An apparatus is used to prepare an atomic beam by heating a collection of atoms to a temperature T and allowing the beam to emer
ge through a hole of diameter d in one side of the oven. The beam then travels through a straight path of length L. Show that the uncertainty principle causes the diameter of the beam at the end of the path to bt larger than d by an amount of order Lh/d Squareroot 3mkT, where m is the mass of an atom.
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To solve the problem, it is necessary to apply the concepts related to the kinematic equations of the description of angular movement.
The angular velocity can be described as
Where,
Final Angular Velocity
Initial Angular velocity
Angular acceleration
t = time
The relation between the tangential acceleration is given as,
where,
r = radius.
PART A ) Using our values and replacing at the previous equation we have that
Replacing the previous equation with our values we have,
The tangential velocity then would be,
Part B) To find the displacement as a function of angular velocity and angular acceleration regardless of time, we would use the equation
Replacing with our values and re-arrange to find
That is equal in revolution to
The linear displacement of the system is,