Question

What spin functions are allowed for the inner pair of electrons (1s²) in the 1s²2s configuration of L_i? What spin functions are allowed for the outer electron (2s) in the same configuration?

Answer 1

Lithium has atomic number, Z = 3

Electronic arrangement is 2,1 and configuration 1s² 2s² in the ground state

According to Pauli’s exclusion principle, ‘no two electrons in atom can have identical set of quantum numbers ‘ ; this emphasizes the fact that an orbital can accommodate maximum two electrons.

On the basis of quantum mechanical model, Linear Combination of Atomic Orbitals is used to arrive the symmetric and antisymmetric functions ( both spatial and spin)   

1

Ψ (r1,r2) = --- [ ψ1s ά ( r1) ψ1s β (r2)] - [ ψ1s ά ( r2) ψ1s β (r1)] for 1s2

√2

For the 2s¹ electron, ψ_2s function is to be used

The quantum numbers are : n       l_n             m_l          s

                              1s²                              1      0             0          + ½

1       0              0 - ½         

                             2s¹ 2       0              0 + ½ or – ½