Ch.8 - Periodic Properties of the ElementsWorksheetSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Effective Nuclear Charge (Zeff) measures the force exerted onto an electron by the nucleus. 

Effective Nuclear Charge & Slater's Rules

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

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.  

Additional Problems
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.
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.
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.
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.
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.
Which will experience the greater effective nuclear charge, the electrons in the n = 3 shell in Ar or the n = 3 shell in Kr?
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?
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
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.
Mercury in the environment can exist in oxidation states 0, +1, and +2. One major question in environmental chemistry research is how to best measure the oxidation state of mercury in natural systems; this is made more complicated by the fact that mercury can be reduced or oxidized on surfaces differently than it would be if it were free in solution. XPS, X-ray photoelectron spectroscopy, is a technique related to PES, but instead of using ultraviolet light to eject valence electrons, X-rays are used to eject core electrons. The energies of the core electrons are different for different oxidation states of the element. In one set of experiments, researchers examined mercury contamination of minerals in water. They measured the XPS signals that corresponded to electrons ejected from mercurys 4f orbitals at 105 eV, from an X-ray source that provided 1253.6 eV of energy. The oxygen on the mineral surface gave emitted electron energies at 531 eV, corresponding to the 1s orbital of oxygen. Overall the researchers concluded that oxidation states were +2 for Hg and –2 for O.Use Slaters rules to estimate Zeff for the 4f and valence electrons of Hg2+ and O2–; assume for this purpose that all the inner electrons with (n – 3) or less screen a full +1.
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
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
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
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? What values do you estimate for Zeff using Slater’s rules?Which approach gives a more accurate estimate of Zeff?
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? What values do you estimate for Zeff using Slater’s rules?Does either method of approximation account for the gradual increase in Zeff that occurs upon moving down a group?
Detailed calculations show that the value of Zeff  for the outermost electrons in Si and Cl atoms is 4.29+ and 6.12+ , respectively.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.What value do you estimate for Zeff experienced by the outermost electron in both Si and Cl by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant? What values do you estimate for Zeff using Slater’s rules?Which approach gives a more accurate estimate of Zeff?
Detailed calculations show that the value of Zeff  for the outermost electrons in Si and Cl atoms is 4.29+ and 6.12+ , respectively.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.Predict Zeff for a valence electron in P, phosphorus, based on the Slaters rule calculations for Si and Cl.
Arrange the following atoms according to decreasing effective nuclear charge experienced by their valence electrons: S, Mg, Al, and Si.
Which electrons experience the greatest effective nuclear charge?(a) the valence electrons in Mg(b) the valence electrons in Al(c) the valence electrons in S
You may want to reference (Pages 260 - 262) Section 7.2 while completing this problem.Which of the following statements about effective nuclear charge for the outermost valence electron of an atom is incorrect?(i) The effective nuclear charge can be thought of as the true nuclear charge minus a screening constant due to the other electrons in the atom.(ii) Effective nuclear charge increases going left to right across a row of the periodic table.(iii) Valence electrons screen the nuclear charge more effectively than do core electrons.(iv) The effective nuclear charge shows a sudden decrease when we go from the end of one row to the beginning of the next row of the periodic table.(v) The change in effective nuclear charge going down a column of the periodic table is generally less than that going across a row of the periodic table.
The iodine monobromide molecule, IBr, has a bond length of 2.49 Å and a dipole moment of 1.21 D. Calculate the effective charges on the I and Br atoms in IBr, in units of the electronic charge, e.
Which statement is true about electron shielding of nuclear charge?a) Outermost electrons efficiently shield one another from nuclear charge.b) Core electrons efficiently shield one another from nuclear charge.c) Outermost electrons efficiently shield core electrons from nuclear charge.d) Core electrons efficiently shield outermost electrons from nuclear charge.
Among elements 1–18, which element or elements have the smallest effective nuclear charge if we use Equation 7.1 to calculate Zeff? Which element or elements have the largest effective nuclear charge?
Which would you expect to experience a greater effective nuclear charge a 2p electron of a Ne atom or a 3s electron of a Na atom?
Which electron in sulfur is most shielded from nuclear charge?
Which statement is true about effective nuclear charge?a) Effective nuclear charge decreases as you move to the right across a row in the periodic table.b) Effective nuclear charge increases as you move to the right across a row in the periodic table.c) Effective nuclear charge remains constant as you move to the right across a row in the periodic table.d) Effective nuclear charge increases and decreases at regular intervals as you move to the right across a row in the periodic table.
Which will be closer to the nucleus, the electrons in the n = 3 shell in Ar or the n = 3 shell in Kr?
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.
Detailed calculations indicate that the effective nuclear charge is 5.6+ for the 3s electrons and 4.9+ for the 3p electrons. Why are the values for the 3s and 3p electrons different?
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?Repeat these calculations using Slater’s rules.
Which electrons experience a greater effective nuclear charge, the valence electrons in beryllium, or the valence electrons in nitrogen?
Rank the following elements by effective nuclear charge, Z eff, for a valence electron.Kr, Se, Ca, K, Ge
Classify each statement about effective nuclear charge, Z eff, as true or false.
Calculate Zeff for the 4s electron in a copper atom, Cu. Express your answer numerically.
In which orbital does an electron in a lithium atom experience the greatest shielding?a. 2pb. 2sc. 3pd. 3se. 1s 
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.)
Detailed calculations show that the value of Zeff  for the outermost electrons in Si and Cl atoms is 4.29+ and 6.12+ , respectively.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?