Question

find the S,L and values that correspond to the each of the following states
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Answer 1

Answer:

Explanation:

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:

Concepts:

The energy levels of multi-electron atoms

Reasoning:

We use the Pauli exclusion principle and the rules for adding angular momentum to find the allowed terms 2S+1L.

Details of the calculation:

The electronic configuration is (1s)2, (2s)2, 2p.

The 1s and 2s shells are full and have L = 0, S = 0, J = 0.

The one 2p electron determines S, L, and J.

s = ½, l = 1, j = ½, 3/2.

The allowed terms are 2P½ and 2P3/2.

Hund's rule:  The component with the smallest value of J (J = ½) has the lowest energy.

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:

Concepts:

The energy levels of multi-electron atoms, angular momentum coupling, Hund's rules

Reasoning:

We use the Pauli exclusion principle and the rules for adding angular momentum to find the allowed terms 2S+1L.

Details of the calculation:

(a)  Electronic configuration, 1s2 2s2 2p6 3s2 3p1 = [Ne] 3s2 3p1

(b)  We have to only consider the open shell.  L = 1, S = ½.

Possible values for J:  J = ½, J = 3/2.

Ground State: J = ½, (Hund's 3rd  rule),  Term symbol: 2P½

(c)  For the open 2p shell (2p5) we have L = 1, S = ½.

Possible values for J:  J = ½, J = 3/2.

Lowest energy term:  J = 3/2, (Hund's 3rd  rule),  Term symbol: 2P3/2

(d)  Electronic configuration, 1s2 2s2 2p5 3s2 3p1

Possible values for L:  L = 0, 1, 2

(e)  Possible values for S:  S = 0, 1

(f)  1S0 3S1 1P1 3P2,0,1 1D2 3D3,2,1<