Discussion Fr 1.7.2005  10:30 - 11:15 am lecture hall SN 20.2

Problem Set 10   (angular momentum, rotation, hydrogen atom)
 

Problem 1

For the hydrogen atom and for almost completely ionized atoms with one electron left the energy levels are given by
E_n  =  −^µ/₂(^Ze²/_4peoh)^{² 1}/_n²  with  n=1,2,3,... 

Determine

1. the bond energy of the electron (which is the ionization energy)?
2. the ionization energy of the electron at a D nucleus (instead of a proton)?
3. the ionization energy of  positronium (instead of a proton the nucleus is a positron, i.e. a "positiv charged electron")?
4. the wavelength for a transition  n=1 to n=2 for hydrogen atoms?
5. that wavelength for deuterium atoms?
6. The He⁺ ion should exist abundantly in the sun. You want to demonstrate that He⁺ is formed in an excited state by observing the emission from n=3 to n=2. At which wavelength do you expect the transition and can you really observe the radiation on earth?
    

Problem 2

The eigenfunction of the H atom ground state is given by:

What is the average distance <r> of the electron from the nucleus in units of a_o?
Note: You have to calculate the expectation value of r:

where the volume element is given by  dτ = r² sinθ dr dJ dj.

Problem 3

1. The Chlorine atom exhibits a ²P_J ground state which is splitted into the two levels J=1/2 and J=3/2 (energy difference ΔE = 882.3515 cm^-1) due to spin-orbit interaction. Calculate the spin-orbit interaction constant c_SL.
2. Determine the constant c_SL for bromine  (ΔE = 3685.24 cm^-1)?

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