Question

Among elements 1-18, which element or elements have the smallest effective nuclear charge if we use Equation 7.1 to calculate \(Z_{\text { eff}}\)? Which element or elements have the largest effective nuclear charge?

Short answer

After calculating the effective nuclear charge (\(Z_{\text { eff }}\)) for elements 1-18 using the equation \(Z_{\text { eff }} = Z - S\), where Z is the atomic number and S is the shielding constant, we can determine the element(s) with the smallest and largest effective nuclear charge by comparing the calculated values. The element(s) with the smallest \(Z_{\text { eff }}\) value will have the smallest effective nuclear charge, while the element(s) with the largest \(Z_{\text { eff }}\) value will have the largest effective nuclear charge.

Step-by-step solution

Write Electron Configurations for Elements 1-18

Write the electron configurations for elements 1-18 considering their atomic numbers. Knowing the electron configurations will enable us to determine the shielding constant for each element.

Calculate the Shielding Constant (S) for Each Element

For each element, determine the shielding constant (S) based on the electron configuration. Consider following rules for calculation: 1. Electrons in the same subshell shield each other by approximately 0.35. 2. Electrons in the immediate preceding shell shield by approximately 0.85. 3. Electrons in shells two or more before the outermost shell have full shielding effect of 1.

Calculate the Effective Nuclear Charge (Z_eff) for Each Element using Equation 7.1

For each element, apply the equation: \(Z_{\text{eff}} = Z - S\) where Z is the atomic number (number of protons) and S is the calculated shielding constant. Calculate the effective nuclear charge (Z_eff) for each element from 1-18.

Identify the Elements with the Smallest and Largest Effective Nuclear Charges

Compare the calculated Z_eff values for all elements 1-18, and determine the elements with the smallest and largest effective nuclear charges. The element(s) with the smallest Z_eff value will have the smallest effective nuclear charge, and the element(s) with the largest Z_eff value will have the largest effective nuclear charge.

Key concepts

Electron Configuration

Understanding electron configuration is like knowing the address of each electron in an atom. Electrons are arranged in energy levels or shells around the nucleus of an atom. The arrangement is crucial as it impacts the atom's chemical properties. For elements 1 to 18, which range from Hydrogen (H) to Argon (Ar), the electron configurations can be written by following the Aufbau principle. This principle suggests filling lower energy levels first before moving to higher ones, like filling up lower floors of a hotel before the higher ones.

An example: Sodium (Na) with atomic number 11 has the electron configuration of 1s² 2s² 2p⁶ 3s¹, where the superscripts represent the number of electrons in each shell. Such configurations help determine how electrons occupy different orbital sites, and this becomes significant when we calculate the shielding constant.

Shielding Constant

The shielding constant ( S ) is an essential component when calculating the effective nuclear charge. It accounts for the protons in the nucleus being obscured or 'shielded' by inner-layer electrons. This reduces the force of attraction experienced by outer electrons, akin to how cloudy glasses can obscure your view of the sun.

Calculating S involves understanding a few rules:

• Electrons in the same subshell contribute about 0.35 to the shielding.
• Electrons in the shell just before the outermost contribute around 0.85.
• Electrons two or more shells within contribute fully, shielding fully at 1 each.

When you know the electron configuration, applying these rules will yield the shielding constant specific to each element. It’s like a math equation using these rules to factor in the number of electrons below the outermost shell.

Z_eff Calculation

The effective nuclear charge ( Z_{ ext{eff}} ) gives an insight into how strongly an outermost electron is attracted to an atom's nucleus. Calculating Z_{ ext{eff}} involves a straightforward formula:\[ Z_{ ext{eff}} = Z - S \] where Z is the atomic number (the number of protons), and S is the shielding constant.To find out Z_{ ext{eff}} , you subtract the shielding effect of inner electrons from the total positive charge (number of protons) of the nucleus. This gives you the net positive charge felt by outer electrons, analogous to how a net sum tells you what remains after all subtractions. It explains why some electrons are more loosely bound, influencing properties like reactivity.

Elements 1-18

The elements 1-18 encapsulate the first three periods of the periodic table, from Hydrogen to Argon. These elements span across different groups such as alkali metals, alkaline earth metals, halogens, and noble gases, each demonstrating unique chemistry.

By understanding the effective nuclear charge across these elements, you can see varying trends. For instance, as you move left to right across a period, Z_{ ext{eff}} increases. This is due to a steadier increase in Z compared to S , as electrons are added to the same outer shell, enhancing attraction to the nucleus.

Such observations list elements like Neon (Ne) and Argon (Ar) with larger Z_{ ext{eff}} due to a complete outer shell, relatively unshielded by additional electron layers. In contrast, elements like Lithium (Li) showcase smaller Z_{ ext{eff}} because of lesser nuclear charge and higher shielding, impacting their chemical behaviors.