Question

the ionization energy for a 1s electron in a silver atom is 2.462 x 10⁶ kJ/mol

Determine an approximate value for Z_eff for the Ag 1s electron. Assume the Bohr model applies to the 1s electron. Z_eff is the apparent nuclear charge experienced by the electrons

How does Z_eff from part a compare to Z for Ag? Rationalize the relative numbers.

Answer 1

Using Slater rules: Shielding constant can be determined (S)

1) Electron configuration for Ag is : [Kr] 4d^10 5s^1

groups of equal screening constant :

or, (1s^2) (2s^2, 2p^6,)(3s^2,3p^6)(3d^10)(4s^2, 4p^6) (4d^10) (4f^0) ( 5s^1,5p^0)

2) Any electron to the right has no contribution to S

3) 5p is in the same group but no electron there ,so its contribution of 0.35 nuclear charge units per electron =0.35*0=0

4)s or p Electrons in n-1 quantum state (5-1=4 ) contributes 0.85 nuclear charge units per electron,and those in n-2 =5-2=3 contributes 1 nuclear charge units per electron.

Contribution from (4s^2, 4p^6) =0.85*8=6.8

Contribution from (3s^2,3p^6)=1*8=8

5) Contribution from d and f electros is 1 nuclear charge units per electron

contributions from 3d and 4d=20*1=20

6)contribution from rest inner electrons=(1s^2) (2s^2, 2p^6,)=1.00*10=10 units

total contribution:=6.8+8+20+10=45.8 =S

Effective nuclear charge=Zeff=Z(actual nuclear charge)-S(shielding constant)

Z=47

Zeff=47-45.8=1.2 units