## Shielding electrons and Slater’s rule

**Shielding electrons** or **screening electrons** decreasing the attractive force between the valence shell electron and the nucleus of the atom. **Slater’s rule** uses for calculating the shielding or screening constant and effective nuclear charge for the outer orbital electron of an atom or ion in chemistry. A hydrogen atom contains one electron, hence the hydrogen atom has no shielding electron or effect. But valence electrons for multi electron atoms are attracted by the nucleus of the atom and repelled by the electrons from inner-shells. These attractive and repulsive forces acting on the valence electrons experience less attraction from the nucleus of an atom.

### What is shielding in chemistry?

The inner electrons which shield the higher energy electron are called shielding electron that is calculating by Slater’s rule, and the effect is called the shielding effect or screening effect. In learning chemistry, the larger the number of inner or shielding electrons, the lesser will be the attraction between the nucleus and outer orbitals electron. When the number of inner electrons increases, the shielding or screening constant also increases but effective nuclear charge decreases which affects the chemical properties of the atom or molecule of the matter and calculating by Slater’s rule.

## What is effective nuclear charge?

Effective nuclear change means the net positive charge which affects the attraction of outer electron particles from the nucleus of a polyelectronic atom. This term is used because the shielding electrons prevent the attraction of the outer orbital electron of an atom. Therefore, the effective nuclear charge (Z_{eff} ) calculating from Slater’s rule = Z – σ, where σ = shielding or screening constant.

## Slater’s rule for calculating shielding constant

### s or p-orbital electrons of an atom or ion

- First we write the electronic configuration of atom or ion by following order and grouping, (1s) (2s 2p) (3s 3p) (3d) (4s 4p) (4d) (4f) (5s 5p), etc.
- Electrons in a certain ns, np-level are screened only by electrons of the same energy level and by the electrons of lower energy levels. Electrons lying above the energy level do not screen any electron to any extent. Therefore, the higher energy electrons have no screening effect on the lower energy electrons
- Electrons of an (ns np) level shield the valence electron in the same group by 0.35 each. This rule is also true for the electrons of the nd or nf level for electrons in the same group.
- Electrons belonging to one lower quantum shell or (n – 1) shell shield the valence electron by 0.85 each.
- Electrons belonging to (n-2) or still lower quantum energy levels shield the valence electron by 1.0 each.

### Shielding or screening constant of sodium

For calculating the value shielding constant of inner electrons of the sodium atom, the electron configuration according to Slater’s rule, (1s)^{2} (2s, 2p)^{8} (3s)^{1}. Therefore, by using Slater’s rule shielding constant and effective nuclear charge for 3s-electron of sodium atom, σ = (2 × 1) + (8 × 0.85) + (0 × 0.35)

= 8.8. Therefore, Z_{eff} = (11 – 8.8) = 2.2

**Problem:** Calculate the shielding or screening constant for the 2p-electron of carbon and oxygen atom.

**Solution:** Electron configuration of carbon and oxygen according to the Slater’s rule for shielding electrons, (1s)^{2} (2s, 2p)^{4}, and (1s)^{2} (2s, 2p)^{6} respectively. Therefore, the shielding constant for carbon atom = (2 × 0.85) + (4 × 0.35) = 3.10 and oxygen atom = (2 × 0.85) + (6 × 0.35) = 3.80.

## Shielding Constant for d or f-orbital Electron

Slater’s rule for s or p-electron is quite well for estimating the screening constant of s and p-orbital. But Slater’s rule for d or f-orbital electrons the four and five rules replaced by new rules for the estimation of screening or shielding effect and effective nuclear charge. The new rule is all electrons below the nd subshell or nf-subshell contribute 1.0 each towards the screening constant.

### Screening Constant and Z_{eff} for Vanadium

Vanadium has atomic number 23 and the electron configuration according to the Slater’s rules for shielding electrons, (1s)^{2} (2s 2p)^{8} (3s 3p)^{8} (3d)^{3} (4s)^{2}. Therefore, the screening constant for 4s electron = (2 × 1.0) + (8 × 1.0) + (8 × 0.85) + (3 × 0.85) + (1 × 0.35) = 19.7.

Hence the effective nuclear charge (Z_{eff}) for 4s-electron =23 – 19.7 = 3.3. Screening constant for 3d electron = (2 × 1.0) + (8 × 1.0) + (8 × 1.0) + (2 × 0.35) = 18.70. Hence, the effective nuclear charge (Z_{eff}) for 3d electron = (23 – 18.70) = 4.30.

### Screening constant and Z_{eff} for Chromium

Chromium has atomic number 24 and the electron configuration according to Slater’s rule for shielding electrons, (1s)^{2} (2s 2p)^{8} (3s 3p)^{8} (3d)^{5} (4s)^{1}. The screening constant for 4s = (2 × 1.0) + (8 × 1.0) + (8 × 0.85) + (5 × 0.85) + (0 × 0.35) = 21.05.

Hence Z_{eff} for 4s-electron = (24 – 21.05) = 2.95. But the screening constant for 3d-electron = (2×1.0) + (8 × 1.0) + (8 × 1.0) + (3 × 0.85) + (4 × 0.35) = 19.40 and Zeff = (24 – 19.40) = 4.60

## Shielding effect and ionization energy

The larger the number of electrons in the inner shell, the lesser the attractive force holding the valence electron to the nucleus, and the lower will be the value of ionization energy. When we move down in the group of the periodic table, the number of shielding electrons increases, and the effective nuclear charge for valence electron calculate from Slater’s rule decreases, and hence the ionization trends also decrease. Therefore, the ionization trends and shielding or screening effect for the group-2 chemical elements, beryllium > magnesium > calcium > strontium > barium. Hence the formation of ionic bonding or polarity trends also increases from Be to Ba.