Question

Hi I need help help with this question. can anybody help?

for Mg and Mg⁺

a) Derive all terms and levels in these two configurations!

b)Find the electric dipole allowed transitions between these levels motivating your answers with for example empirical rules and angular momentum coupling.

c)Discuss the contributions to energy differences between different configurations, terms and levels Why does the two configurations have different energies? Why do terms with different spin have different energies? Why do levels with different J-values have different energies?

Answer 1

(a) Outer shell configuration of Mg is $s^2$ and that of $Mg^+$ is $s^1$ . Term symbols for both are provided in the adjoining picture.
for A sl 1 Eme o refers to s S = 1 (spin meeltipliciter 2 small letter OST 25 + 1 = 2. term symbol is 25. I value (Lts) to (L-8) 0 + 1 So, For 2 - Hence, term symbol 25 / For S2 - IL Eml=0 7 refers to s spin multiplicity, s= 1 et al 25+1=3 J values = (2+8) to (1-3) (0+1) to (0-1) Hence, . term symbols are 3
Hence, there are only one term symbol for both
Mg and Mgt
which respectively are $^3S_1$ and $^2S_{1/2}$ .

(b) Electronic transitions between these two levels is completely forbidden.

According to the spin selection rule any transition that involves a change in the spin multiplicity of the electron is not allowed i.e.
AS=0
. Here
AS = 3 - 2 = 1
(hence, spin forbidden).

The laporte selection rule states that only those transitions are allowed which involve a change in the L value, i.e.
07 IV
. But in this transition both have S term, so
AL=0
.

Also only those transitions are allowed which have
= 0
. In this case
AJ =1-1/2 = 1/2

(c) Those configurations having lower S values are higher in energy and those having higher S values are lower in energy. energy increases as we mmove from S term to higher terms.