Question

How do you find effective nuclear charge in each shell of an atom? (general chem)

Answer 1

Following Slater's rules:

1. Group electrons in increasing quantum numbers.

2. Electrons in groups to the right do not shield electrons to their left.

3. Determine the shielding constant, S, for each valence electron following these rules (for s and p electrons):
   a. Each electron in the same group contributes 0.35, except 1s electrons, which contribute 0.3.
   b. Each electron in the n-1 energy level contribute 0.85 to S.
   c. Each electron in the n-2 or lower contributes 1.00 to S.

4. For d and f electrons:
   a. Each electron in the same group contributes 0.35.
   b. Each electron in groups to the left contributes 1.00.

`Z_(eff) = n_(protons) -S`

Si: `(1s^2)(2s^2,2p^6)(3s^2,3p^2)`
Level 1: S=2*0.3=0.6
Z=14-0.6=13.4

Level 2: S=20.85+0.356=3.8
Z=14-3.8=10.2

Level 3: S=21.00+60.85+4*0.35=8.5
Z=14-8.5=5.5

C: `(1s^2)(2s^2,2p^2)`
Level 1: S=2*0.3=0.6
Z=6-0.6=5.4

Level 2: S=20.85+0.354=3.1
Z=6-3.1=2.9

Level 3: S=21.00+40.85=5.4
Z=6-5.4=0.6

F: `(1s^2)(2s^2,2p^5)`
Level 1: S=2*0.3=0.6
Z=9-0.6=8.4

Level 2: S= 20.85+0.357=4.15
Z=9-4.15=4.85

Level 3: S= 21.00+0.857=7.95
Z=9-7.95=1.05