Subjects

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Electron Configuration | 27 mins | 0 completed | Learn Summary |

Paramagnetic and Diamagnetic | 10 mins | 0 completed | Learn Summary |

Effective Nuclear Charge | 25 mins | 0 completed | Learn |

The Spin Quantum Number | 9 mins | 0 completed | Learn |

Orbital Shapes | 5 mins | 0 completed | Learn Summary |

Periodic Trends: Atomic Radius | 4 mins | 0 completed | Learn |

Periodic Trends: Ionic Radius | 6 mins | 0 completed | Learn Summary |

Periodic Trends: Ionization Energy | 20 mins | 0 completed | Learn Summary |

Periodic Trends: Electron Affinity | 12 mins | 0 completed | Learn Summary |

Additional Practice |
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Orbital Diagrams |

Coulomb's Law |

Quantum Numbers |

Periodic Trends |

Periodic Trends: Metallic Character |

Additional Guides |
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Atomic Radius |

Ionization Energy |

**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.

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.

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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 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.

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 penetrates into the region occupied by core electrons more than electrons in a 3p orbital penetrates into the region occupied by core electrons.

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.

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?

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.

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?

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.

A tin atom has 50 electrons. Electrons in the __________ subshell experience the lowest effective nuclear charge.A) 1sB) 3pC) 3dD) 5sE) 5p

Rank the following elements by effective nuclear charge, Zeff, for a valence electron. Pb Bi Po Rn Ba

The shielding of electrons gives rise to an effective nuclear charge, Zeff, which explains why boron is larger than oxygen. Estimate the approximate Zeff felt by a valence electron of boron and oxygen, respectively?a) +5 and +8b) +3 and +6c) +5 and +6d) +3 and +8e) +1 and +4

The shielding of electrons gives rise to an effective nuclear charge, Zeff , which explains why boron is larger than oxygen. Estimate the approximate Zeff felt by a valence electron of boron and oxygen, respectively?A) +5 and +8B) +3 and +6C) +5 and +6D) +3 and +8E) +1 and +4The atomic radius of an element can be predicted based on its periodic properties. Atomic radii increase going down a group in the periodic table, because successively larger valence-shell orbitals are occupied by electrons. Atomic radii generally decrease moving from left to right across a period because the effective nuclear charge increases.

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

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.

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?

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

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

The effective nuclear charge for an atom is less than the actual nuclear charge duea. shielding.b. penetration.c. paramagnetism.d. electron-pair repulsion.e. relativity.

Part A: Calculate Zeff for a valence electron in an oxygen atom.Part B: Calculate Zeff for the 4s electron in a copper atom, Cu.Part C: Calculate Zeff for a 3d electron in a copper atom, Cu.

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 electrons from nuclear charge.

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

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.

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 electron in sulfur is most shielded from nuclear charge?

What is the effective nuclear charge (Zeff) felt by a valence electron in a Cl atom?A) 5B) 6C) 7D) 8E) 9

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

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

Rank the following elements by effective nuclear charge, Zeff, for a valence electron. F Li Be B N

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)

Calculate Zeff for a valence electron in an oxygen atom.Effective nuclear charge, Zeff, is defined asZeff = Z − Swhere ZZ is true nuclear charge and SS is the amount of shielding. In 1930, John C. Slater devised the following set of empirical rules to estimate SS for a designated ns or np electron:i. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f ), (5s, 5p), and so on. ii Electrons in groups to the right of the (ns np) group contribute nothing to the shielding constant for the designated electroniii. All the other electrons in the (ns, np) group shield the designated electron to the extent of 0.35 each. iv. All electrons in the n − 1 shell shield to the extent of 0.85 each. v. All electrons in the n − 2 shell, or lower, shield completely—their contributions to the shielding constant are 1.00 each. When the designated electron is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following: vi. Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant. These rules are a simplified generalization based on the average behavior of different types of electrons.

Calculate Zeff for the 4s electron in a copper atom, Cu.Effective nuclear charge, Zeff, is defined asZeff = Z − Swhere ZZ is true nuclear charge and SS is the amount of shielding. In 1930, John C. Slater devised the following set of empirical rules to estimate SS for a designated ns or np electron:i. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f ), (5s, 5p), and so on. ii Electrons in groups to the right of the (ns np) group contribute nothing to the shielding constant for the designated electroniii. All the other electrons in the (ns, np) group shield the designated electron to the extent of 0.35 each. iv. All electrons in the n − 1 shell shield to the extent of 0.85 each. v. All electrons in the n − 2 shell, or lower, shield completely—their contributions to the shielding constant are 1.00 each. When the designated electron is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following: vi. Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant. These rules are a simplified generalization based on the average behavior of different types of electrons.

Calculate Zeff for the 3d electron in a copper atom, Cu.Effective nuclear charge, Zeff, is defined asZeff = Z − Swhere ZZ is true nuclear charge and SS is the amount of shielding. In 1930, John C. Slater devised the following set of empirical rules to estimate SS for a designated ns or np electron:i. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f ), (5s, 5p), and so on. ii Electrons in groups to the right of the (ns np) group contribute nothing to the shielding constant for the designated electroniii. All the other electrons in the (ns, np) group shield the designated electron to the extent of 0.35 each. iv. All electrons in the n − 1 shell shield to the extent of 0.85 each. v. All electrons in the n − 2 shell, or lower, shield completely—their contributions to the shielding constant are 1.00 each. When the designated electron is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following: vi. Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant. These rules are a simplified generalization based on the average behavior of different types of electrons.

An electron in a(n) __________ subshell experiences the greatest effective nuclear charge in a many-electron atom.A) 3fB) 3pC) 3dD) 3sE) 4s

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

In which orbital does an electron in a phosphorus atom experience the greatest effective nuclear charge?a) 1sb) 2sc) 2pd) 3se) 3p

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.

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)HF0.921.91.82HCl1.270.91.08HBr1.410.70.82HI1.610.40.44

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.

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

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

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.

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.)

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

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. Core electrons are the easiest of all electrons to remove.d. Valence electrons are most difficult of all electrons to remove.e. All of the above are true.

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?

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.

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?

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