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6-HW Solutions

6-HW Solutions - HW#6 Atomic Physics Phys320 Spring...

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HW #6: Atomic Physics Phys320 – Spring 2007 (Reshchikov) p. 1 Homework #6 Due on Monday, Apr 2 Problem 1 For the hydrogen atom in the 2 p state explicitly calculate the probability P(r) r of finding the electron between r = 3.8a o and 4.2a o . Compare your answer with numerical solution by using http://webphysics.davidson.edu/faculty/dmb/hydrogen/default.html. (Section 2). [ ] ( ) ( ) 0 0 0 2 2 210 210 2 210 1.5 0 0 4 2 0 210 1.5 1.5 0 0 0 210 0 0 1.5 0 2 2 ( ) ( ) where 4 and 0.4 ( ) from lecture notes with Z =1 3(2 ) 4 0.1105 ( 4 ) 3(2 ) 0.1105 ( ) 4 0.4 o o r a a a o P r r r R r r r a r a r e R r a a a e R r a a a a P r r a a a = = = = = = = = = 0.078 or 7.8% Numerical integration gives 8%. Problem 2 If a hydrogen atom is in the 5 f state, find the possible j , J, and J z values accounting for the spin-orbit interaction with electron spin s = ½. How many distinguishable energy levels exist with and without an applied external magnetic field? Note that the 5f state indicates n = 5 and l =3 .
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