detail of a single collision.