Question

Determine the atomic term symbols for the first excited state of the above atoms lithium to neon ( 3 < Z < 10).

Answer 1

The atomic term symbol is a description of angular momentum quantum numbers in a multi-electron atom. The general formula for the term symbols is ^2s+1 L_{J ;}

S= total spin quantum number,

2S+1= Spin multiplicity

J = Total angular quantum numbers

L= Orbital quantum numbers

Term symbols for Lithium (Z=3):

The electronic configuration of Li is 1s²2s¹ and its term symbol is same as hydrogen that is ²S _1/2.

Term symbols for Beryllium (Z=4):

The electronic configuration of Be is 1s²2s² and its term symbol is same as helium that is ¹S _0.

Term symbols for Boron (Z=5):

The electronic configuration of B is1s²2s²2p ¹

Consider p orbital, whee l=1, L=1, s=1/2 hence, 2s+1=2, J=3/2 or 1/2. Therefore term symbol for boron is ² P_3/2 or ²P_1/2.

Term symbols for Carbon (Z=6):

The electronic configuration of B is1s²2s²2p^2. We consider only P electrons. therefore, l=1, hence m_l = +1, 0, -1, L= 2,1,0 for D, P, and S term respectively. Here, two electrons spin parallell to each other, thus, S=0, therefore 2S+1 = 1, J=3,2, 1, 0. Hence the term symbol for carbon is ¹D₂, ³P₂, ³P₁, ³P₀ and ¹S_0.   

Similarly for nitrogen the electronic configuration is 1s²2s²2p³ and its term symbol is ⁴S, ²P and ²D. The electronic configuration for oxygen is 1s²2s²2p⁴ . Here, consider that oxygen has 2P⁶ in the last orbit plus 2 positrons which forces them to take 2 electrons. Positrons differ in electron only in charge.Hence, the term arise form the np⁴ and np² configuration is almost same and np⁵ is similar to np¹.