Effective Nuclear Charge Concepts

Questions and Answers

What is the relationship between effective nuclear charge (Zeff) and the actual nuclear charge (Z)?

Zeff equals Z when there are no inner electrons.

Zeff is always greater than Z.

Zeff and Z are identical in many-electron atoms.

Zeff is less than Z due to screening effects. (correct)

Which factor contributes to the decrease in effective nuclear charge experienced by outer electrons?

Absence of inner electrons.

Greater distance of the outer electron from the nucleus. (correct)

Decrease in the number of protons in the nucleus.

Increase in electron affinity of the atom.

What does the screening constant (S) represent in the equation Zeff = Z - S?

The total positive charge in the nucleus.

The number of valence electrons in an atom.

The average distance between the outer electron and the nucleus.

The extent of electron-electron repulsion affecting outer electrons. (correct)

According to Coulomb's law, what increases the attractive force between an electron and the nucleus?

Decreasing the distance between the electron and the nucleus. Signup and view all the answers

How does the presence of inner electrons affect outer electrons in a many-electron atom?

They partially screen the outer electrons from the nuclear attraction. Signup and view all the answers

What is the primary reason effective nuclear charge (Zeff) is less than actual nuclear charge (Z)?

Electron-electron repulsion lowers the net positive charge felt. Signup and view all the answers

Which statement best describes the concept of effective nuclear charge?

It is the net charge experienced by an electron after considering repulsions. Signup and view all the answers

When calculating effective nuclear charge, which of the following cannot be changed to increase Zeff?

Increasing the number of inner electrons. Signup and view all the answers

What is represented by the variable S in the context of inner electrons?

Number of core electrons in an atom Signup and view all the answers

What is the primary effect of shielding on the attractive force between the nucleus and valence electrons?

It decreases the attraction Signup and view all the answers

Given sodium's electron configuration [Ne]3s1, what is the expected effective nuclear charge (Zeff) for the 3s electron?

1+ Signup and view all the answers

What causes an increase in effective nuclear charge (Zeff) for the 3s electron in sodium beyond the expected model?

Probability of proximity to the nucleus Signup and view all the answers

How does the energy of orbitals with the same n value change with increasing l value in a multi-electron atom?

It increases with increasing l value Signup and view all the answers

Which of the following best explains why core electrons are most effective at shielding valence electrons?

Core electrons occupy lower energy orbitals Signup and view all the answers

What is the result of the repulsive effect among electrons in an atom?

It leads to a decrease in effective nuclear charge Signup and view all the answers

In a sodium atom, how would the effective nuclear charge (Zeff) for the 3s electron change if its probability of being closer to the nucleus was eliminated?

Zeff would decrease to 1+ Signup and view all the answers

What is the relationship between the 2s and 2p orbital energies in many-electron atoms?

The 2s orbital has lower energy than the 2p orbital. Signup and view all the answers

How does the effective nuclear charge (Zeff) change across a period in the periodic table?

Zeff increases as you move from left to right. Signup and view all the answers

What is the approximate Zeff experienced by the 2s electron in beryllium (Be)?

2+ Signup and view all the answers

What factor primarily contributes to the increase in Zeff as you move down a column in the periodic table?

More diffuse core electron cloud. Signup and view all the answers

What is the value of Zeff for the valence electrons in sodium (Na)?

2.5+ Signup and view all the answers

What is the formula to estimate the effective nuclear charge (Zeff)?

Zeff = Z - S Signup and view all the answers

Which of the following statements about core electrons is true?

Core electrons do not participate in bonding. Signup and view all the answers

In which situation would the effective nuclear charge (Zeff) be highest?

For 2s electrons in beryllium. Signup and view all the answers

Study Notes

Effective Nuclear Charge (Zeff)

Effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom, influenced by both nuclear charge and electron shielding.
The attractive force between an electron and the nucleus is determined by the strength of nuclear charge and the distance from the nucleus.
Coulomb’s law explains that greater nuclear charge increases attraction, while increased distance decreases it.

Electron Interactions

In multi-electron atoms, electrons experience both attraction to the nucleus and repulsion from other electrons.
It’s difficult to precisely calculate these interactions due to complex electron-electron repulsions.
Instead, the effective nuclear charge is treated as a single positive charge at the nucleus, modified by the presence of other electrons.

Screening Effect

Inner electrons provide a screening effect, reducing the attraction experienced by outer (valence) electrons.
Screening constant (S) is used to quantify the amount of nuclear charge that is shielded from valence electrons.
Zeff is calculated using the formula: Zeff = Z - S, where Z is the actual nuclear charge.

Example: Sodium Atom (Na)

Sodium has an electron configuration of [Ne]3s1, with a nuclear charge of +11 and 10 core electrons.
The expected screening constant (S) for sodium is 10, leading to an initial Zeff of 1+.
Due to the 3s electron’s proximity to the nucleus, the effective nuclear charge is increased to approximately 3+.

Orbital Energy Levels

The concept of Zeff explains energy differences in orbitals; in general, energies increase with increasing l value when n (principal quantum number) is constant.
For example, in carbon (1s² 2s² 2p²), the 2s orbital is lower in energy than the 2p orbital due to stronger nuclear attraction.

Trends in Effective Nuclear Charge

Effective nuclear charge increases across a period in the periodic table due to increased nuclear charge (more protons) with constant core electrons.
Valence electrons become less effective at screening each other as nuclear charge increases, resulting in higher Zeff values.
For lithium (Li), Zeff is around 1+, while for beryllium (Be), it is about 2+ due to less effective screening from core electrons.

Vertical Trends in Effective Nuclear Charge

Across columns of the periodic table, Zeff does not change significantly; however, it generally increases slightly down a group due to less effective screening from more diffuse core electron clouds.
For alkali metals, Zeff values increase from lithium (1.3+) to sodium (2.5+) to potassium (3.5+), despite similar core electron configurations.

Conclusion

The formula Zeff = Z - S serves as an estimate; actual values of Zeff may vary but provide insight into an atom's structure and behaviors.

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Description

This quiz focuses on understanding and explaining the concept of effective nuclear charge in atomic structure. It covers the relationship between electron configuration and the attraction of outer electrons to the nucleus. Familiarity with Coulomb's law will enhance comprehension of the topic.