The document discusses the concept of effective nuclear charge. It explains that the actual charge experienced by valence electrons is less than the true nuclear charge due to shielding by inner electrons. This decreased charge is called the effective nuclear charge (Zeff). Slater's rules provide a method to calculate the screening constant σ and thus determine Zeff. The concept of Zeff is applied to explain trends in ionization energy, filling of electron shells, and properties of cations, anions, and across the periodic table.

1. Effective Nuclear
Charge

2. Shielding or screening effect
• In a multi-electron atom the valence-shell electrons are
attracted by the nucleus and also at the same time repelled
by the electrons present between the nucleus and the
valence-shell electrons.
• Thus the nucleus exerts an attractive force on the valence
shell electrons while the inner-shell electrons exert a
repulsive force on the valence-shell electrons.
• The combined effect of these two forces is that the actual
force exerted by the nucleus on the valence-shell electrons
is partially decreased or weakened by the presence of
repulsive forces exerted by the inner-shell electrons on the
valence-shell electrons.
• Thus the valence shell electrons experience less attraction
or pull towards the nucleus.

3. Figure: The valence shell electron experience less attraction
from the nucleus due to the presence of inner shell electrons
called shielding or screening effect of inner shell electrons.

4. "This decrease in the attractive force exerted by the
nucleus on the valence shell electron, which is obviously
due to the presence of the electrons lying between the
nucleus and valence shell electrons (called intervening
electrons) is called shielding effect or screening effect".
• In other words, the intervening electrons screen or shield
the valence-shell electrons from the nucleus.
• This concept has the following applications:
– The concept of shielding effect has been used to
explain why the ionization potential values of the
elements of a given group decrease on descending the
group.
– This concept has also been used to explain that when
we proceed from an inert gas to alkali metal, a large
decrease in the ionization potential is observed.

5. Effective nuclear charge (Zeff)
• With the decrease in the force of attraction caused by the
shielding effect of intervening electrons, the actual
nuclear charge (which is equal to the atomic number, Z of
the element) is decreased by the quantity, σ (sigma) which
is called screening constant.
• The decreased nuclear charge which is obviously equal to
(Z - σ) is called effective nuclear charge and is denoted by
Zeff.
• Thus:
• σ is a measure of the extent to which the intervening
electrons screen the outer-most shell electron from the
nuclear pull on it.

6. • Above equation suggests that effective nuclear charge
(Zeff) is defined as:
"The actual nuclear charge (Z or Zactual) minus the
screening constant (σ) produced by the electrons residing
between the nucleus and the outer-most shell electron
(intervening electrons)".
Factors affecting the magnitude of σ (screening constant)
and Zeff and their variation in the periodic table
• Following are the important factors which affect the
magnitude of σ and Zeff and predict their variation in the
periodic table.
Number of intervening electrons
• Greater is the number of electrons intervening between the nucleus
and the outer most shell (i.e., intervening electrons), more will be
the magnitude of σ and hence the magnitude of Zeff will decrease
(Zeff = Zactual - σ) to a greater extent.

7. • When we move down a group, the number of interveening
electrons increases and hence the magnitude of σ also
increases.
• The increase in the value of σ, decreases the value of Zeff.
• Thus on going down a group, the magnitude of Zeff goes
on decreasing.
• For example in the elements of group IA, with the
increase of the number of inner shells and electrons in
them, the shielding effect caused by these electrons on the
valence-shell electron also increases from Li to Cs as
shown below:

8. Size of the atom
• With the increase in the size of the atom, Zeff decreases.
• Thus:
– Since atomic size increases in going down a group, Zeff
decreases in the same direction.
– Since the size of atoms decreases as we move along a
period from left to right, Zeff increases in the same
direction.

9. Slater's rules for effective nuclear charge
• This set of simple rules for approximating the effective
nuclear charge was proposed a number of years ago by
Professor John C. Slater, a former faculty member at
M.I.T.
Slater's rules for calculating σ and Zeff
• The value of σ and hence that of Zeff can be calculated by
using Slater's rules.
• According to these rules the value of σ for a given
electron is estimated as follows:
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.
• Orbitals within a bracket are said to belong to the same group.

10. 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:
Type of electron Contribution to σ for each
electron of this type
a All electrons in groups outside the
electron chosen
0
b All other electrons in the same
group as chosen one
0.35 (or 0.30 for 1s electron)
c All electrons in shell immediately
inside
0.85
d All electrons further inside 1.00

11. 3) Slater's Rules is now broken into two cases:
– The shielding experienced by an s- or p- electron
– The shielding experienced by a d- or f- electron

12. s- and p-Orbital electrons
For ns or np valence electrons:
– Electrons within same group shield 0.35, except the
1s which shield 0.30
– Electrons within the n-1 group shield 0.85
– Electrons within the n-2 or lower groups shield 1.00
d- and f-Orbital electrons
For nd or nf valence electrons:
– Electrons within same group shield 0.35
– Electrons within the lower groups shield 1.00
• These rules are summarized in the following table.

13. Table: Slater's rules for calculating shieldings.
In order to understand the above rules let us consider the
following examples.

14. YouTube Lectures
• Effective Nuclear Charge
– https://www.youtube.com/watch?v=IvSmfgxCSNQ
• Effective Nuclear Charge, Shielding effect, & Periodic Properties
– https://www.youtube.com/watch?v=hs5t-6iq6-c
• How To Use Slater's Rule to Estimate The Effective Nuclear
Charge
– https://www.youtube.com/watch?v=TaYUOiEe6OA
• Using Slater's Rules: 3 Examples
– https://www.youtube.com/watch?v=7wrTWlXI2IY
• Learn Slater's Rule | Effective Nuclear Charge Calculation
– https://www.youtube.com/watch?v=F4Fx6zbcddU
• Trick for Slater's Rule, calculation of screening constant and
effective nuclear charge
– https://www.youtube.com/watch?v=iz2_J4fjJdY

19. Variation of screening effect or σ in the periodic table

20. Variation of effective nuclear charge in the periodic table

21. Applications of Slater's rules and concept of effective
nuclear charge
• Slater's rules and the concept of effective nuclear charge
have been used to explain the following:
Why is 4s orbital filled earlier than 3d orbitals in
potassium atom (Z = 19)?
(4s Orbital is filled before 3d orbitals)
• We know that the configuration of Ar (Z = 18) which is
the last element of 3rd period of the periodic table is:
1s2, 2s2p6, 3s2p6
• 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.

22. • Why 4s orbital is filled in preference to 3d orbitals can be
explained as follows:
• The two configurations that are theoretically possible for
K-atom are:
• The calculated value of Zeff experienced by 4s1 electron of
K-atom [configuration (a)] equal to 2.20.
• The value of Zeff experienced by 3d electron of K-atom
[configuration (b)] can be calculated as follows:
– σ for 3d electron in structure (b) = 0.35 x 0 + 1.0 x 18 = 18
– Zeff experienced by 3d electron = 19 – 18 = 1.0
4s1 → Zeff → 2.20
3d1 → Zeff → 1.0

23. • Since Zeff for 4s1 electron is greater than that for 3d1
electron, the attraction between 4s1 electron and the
nucleus is greater than that between the 3d1 electron and
nucleus of K-atom.
• Lower value of effective nuclear charge acting on 3d
electron as compared to that acting on 4s electron makes
it evident that in potassium atom 3d electron is less tightly
bound to the nucleus than the 4s electron.
• Consequently the additional electron in potassium atom
prefers to enter 4s orbital than 3d orbital.
• Thus 1s2, 2s2p6, 3s2p6, 4s1 configuration would be more
stable than 1s2, 2s2p6, 3s2p6d1 configuration.
• In other words 4s orbital is filled earlier than 3d orbital.

24. Formation of cations from the isolated gaseous atoms of
transition metals
(4s Electrons are removed before 3d electrons in the
conversion of 3d transition elements into cations)
• When transition metals are converted into cations, it is ns
electrons, and not (n – 1)d electrons, which are removed
first from the isolated gaseous atoms of transition metals.
• In order to explain this fact let us consider the
configuration of vanadium atom (atomic number = 23)
which is 1s2, 2s2p6, 3s2p6d3, 4s2.
• Suppose this atom is to be converted into V2+ cation.
• Quite obviously this cation is formed by the removal of
two electrons from 4s orbital and not from 3d orbital.
• Thus:

25. • Why 4s electrons prefer to be removed than 3d electrons
can be explained by calculating the value of effective
nuclear charge acting on one of the 4s or 3d electrons.
• Effective nuclear charge acting on one of the 4s electrons
is given by:
Zeff (4s) = Z – σ
• Effective nuclear charge acting on one of the 3d electrons
is given by:
Zeff (3d) = Z – σ

26. • Greater value of effective nuclear charge acting on one of
the 3d electrons as compared to that acting on one of the
4s electrons in vanadium atom makes it evident that in
this atom 3d electrons are more tightly bound to the
nucleus than the 4s electrons.
• Consequently in the conversion of vanadium atom into
V2+ cation the electrons to be removed are 4s electrons
and not 3d electrons.

27. A cation is smaller in size than its parent atom
• A cation is formed by the loss of one or more electrons
from an atom.
• It may be represented as:
M → Mn+ + ne-
• The decrease in the radius or size of cation as compared to
its parent atom can be explained on the basis of the
concept of effective nuclear charge.
• A cation is formed by the removal of one or more
electrons from the parent atom.
• Thus a cation has lesser number of electrons, than its
parent atom.
• With the decrease of the number of electrons, the
magnitude of the screening constant, σ, also decreases.
• The decrease in the value of σ increases the magnitude of
effective nuclear charge.

28. • The increased effective nuclear charge pulls the electron
cloud of cation inward nearer to the nucleus and thus
makes the cation smaller in size than its parent neutral
atom.
• The size of the cations of the same element in different
oxidation states decrease with the increase in the
oxidation state.
• For example in case of pair: Fe2+ - Fe3+, the radius of Fe2+ is greater
than that of Fe3+ ion (Fe2+ = 76 pm, Fe3+ = 64 pm).
• The same argument also applies to this decrease as explained
above.

29. An anion is larger in size than its parent atom
• An anion is formed by the gain of one or more electrons.
• The increase in the size of anion as compared to its parent
atom can also be explained on the basis of the concept of
effective nuclear charge.
• With the increase in the number of electrons the
magnitude of screening constant, σ, also increases.
• The increase in the magnitude of σ decreases the
magnitude of effective nuclear change, which pulls the
electron cloud of anion less tightly from the nucleus and
thus makes the anion larger in size than its parent atom.
• Thus halides ions are bigger in size than the halogen
atoms.

30. Variation of atomic and ionic radii of the atoms of
representative elements in a period and a group
a) In a period
• We know that the number of shells in all the elements of a
given period remains the same but the value of effective
nuclear charge, as calculated by Slater's rules, increases
from left to right.
• The increased effective nuclear charge pulls the electron
cloud of the atom nearer to the nucleus and thus the size
of the atoms and ions goes on decreasing from left to
right.

31. • Thus in going from left to right in a period of s- and p-
block elements atomic and ionic radii decrease with the
increase of atomic number.
• This fact can be illustrated by considering the atomic
(covalent) and ionic radii of the elements of 2nd period as
shown below:

32. • Thus in any period the alkali metals (that are present at
the extreme left of the periodic table) have the largest size
while the halogens (that are present at the extreme right,
excluding zero group elements) have the smallest size.
• However, the size of the atoms of inert gases is larger than
that of the preceding halogen.
b) In a group
• In going down a group of s- and p-block elements the
atomic and ionic radii both increase with the increase of
atomic number.
• For example the atomic (covalent) and ionic radii of alkali
metals increase on proceeding from Li to Cs as shown
below:

33. • We have seen that on descending a group the magnitude of
effective nuclear charge acting on the valence-shell electron of the
elements remains the same (the first element is a typical case).
• Thus the concept of effective nuclear charge cannot be used to
explain the successive increase in the atomic or ionic radii of the
elements of a given group.

34. • However, the other factor namely the number of shells or
principal quantum number (n) can be used to explain the
increase in radii.
• As the number of shells or principal quantum number (n)
increases from 2 (in case of Li) to 6 (in case of Cs), the
outer-most shell electrons get farther and farther away
from the nucleus and hence atomic and ionic radii
increase.
• Thus it is due to the progressive addition of a new shell
(or the increase in the number of shells) that the atomic
or ionic radii increase when we proceed from top to
bottom in a group.
• The variation of atomic and ionic radii of representative
elements (s- and p-block element) in a period and a
group of the periodic table can be shown as given in
following figure.

36. Variation of electronegativity values in a period and a
group of representative elements
a) In a period
• In going from left to right in a period of s- and p-block
elements, the electronegativity values increase.
• This increase can be explained on the basis of any of the
following facts.
i) On moving from left to right in a period, there is a
decrease in the size of the atoms.
• Smaller atoms have greater tendency to attract the
electrons towards themselves i.e. smaller atoms have
higher electronegativity values.
ii) On moving from left to right in a period there is an increase of
ionisation energy and electron affinity of the elements.
• The atoms of the elements which have higher value of ionisation
energies and electron affinities also have higher electronegativities.

37. b) In a group
• In going down a group of s- and p-block elements, the
electronegativity values decrease.
• This decrease can also be explained on the basis of any of
the following facts.
i) As we move down a group, there is an increase in the size
of the atoms.
• With the increase in size of the atoms, their
electronegativity values decrease.
ii) Ionisation energy and electron affinity on which
electronegativity depends decrease as the group is
descended.
• With the decrease of these quantities the electronegativity
values also decrease.
• The heavier elements of group III A (i.e. Ga, In and TI)
show reverse trend due to the intervening transition series.

38. • The variation of electronegativity values discussed above reveals
that the halogens (VII A group elements) which lie on the
extreme right of the periodic table are the most electronegative
(i.e. least electropositive) elements and the alkali metals (IA
group elements) which lie on the extreme left of the periodic
table are the least electronegative (i,e. most electropositive)
elements.
• Thus we see that the most electronegative element is flourine
which occurs at the top right hand corner and the least
electronegative element is cesium which occurs at the bottom
left hand corner of the periodic table.
• Being the most electronegative, F does not show any basic
character, i.e., it has no tendency to form positive ions in any of
its known compounds.
• On the other hand, there is, however, evidence to show that Cl,
Br and I have a tendency to form positive ions.
• The variation of electronegativity in a period and a group of (s•
and p•block elements) is shown in following figure.

40. Variation in the values of successive ionisation energies
of a given element
• The successive ionisation energies (IE1, IE2, 1E3 etc.) of a
given element (M) increases in the order:
IE1 < IE2 < IE3 < …..
• This order has been explained on the basis of the concept
of effective nuclear charge experienced by the last
electron in M, M+, M2+ etc.

41. Applications of Slater's rules
• Also see from Satya Parakash and Haq Nawaz
• Self Study – should be included in syllabus…

42. The End