Multi-electron atoms

Problem:

Give the electronic configuration for the Boron atom (Z = 5).  Then enumerate the allowed term symbols 2S+1LJ for the ground state from the point of view of angular momenta alone.

Solution:

Problem:

Aluminum (Al) is element No. 13 in the periodic table
(a)  Write down the electronic shell configuration of Al.
(b)  Find the total L (orbital angular momentum), total S (spin angular momentum), and J (total angular momentum) for the ground state of the aluminum atom.
(c)  The Al atom is singly ionized by photoionization of the 2p level.
Find the “term symbol” 2S+1LJ  for the open 2p shell, assuming that the ion is in its lowest energy state.
(d)  Couple the orbital angular momentum you found in (b) with the total orbital angular momentum you found in (c).  What possible values of L do you get?
(e)  Couple the total spin angular momentum you found in (b) with the total spin angular momentum you found in (c).  What possible values of S do you get?
(f)  Find all possible term symbols for the Al ion.

Solution:

Problem:

(a)  A configuration is an enumeration of the values of n and l for all electrons of an atom.  Give the ground and the lowest two excited configurations of atomic Helium.
(b)  Give the spectroscopic terms in Russell-Saunders (LS) notation.
[The term specifies the total spin S and the total orbital angular momentum L.]
(c)  Which of the excited states has the shortest radiative lifetime?  Why?

Solution:

Problem:

Among the values of L and S obtained from the general rules for addition of angular momenta are those which correspond to states forbidden by the Pauli principle.  Consider the configuration np2, i.  e.  two electrons with the same principal quantum number n and the same angular momentum quantum number l = 1.
Find the allowed terms 2S+1LJ.

Solution:

Problem:

For the Nitrogen atom (Z = 7) find the three terms in the LS coupling scheme which lie lowest in energy.

Solution:

Problem:

For an atom with 3 valence electrons, find the spectroscopic terms 2S+1L that characterize the system when the electron distribution is:
(a)  (3p) (4p) (5p)
(b)  (3p)2 (4p)
The electrons are specified by (nl).

Solution:

Problem:

If the spin of the electron were (3/2)ħ,what spectroscopic terms 2S+1LJ would exist for the electron configuration (2p)2?

Solution: