Question

An apparatus is used to prepare an atomic beam by heating a collection of atoms to a temperature T and allowing the beam to emerge 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.

Answer 1

As shown in the attachment

Step-by-step explanation:

The detailed steps and mathematical assumptions and manipulation is as shown in the attachment.