Physical Chemistry III
- Structure of Matter -

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
En = −µ/2(Ze²/4pe o h)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:

Y100(r,J,j) = R10(r) Y00(J,j) = 1/Ö(πao³)· e−r/ao

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

<r> = oò2πoòpoò¥ |y100|² r dτ

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

oò¥ x³ e-bx dx = 6/b4

Problem 3

1. The Chlorine atom exhibits a ²PJ 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 cSL.
2. Determine the constant cSL for bromine (ΔE = 3685.24 cm-1)?