## Shielding Effect of Inner Electrons

Slater’s set an empirical rule for calculating the **shielding** effect and effective nuclear charge of an electron in an atom or ion. The electron of different energy orbital shielding by inner electrons. Therefore Slater rule uses to calculating the shielding or screening effect for inner electrons.

The valence electrons for a multi-electron atom attracted by the nucleus of an atom and repelled by the electrons from inner-shells.

Therefore this attractive and repulsive force acting on the valence electrons experience less attraction from the nucleus of an atom. Hence larger the number of inner electrons, the lesser the attraction between the nucleus and outer electrons.

The inner electrons which shield the higher energy electron are known as **shielding electron**. And the effect is known as the **shielding effect** or screening effect.

### Effective nuclear charge atoms and ions

When the nuclear charge of an atom or ion less than the actual nuclear charge, we can easily calculate Z_{eff} by the following equation.

Effective nuclear charge

Z_{eff}= Z – σ

where σ = shielding constant

Thus the effective nuclear change means the net positive charge which affects the attraction of outer electrons from the nucleus of polyelectronic atom.

This term used because the **shielding electrons** prevent the attraction of outer orbital electrons of an atom.

### Slater’s rule for calculating shielding constant

#### For s and p electron orbitals

- First, we write the electron configuration of elements of the atom or ion in the following order and grouping.

(1S) (2S, 2P) (3S, 3P) (3d) (4S, 4P) (4d) (4f) (5S, 5P) etc.

- The shielding effect concerned the nS and nP electron belonging to the same energy level have the same effect advocated by
**Slater’s rule**.

(1S)^{2} (2S, 2P)^{8} (3S)^{1}

- Electron in a certain nS, nP level screened only by electrons at the same energy level and by the electrons of lower energy levels of an atom, or ion.

- Electrons of higher energy levels did not shield the lower-energy level.

Therefore for calculating the value shielding effect of inner electrons of sodium, the electron configuration according to Slater’s rule

(1S)^{2} (2S, 2P)^{8} (3S)^{8}

Hence the value of the shielding constant for the 3P-electrons, the valence electron, or 3S electron will be excluded from our calculation.

- Electrons lying nS and nP atomic level shield a valence electron in the same group by 0.35 each. This rule also true for the electrons of the nd or nf atomic level of atom or ion.
- But the electrons belonging to one lower energy level shield the valence electron by 0.85 each.
- Electrons belonging to (n-2) or still lower quantum energy level shield the valence electron by 1.0 each.

### Slater’s rule for sodium

Using Slater’s rule shielding constant and effective nuclear charge of sodium

σ = (2 × 1) + (8 × 0.85) + (0 × 0.35)

= 8.8

∴ Z_{eff} = (11 – 8.8) = 2.2

Question

Comment on the variation in effective nuclear charge for a 2P electron from carbon to oxygen.

Answer

Electron configuration according to the Slater’s rule

Carbon: (1S)^{2} (2S, 2P)^{4}

Nitrogen: (1S)^{2} (2S, 2P)^{5}

Oxygen: (1S)^{2} (2S, 2P)^{6}

In carbon atom, the 2P orbital shield by 1S^{2} 2S^{2} 2P^{1}. But in nitrogen and oxygen shielded by 1S^{2} 2S^{2} 2P^{2} and 1S^{2} 2S^{2} 2P^{3} respectively.

∴ Z_{eff} of nitrogen = Z_{eff} of carbon + (1 nuclear charge) – shielding due to one 2P

or, Z_{eff} of nitrogen = Z_{eff} of carbon + 1 – 0.35 = Z_{eff} of carbon + 0.65.

But Z_{eff} of oxygen = Z_{eff} of nitrogen + 0.65

Thus the effective nuclear charge will go up by the same amount from carbon to nitrogen and then to oxygen.

### Shielding effect of inner d and f electrons

Previous rules are quite well for estimating the screening constant of S and P orbitals. But for inner shielding electrons of d subshell or f subshell the four and five rule replaced by new rules for the estimation of screening or shielding effect and effective nuclear charge. New rule is

- All electrons below the nd subshell or nf-subshell contribute 1.0 each towards the screening constant.

### Shielding effect and Z_{eff} for vanadium electron

Vanadium has atomic number 23 and the electron configuration according to the Slater’s rules

(1S)^{2} (2S, 2P)^{8} (3S, 3P)^{8} (3d)^{3} (4S)^{2}

∴ Shielding constant for 4S

= (2×1.0)+(8×1.0)+(8×0.85)+(3×0.85)+(1×0.35)

= 19.7

Thus the Z_{eff} for 4S

=23 – 19.7 = 3.3

Shielding constant for 3d

= (2×1.0)+(8×1.0)+(8×1.0)+(2 ×0.35)

= 18.70

Thus Z_{eff} for 3d

= (23 – 18.70) = 4.30

### Ionization energy and electron shielding

In the first transition series electron filling up process begins in the 3d energy level below a filled 4S energy level. But during the ionization process, 4s energy level electron lost first.

We can explain this with the reference of chromium. Chromium has atomic number 24 and the electron configuration according to slater’s rule

(1S)^{2} (2S, 2P)^{8} (3S, 3P)^{8} (3d)^{5} (4S)^{1}

∴ Shielding constant for 4S

= (2×1.0)+(8×1.0)+(8×0.85)+(5×0.85)+(0×0.35)

= 21.05

Thus Z_{eff} for 4S

= (24 – 21.05) = 2.95

But the screening constant for 3d

= (2×1.0)+(8×1.0)+(8×1.0)+(3×0.85)+(4×0.35)

= 19.40

∴ Z_{eff} for 3d

= (24 – 19.40) = 4.60

The shielding constant of 3d electron lower than the 4S electron but the affective nuclear change in reverse trend.

Thus 3d electron is more tightly bound within the nucleus than 4S electron. Thus during the ionization, outer energy electron loses rather than shielding electron.