Slater's Rule
What is Slater's Rule and its significance?
How to calculate value of σ and Zeff using Slater'
Rule:
Slater's Rule:
Slater’s rules are a set of
empirical guidelines used to calculate the shielding constant (σ) and
the effective nuclear charge (Zeff) experienced by an electron in a
multi-electron atom.
They were introduced by John C.
Slater to simplify the complex quantum mechanical interactions between
electrons. These rules estimate how much the inner electrons reduce the
attractive force of the nucleus on outer electrons.
Mathematically:
Zeff=Z−S
where: Z = atomic number (total
nuclear charge)
S = shielding constant (calculated using Slater’s rules
Significance of Slater's Rule:
- To quantify shielding in multi-electron atoms.
- To provide a systematic method for calculating
effective nuclear charge without solving complex quantum equations.
- To make predictions about electron behavior in
different orbitals.
How to calculate value of σ and Zeff using Slater'
Rule:
1. Write down the complete electronic configuration of the
element and divide the electrons into the following orbital groups starting
from the inside of the atom.(1s),(2s) (2p) (3s,3p) (3d) (4s, 4f) (4d) (4f)
(5s,5p) (6s,6p) etc.
2. Now select the electron for which the value of σ is
to be calculated. For this calculation add up the contributions to σ for
the other electrons according to the following rules.
Types of electronic contribution
to σ for each electron of this type.
(i) All the electrons in
groups outside the electron chosen.
0
(ii) All the electrons in the
same group as chosen one.
0.35 or 0.30 for 1s electron
(iii) All electrons in shell
immediately outside.
0.85
(iv) All electrons further
inside.
1.00
(v) There will be no contribution to
the value of σ by electrons residing
in the orbitals having higher values
of their principal quantum number
than the orbital containing the
electron for which σ is being calculated.
Thus σ for an
electron residing in ns or np orbital = 0.35×(Number of remaining electrons in
ns or np orbital)+0.85(Number of electrons in (n-1)th shell+1.0(Number of
electrons in the inner shell)
Now, let's solve a problem following following Slater's
Rule
Q:Why
is 4s orbital filled earlier than 3d orbitals in potassium atom (Z = 19)?
We know that configuration of Ar (Z
= 18) is 1s2 2s22p6 3s23p6 . Thus 3rd shell is not completely filled in Ar
atom, since 3d orbitals remain vacant in it. After 3p orbitals have been filled
completely in Ar, the 19th electron in K(Z = 19) does not enter 3d orbitals;
rather it goes to 4s orbital.The reason can be explained as follows:
(a) K(Z = 19)
= 1s2 2s2 2p6 3s2 3p6 4s1
σ
= 0.35× 0+0.85×8+1.0×10=16.8 Zeff = 19-16.8=2.20
(b) K(Z = 19)
= 1s2 2s2 2p6 3s2 3p6 3d1
σ = 0.35×0+1.0×18=
18
Zeff = 19-18=1.0
The value of Zeff experienced by 4s1electron
of K-atom in (a) is equal to 2.20. The value of Zeff experienced
by 3d electron of K-atom in (b) is 1.0. Since the Zeff for 4s1 electron
is greater than that for 3d1 electron, teh attraction between 4s1 electeron and
nucleus is greater than between 3d1 electron and nucleus of K-atom.Thus
configuration (a) would be more stable than configuration (b). In other words
4s orbital is filled earlier than 3d orbital.
Let us consider the formation of Mn+ ion from Mn(Z = 25).
Mn(Z =25)= 1s2 2s2 2p6 3s2 3p6 3d5 4s2
Zeff experienced by 4s1 electron in this atom is equal to 3.60 while Zeff
for 3d1 electron is 5.60. Thus the removal of electron from 4s orbital is
easier than from 3d orbital.
For electron in 4s orbital:
σ
= 0.35× 1+0.85×13+1.0×10=21.4 Zeff
= 25-21.4=3.60
For electron in 3d orbital:
σ = 0.35× 4+1.0×18=19.4 Zeff = 25-19.4=5.60
Comments
Post a Comment