CHEMISTRY 562 – Fall 2013 PROBLEM SET 5 – October 11, 2013 Due on Friday, October 18, 2013 Problem 1: Is an electron on average further away from the nucleus when it occupies a 2p orbital in hydrogen than when it occupies a 2s orbital? Justify your conclusions by calculating the average distances. (6 points) Hint: Note that the normalization integral for spherical harmonics is ( ) ( ) 2 * 0 0 sin ml , ml , 1 l l d d Y Y p p ? f ? ? ? ? f ? f = Problem 2: Calculate the form of the Zeeman Effect, which occurs when a homogeneous magnetic field of 4.0 T (40 kG) is applied to a hydrogen atom in which the transition from the 2p-to the 3d-state is monitored. Which transitions are allowed ( l ?m = 0,±1), how many lines can be seen in the absorption spectrum, and what are the spacings of the visible lines? (8 points)