Slater’s rule shielding electron

Slater’s rule shielding electron of an atom

Slater’s set an empirical rule for calculating the shielding constant and effective nuclear charge of an electron in an atom or ion. The electron cloud of different energy orbital is to shield the inner electron to a different extent.

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

Shielding electron cloud of an atom
Shielding

Thus this attractive and repulsive force acting on the valence electrons experience less attraction from the nucleus of an atom.

So 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 or force of attraction between the nucleus and valence electron are known shielding electrons.  And the effect is known as the shielding effect or screening effect.

Shielding and effective nuclear charge

Thus the nuclear charge of an atom or ion less than the actual nuclear charge and easily calculated by the following equation.

Effective nuclear charge
Zeff= Z – σ
where σ = shielding constant

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 electron prevents the attraction of outer orbital electrons of an atom.

Shielding effect of S and P energy level

  • 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.
Slater's rule formula for s and p energy levels
Slater’s rule formula
  • Electrons of higher energy levels did not shield the lower-energy level of an atom.

Thus for calculating the value screening constant of a sodium atom, the electron configuration according to Slater’s rule

(1S)2 (2S, 2P)8 (3S)8

So 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.

Shielding constant and effective nuclear charge

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

σ = (2 × 1) + (8 × 0.85) + (0 × 0.35)
= 8.8

∴ Zeff = (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 1S2 2S2 2P1. But in nitrogen and oxygen shielded by 1S2 2S2 2P2 and 1S2 2S2 2P3 respectively.

∴ Zeff of nitrogen = Zeff of carbon + (1 nuclear charge) – shielding due to one 2P
or, Zeff of nitrogen = Zeff of carbon + 1 – 0.35 = Zeff of carbon + 0.65.

But Zeff of oxygen = Zeff 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 d and f orbitals

Previous rules are quite well for estimating the screening constant of S and P orbitals. But for shielding by d subshell or f subshell the four and five rule replaced by new rules for the estimation of screening or shielding constant 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 of d and f energy level
Shielding effect of d and f orbitals

Shielding effect and effective nuclear charge of vanadium

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 Zeff 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 Zeff for 3d
= (23 – 18.70) = 4.30

Ionization energy and shielding electron

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, the electron of the 4S energy level will be 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 Zeff 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

∴ Zeff 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 cloud is more tightly bound within the nucleus than 4S electron. Thus during the ionization, higher energy level or less tightly bound electron losses first.