Question

Which of the following statements is true about effective nuclear charge? (a) \(Z_{\text {eff }}\) decreases from top to bottom (b) \(Z_{\text {eff }}\) increases from top to bottom (c) \(Z_{\text {eff }}\) increases as we move from left to right in periodic table (d) \(Z_{\text {eff }}=Z \times \sigma\) (here \(\sigma\) is screening constant)

Short answer

(c) \(Z_{eff}\) increases as we move from left to right in the periodic table.

Step-by-step solution

Understanding Effective Nuclear Charge

The effective nuclear charge, \(Z_{eff}\), is the net positive charge experienced by an electron in a multi-electron atom. It is calculated using the formula \(Z_{eff} = Z - S\), where \(Z\) is the atomic number (nuclear charge) and \(S\) is the shielding or screening constant.

Analyze Statement A and B

Statement (a) claims \(Z_{eff}\) decreases from top to bottom, and statement (b) claims it increases. As we move down a group in the periodic table, the number of inner shell electrons increases, leading to a greater shielding effect, but the increase in nuclear charge generally causes a slight increase or no significant change in \(Z_{eff}\). Therefore, neither is consistently true, as \(Z_{eff}\) tends to remain relatively stable or slightly increase down a group.

Analyze Statement C

Statement (c) claims that \(Z_{eff}\) increases as we move from left to right across a period. This is true because, across a period, the number of protons (\(Z\)) increases while the shielding effect due to core electrons remains relatively constant. This causes an increase in \(Z_{eff}\), making it easier to observe an increase in the attraction for outer electrons, hence making this statement true.

Analyze Statement D

Statement (d) proposes \(Z_{eff} = Z \times \sigma\). This is incorrect because the correct way to calculate \(Z_{eff}\) is \(Z_{eff} = Z - S\), not a product of \(Z\) and a screening constant. \(\sigma\) acts to represent effective shielding rather than being directly multipliable with \(Z\).

Key concepts

Periodic Table Trends

The periodic table is a powerful tool that reveals various trends in chemical properties as you move across periods (rows) and down groups (columns). Understanding how these trends affect elements can help explain numerous chemical behaviors and phenomena. One key trend is the effective nuclear charge, denoted as \( Z_{eff} \), which refers to the net positive charge felt by an electron from the nucleus.

As you move from left to right across a period, the effective nuclear charge generally increases. This is because the number of protons (which make up the atomic number \( Z \)) increases, while the number of shielding electrons remains relatively constant. This results in a stronger attraction between the nucleus and the outer electrons, thereby increasing \( Z_{eff} \).

In contrast, the trend from top to bottom within a group is more nuanced. The number of electron shells increases as you descend, which means there are more inner-shell electrons available for shielding. This can moderate the increase in \( Z_{eff} \). Thus, although there is an increase in nuclear charge (more protons), the increased shielding typically keeps \( Z_{eff} \) either stable or slightly increased.

• Across a period: \( Z_{eff} \) increases.
• Down a group: \( Z_{eff} \) tends to stay constant or increase slightly.

Shielding Effect

The shielding effect, also called the screening effect, plays a crucial role in atomic structure and periodic trends. It refers to the phenomenon where inner-shell electrons partially block the attraction of outer-shell electrons to the nucleus. This happens because electrons that exist closer to the nucleus can repel electrons that are further out, reducing the overall effect of nuclear charge on those outer electrons.

In multi-electron atoms, the shielding effect is particularly significant. Inner electrons repel outer electrons, decreasing the net positive charge felt by those outer electrons. This is why \( Z_{eff} \), or the effective nuclear charge, is often lower than the actual nuclear charge \( Z \). The shielding constant \( S \), in the formula \( Z_{eff} = Z - S \), quantifies the extent of this shielding.

Moreover, the strength of the shielding effect varies across the periodic table. As you move down a group, because there are more inner electrons, the shielding effect becomes more pronounced, reducing the impact of the increased nuclear charge. However, across a period from left to right, the shielding effect remains relatively constant since the extra electrons are added to the same shell.

• Inner-shell electrons block nuclear attraction to outer-shell electrons.
• Stronger down a group due to additional inner electrons.
• Remains the same across a period as electrons fill the same shell.

Atomic Structure

The concept of atomic structure is fundamental to understanding how elements behave and interact. An atom consists of a central nucleus surrounded by electrons in various orbitals. The nucleus contains protons and neutrons, with protons contributing to the atomic number \( Z \) and thus determining the element's identity.

Electrons orbit the nucleus in defined shells or energy levels, and each electron interacts with both the other electrons and the protons in the nucleus. The effectiveness of this interaction is described by the effective nuclear charge, \( Z_{eff} \).

Atomic structure influences periodic trends and the shielding effect. As electrons are added to the same shell across a period, electron-electron interactions increase but don't significantly affect shielding, allowing \( Z_{eff} \) to increase.

Down a group, the atomic structure grows more complex with additional shells, increasing the distance of valence electrons from the nucleus. This increases electron shielding and impacts chemical properties like reactivity.

• Nucleus contains protons and neutrons; electrons orbit in shells.
• \( Z_{eff} \) influenced by electron interactions.
• Valence electrons experience varying levels of shielding.