Problem 17 - Chemistry and Chemical Reactivity

Question

The effective nuclear charge, \(Z^{*},\) is the net force of attraction experienced by the outermost electron in an atom. Which of the following statements best describes how \(Z^{*}\) varies among the elements of the second period (Li to \(\mathrm{F}\) )? (a) regular increase from Li to \(\mathrm{F}\) (b) regular decrease from Li to \(\mathrm{F}\) (c) general increase from Li to F, but with exceptions

Step-by-Step Solution

Answer

The effective nuclear charge \( Z^* \) regularly increases from Li to F (option a).

Step 1: Understand Effective Nuclear Charge

The effective nuclear charge, denoted as \( Z^* \), is the apparent net positive charge experienced by an electron in a multi-electron atom. It is principally affected by two factors: the actual nuclear charge (number of protons) and the screening effect caused by other electrons.

Step 2: Consider the Elements of the Second Period

The second period elements in the periodic table range from Lithium (Li) to Fluorine (F). These elements have increasing atomic numbers as you move from left to right across the period, meaning they gain more protons.

Step 3: Analyze the Trend in Effective Nuclear Charge

As we move from Li to F across the second period, each successive element has an additional proton in the nucleus, increasing the net positive charge. While electrons are also added, these new electrons are being added to the same electron shell and thus do not completely shield the increased nuclear charge.

Step 4: Determine the Trend Description

With each element from Li to F gaining one more proton and the same number of inner shielding electrons, the effective nuclear charge \( Z^* \) increases regularly. The added outer electrons in the same shell do not fully shield the increased nuclear charge from the additional protons.

Step 5: Conclude the Best Description

The increase in effective nuclear charge from Li to F is regular without exceptions because of the consistent increase in nuclear charge coupled with relatively inadequate shielding by added electrons in the same shell.

Key Concepts

Periodic Trends

Periodic trends refer to how certain properties of elements change as you move across a period in the periodic table. One of the key trends is that the effective nuclear charge, or \( Z^* \), experiences predictable changes. As you move from left to right across a period, such as from Lithium (Li) to Fluorine (F) in the second period, \( Z^* \) generally increases. This is because each element has one more proton than the last, increasing the positive charge of the nucleus. With each step to the right:

• The nuclear charge increases due to more protons.
• Electrons are added to the same electron shell.
• The increased nuclear charge is not fully shielded by these electrons, enhancing \( Z^* \).

This trend is consistent and helps explain why elements become more electronegative across a period.

Nuclear Shielding

Nuclear shielding, or the screening effect, is a crucial concept that affects an electron's experience inside an atom. It describes how inner electrons can "shield" outer electrons from the full effect of the positive charge from the protons in the nucleus. Imagine each electron as a small shield, reducing the pull felt by outer electrons.However, when new electrons are added to the same shell, as seen in periods like the second one, they do not add much additional shielding compared to the substantial increase in protons. The protons' pull is still felt more strongly than the newly added electrons in the same shell can shield. Hence:

• Inner shell electrons effectively reduce \( Z^* \) for outer electrons.
• Electrons in the same shell don’t shield effectively against each other.
• This poor shielding leads to a gradual increase in \( Z^* \).

Understanding nuclear shielding helps explain why effective nuclear charge increases steadily within a period.

Atomic Structure

The atomic structure is the arrangement of protons, neutrons, and electrons in an atom, and it's fundamental to understanding elements' properties. At the core is the nucleus, containing positively charged protons, which determine the atomic number and the element's identity.Electrons orbit the nucleus in shells or energy levels and all have negative charges. The structure affects how these electrons experience nuclear charge. As more protons are added across a period, the atom's positive charge grows. With a fixed inner shell,

• The more protons in the nucleus, the stronger the pull on outer electrons.
• Despite additional same-shell electrons, their shielding effect is minimal.
• \( Z^* \) increases because the protons pull more effectively than these electrons shield.

Understanding atomic structure helps us consider how elements develop stronger attractions to electrons, impacting their chemistry.

Second Period Elements

Second period elements, from Lithium (Li) to Fluorine (F), allow us to observe consistent periodic trends. These elements share a similar energy level for their electrons, as they all add electrons to the same principal energy level.The second period displays a systematic pattern of properties due to this consistent addition of protons and electrons. Such elements show regular increases in their effective nuclear charge \( Z^* \) across the period, as each step:

• Adds a proton to the nucleus, enhancing its positive charge.
• Adds an electron to the same energy level, providing minimal additional shielding.
• Results in effective nuclear charge increasing, affecting the element's reactivity and electronegativity.

Exploring these transitions within the second period helps illustrate how subtle changes in atomic composition govern noticeable differences in element behavior and chemical properties.