Answer to Question #285546 in Quantum Mechanics for samir seikh

Question

The quantum numbers of two electrons in a two-valance electron atom are:

n1=6, l1=1, s1=1/2 and

n2=5, l2=1, s2=1/2.

Assuming L-S coupling, find possible spectroscopic terms. Show them in an energy level diagram.

Answer 1

$l_1=l_2=1\\s_1=s_2=\frac{1}{2}$

For

$l_1-l_2<l<l_1+l_2$

l=0,1,2

s=0,1

Case (1)

s=0

l=0,2

l=0 ;s

l=2;D

Multiplicity (m) =2s+1

m=1

s=0,l=0,j=0

s=0,l=2,j=1

Notation

¹S₀,¹D₂

case(2)

l=1 ,P

s=1

Multiplicity (m)= 2s+1=3

J=l+s tol-s

J=0,1,2

Notation

³P_0,1,2

Final notation

¹S₀,¹D₂;³P_0,1,2