**Effective Nuclear Charge (Z _{eff})** measures the force exerted onto an electron by the nucleus.

Within any given atom there are electrons that experience both attractive and repulsive forces.

Concept #1: Effective Nuclear Charge

Concept #2: Effective Nuclear Charge

Concept #3: Effective Nuclear Charge

Concept #4: Effective Nuclear Charge

Example #1: Using Slater’s Rules calculate the effective nuclear charge of a 3p electron in argon.

Example #2: Using Slater’s Rules calculate the effective nuclear charge of the 4s electron in potassium.

Example #3: Using Slater’s Rules calculate the effective nuclear charge of a 3d electron in bromine.

Arrange the following atoms according to decreasing effective nuclear charge experienced by their valence electrons S, Al, Si, Mg
a. S > Al > Si > Mg
b. Mg > Al > Si > S
c. Al > S > Si> Mg
d. S > Si > Al > Mg
e. Si > Al > Mg > S

Electrons in the 1s subshell are much closer to the molecules in Ar than in He due to the larger ______ in Ar.
a) azimuthal quantum number
b) paramagnetism
c) magnetic quantum numbers
d) Hund's rule
e) nuclear charge

Screening by the valence electrons in atom is ______.
a) responsible for a general increase in atomic radius going across a period.
b) less efficient than that by core electrons
c) essentially identical to that by core electrons
d) more efficient than that by core electrons
e) both more efficient than that by core electrons and responsible for a general increase in atomic radius going across a period

Which of the following statements is TRUE?
A. An orbital that penetrates into the region occupied by core electrons is less shielded from nuclear charge than an orbital that does not penetrate and therefore has a lower energy.
B. An orbital that penetrates into the region occupied by core electrons is more shielded from nuclear charge than an orbital that does not penetrate and therefore has a lower energy.
C. It is possible for two electrons in the same atom to have identical values for all four quantum numbers.
D. Two electrons in the same orbital can have the same spin.
E. None of the above are true.

In which orbital does an electron in a phosphorus atom experience the greatest shielding _____?
a) 3p
b) 3s
c) 2p
d) 2s
e) 1s

In which orbital does an electron in a phosphorus atom experience the greatest effective nuclear charge?
a) 1s
b) 2s
c) 2p
d) 3s
e) 3p

In which orbital below would an electron (on average) be closest to the nucleus?
a. 2p
b. 4s
c. 2s
d. 5d
e. 3p

The radii of the ions in this series decrease because
a) the elements are in the same period.
b) the effective nuclear charge is increasing.
c) the atomic radius of Na decreases from Na to Al.
d) the first ionization energies increase from Na to Al.

Choose the statement that is TRUE.
a) Outer electrons efficiently shield one another from nuclear charge.
b) Core electrons effectively shield outer electrons from nuclear charge.
c) Valence electrons are most difficult of all electrons to remove.
d) Core electrons are the easiest of all electrons to remove.
e) All of the above are true

What factor best explains the reduction in the effective nuclear charge (Z eff) experienced by the outermost electrons of a multi-electron atom?
(a) Orbital splitting by the increased nuclear charge.
(b) The outermost electrons are moving too quickly to feel the full pull of the nucleus.
(c) Hund’s rule.
(d) The inner electrons shield the outer electrons from the nuclear charge.
(e) Pauli’s exclusion principle.

Figure shows the radial probability distribution functions
for the 2s orbitals and 2p orbitals.
How would
you modify Slater’s rules to adjust for the difference in electronic
penetration of the nucleus for the 2s and 2p orbitals?

In an atom, which electrons tend to do the most shielding (core electrons or valence electrons)?

What is penetration?

How does the penetration of an orbital into the region occupied by core electrons affect the energy of an electron in that orbital?

What is effective nuclear charge?

What is shielding?

Estimate the effective nuclear charge experienced by the valence electron in Li.

You may want to reference (Pages 353 - 356) Section 8.6 while completing this problem.
If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at all, what would be the effective nuclear charge experienced by the valence electrons of the following atoms?K

You may want to reference (Pages 353 - 356) Section 8.6 while completing this problem.
If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at all, what would be the effective nuclear charge experienced by the valence electrons of the following atoms?Ca

You may want to reference (Pages 353 - 356) Section 8.6 while completing this problem.
If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at all, what would be the effective nuclear charge experienced by the valence electrons of the following atoms?O

You may want to reference (Pages 353 - 356) Section 8.6 while completing this problem.
If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at all, what would be the effective nuclear charge experienced by the valence electrons of the following atoms?C

Detailed calculations show that the value of Zeff for the
outermost electrons in Na and K atoms is 2.51+ and 3.49+ , respectively.What value do you estimate for Zeff experienced by the outermost electron in both Na and K by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant?

Detailed calculations show that the value of Zeff for the
outermost electrons in Na and K atoms is 2.51+ and 3.49+ , respectively.What values do you estimate for Zeff
using Slaters rules?

Detailed calculations show that the value of Zeff for the
outermost electrons in Na and K atoms is 2.51+ and 3.49+ , respectively.Predict
Zeff for the outermost electrons in the Rb atom based
on the calculations for Na and K using Slaters rules.

Detailed calculations show that the value of Zeff
for the
outermost electrons in Si and Cl atoms is 4.29+ and 6.12+ , respectively.
You may want to reference (Pages 260 - 262) Section 7.2 while completing this problem.What value do you estimate for Zeff experienced by the outermost electron in both Si and Cl, assuming that core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant?

Detailed calculations show that the value of Zeff
for the
outermost electrons in Si and Cl atoms is 4.29+ and 6.12+ , respectively.
You may want to reference (Pages 260 - 262) Section 7.2 while completing this problem.What values do you estimate for Zeff using Slaters rules?

Detailed calculations show that the value of Zeff
for the
outermost electrons in Si and Cl atoms is 4.29+ and 6.12+ , respectively.
You may want to reference (Pages 260 - 262) Section 7.2 while completing this problem.Which method of approximation more accurately accounts for the steady increase in Zeff that occurs upon moving left to right across a period?

Detailed calculations show that the value of Zeff
for the
outermost electrons in Si and Cl atoms is 4.29+ and 6.12+ , respectively.
You may want to reference (Pages 260 - 262) Section 7.2 while completing this problem.Predict Zeff for a valence electron in P, phosphorus,
based on the Slaters rule calculations for Si and Cl.

From the data in the following table, calculate the effective charges on the H atom of the HBr molecule in units of the electronic charge, e.
Table - Bond Lengths, Electronegativity Differences, and Dipole Moments of the Hydrogen Halides
Compound
Bond Length (Å)
Electronegativity Difference
Dipole Moment (D)
HF
0.92
1.9
1.82
HCl
1.27
0.9
1.08
HBr
1.41
0.7
0.82
HI
1.61
0.4
0.44

Calculate the effective charges on the Br atom of the HBr molecule in units of the electronic charge, e.

You may want to reference(Pages 353 - 356) Section 8.6 while completing this problem.Arrange the following atoms according to decreasing effective nuclear charge experienced by their valence electrons: S, Mg, Al, and Si.

The substance chlorine monoxide, ClO (g), is important in atmospheric
processes that lead to depletion of the ozone layer. The ClO molecule has has an experimental dipole moment of 1.24 D and the Cl - O bond length is 1.60 Å.Determine
the magnitude of the charges on the Cl and O atoms in units of the electronic charge, e.

In a complete sentence describe the relationship between
shielding and penetration.

Which electrons experience a greater effective nuclear charge, the valence electrons in beryllium, or the valence electrons in nitrogen?

In Section 8.6 in the textbook, we estimated the effective nuclear charge on beryllium’s
valence electrons to be slightly greater than 2+. What
would a similar process predict for the effective nuclear charge
on boron’s valence electrons? Would you expect the effective
nuclear charge to be different for boron’s 2s electrons compared
to its 2p electron? How so? (Hint: Consider the shape of the 2p
orbital compared to that of the 2s orbital.)

Among elements 1–18, which element or elements have the
smallest effective nuclear charge if we use the equation Zeff = Z - S to
calculate Zeff?

As discussed in the text, we can draw an analogy between the
attraction of an electron to a nucleus and the act of perceiving light from a light bulb through a frosted glass shade, as
shown in the illustration. Using the simple method of estimating effective nuclear
charge how does the intensity of the light bulb
and/or the thickness of the frosting change in the following
cases:
Moving from boron to carbon?

As discussed in the text, we can draw an analogy between the
attraction of an electron to a nucleus and the act of perceiving light from a light bulb through a frosted glass shade, as
shown in the illustration. Using the simple method of estimating effective nuclear
charge how does the intensity of the light bulb
and/or the thickness of the frosting change in the following
cases:
Moving from
boron to aluminum?

Determine whether each statement regarding penetration and
shielding is true or false. (Assume that all lower-energy orbitals
are fully occupied.)An electron in a 3s orbital is more shielded than an electron in a 2s orbital.

Determine whether each statement regarding penetration and
shielding is true or false. (Assume that all lower-energy orbitals
are fully occupied.)An electron in a 3s orbital penetrates into the region occupied by core electrons more than electrons in a 3p orbital penetrates into the region occupied by core electrons.

Determine whether each statement regarding penetration and
shielding is true or false. (Assume that all lower-energy orbitals
are fully occupied.)An electron in an orbital that penetrates closer to the nucleus always experiences more shielding than an electron in an orbital that does not penetrate as far.

Determine whether each statement regarding penetration and
shielding is true or false. (Assume that all lower-energy orbitals
are fully occupied.)An electron in an orbital that penetrates close to the nucleus
tends to experience a higher effective nuclear charge than an
electron in an orbital that does not penetrate close to the
nucleus.

You may want to reference(Page)Section 8.3 while completing this problem.Which electron in sulfur is most shielded from nuclear charge?

Which will experience the greater effective nuclear charge, the electrons in the n = 3 shell in Ar or the n = 3 shell in Kr?

You may want to reference (Pages 260 - 262) Section 7.2 while completing this problem.Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the n = 3 electron shell: K, Mg, P, Rh, and Ti.

In Section 7.2 in the textbook we said that Zeff
generally increases when you move down a column of the periodic table, whereas in Chapter 6 we saw that the "size" of an orbital increases as the principal quantum number n increases.Which effect is larger?

If the core electrons were totally effective at screening
the valence electrons and the valence electrons provided
no screening for each other, what would be the effective
nuclear charge acting on the 3s and 3p valence electrons in P?

Classify each statement about effective nuclear charge, Z eff, as true or false.

In which orbital below would an electron (on average) be closest to the nucleus?A) 2pB) 2sC) 3pD) 4sE) 5d

In which orbital below would an electron (on average) be farthest from the nucleus?
A) 4f
B) 2p
C) 3d
D) 3s
E) 1s

The effective nuclear charge for an atom is less than the actual nuclear charge due to ________.a. shieldingb. paramagnetismc. electron-pair repulsiond. penetratione. relativity

Which would you expect to experience a greater effective nuclear charge, a 2p electron or a 2s of an atom? a. 2s electron of an atomb. 2p electron of an atomc. Both experience the same effective nuclear charged. Requires a table of shielding constants to make an estimation

Calculate Zeff for the 4s electron in a copper atom, Cu. Express your answer numerically.

Rank the following elements by effective nuclear charge, Z eff, for a valence electron.
Kr, Se, Ca, K, Ge

Determine the effective nuclear charge Zeff for a 4f electron in Ce, Pr, and Nd. There is a decrease in size, commonly known as the lanthanide contraction, with increasing atomic number in the lanthanides. Report the sizes of these atoms.

Rank the following elements by effective nuclear charge,Z eff, for a valence electron from highest to lowest Zeff:
Po, Rn, Ba, Bi, Pb (same as ionization energy)

Classify each statement about effective nuclear charge, Zeff, as true or false.
1. A 1s electron in a B atom has a smaller Zeff than a 1s electron in a Be atom.
2. Effective nuclear charge does not depend on the number of electrons present in an atom.
3. Across a period, as Zeff increases, atomic size increases.
4. Effective nuclear charge increases from left to right across a period on the periodic table.
5. In a Be atom, 1s electron has a greater Zeff than a 2s electron.
6. Electrons in an s orbital are more effective than those in other orbitals at shielding other elctrons from nuclear charge.

Calculate Zeff for the 4s electron in a copper atom, Cu and then Calculate Zeff for a 3d electron in a copper atom, Cu.

In which orbital does an electron in a lithium atom experience the greatest shielding?a. 2pb. 2sc. 3pd. 3se. 1s