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Unformatted text preview: Homework 1 1. Problem: Streetman, Sixth Ed., Problem 2.2: Show that the third Bohr postulate, Eq. (2-5) (that is, that the angular momentum p around the polar axis is an integer multiple of the reduced Planck constant h , so p = n h ) is equivalent to an integer number of de Broglie waves fitting within the circumference a Bohr circular the orbit. Solution: (a) The easy way : Lets write the electron angular momentum along the z axis, L as: L = mr 2 = mr , (1) where m is the mass of the electron, r is the radius of the orbit, h is the reduced Planck constant, h = h/ (2 ) , is the magnitude of the electron velocity, and = /r is the angular velocity. Lets write Bohrs postulate as: L = n h . (2) Then, substituting Eq. (1) into Eq. (2): mr = n h = nh 2 . (3) Lets multiply both sides of this equation by 2 / ( m ) : 2 r = nh m . (4) Since deBroglies assumption implies = h/ ( m ) , Eq. (4) is simply 2 r = n , (5) which is what the problem asked. ECE344 Fall 2009 1 (b) The hard way : Lets write the third Bohr postulate as in Eq. (3): mr = n h , (6) Now, as done in class, lets consider the magnitude of the attractive electrostatic force between the electron and the nucleus and set it equal to the magnitude of the centrifugal force so that the electron remains in a stable orbit: e 2 4 r 2 = m 2 r . (7)...
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This note was uploaded on 09/13/2010 for the course ECE ECE344 taught by Professor Polizinni during the Spring '10 term at University of Massachusetts Boston.
- Spring '10