Following selection rules for multi-electron atoms, imagine a ...

[neverstopbelieb]

Following selection rules for multi-electron atoms, imagine a titanium atom in the ground state with two electrons in each of the 3d and 4s shells. In the 3d shell, which of the following scenarios is least likely to be true?
  a. The electrons orbital angular momentum is aligned.
  b. The electrons' spins are antialigned to minimize energy.
  c. The spin and angular momentum of the electrons are aligned to minimize energy.
  d. The energy levels of the electrons are split due to LS coupling.
  e. The magnetic quantum numbers of the electrons are either both positive or both negative.

Question 2

Which of the following statements is true about the spin-orbit coupling effects on the transitions of an atom such as sodium? Assume sodium is modeled by a single electron atom.
 

a.The difference in the energy of a split state does not depend on the electron's angular momentum, but instead the angular momentum of the nucleus.
  b. The differences in energy level transitions are significant enough to change the order of filling of the subshells.
  c.Electrons with a state of l = 0 never have split energy levels.
  d. For single electron atoms (or atoms with one electron outside a filled shell) each nl state is made a doublet.

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Answer to Question 1

b.
By Hund's rules the 3d shell fills first to maximize S. Since the value of S would be at a maximum for aligned spins of the two electrons and zero for antialigned spins, the answer is not likely to be true.

Answer to Question 2

c.
Electrons in the states with lowest angular momentum cannot have split energy levels because the spin-orbit coupling that splits the energies depends on j, which is determined by j = l  s. If l = 0, however, j = 1/2 for single electron atoms. The electron has only one energy level.

[neverstopbelieb]

TYSM

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