Question

If the core electrons were \(100 \%\) effective at shielding the valence electrons from the nuclear charge and the valence electrons provided no shielding for each other, what would be the effective nuclear charge felt by a valence electron in (a) \(\mathrm{Mg}\), (b) \(\mathrm{Si}\), (c) \(\mathrm{Br}\) ?

Short answer

The effective nuclear charge felt by a valence electron would be +2 for Mg, +4 for Si, and +7 for Br.

Step-by-step solution

Determine the Atomic Number

Find the atomic number for each element. The atomic number gives the number of protons in the nucleus, and for a neutral atom, also the total number of electrons.

Identify Core and Valence Electrons

Determine the number of core electrons for each element. Core electrons are the inner electrons in an atom and do not include the valence electrons which participate in bonding. Subtract the core electrons from the total number of electrons to find the number of valence electrons.

Calculate Effective Nuclear Charge (Z_eff)

Use the assumption that the core electrons shield the valence electrons 100% from the nuclear charge. The effective nuclear charge is then the nuclear charge (the atomic number) minus the number of core electrons.

Apply Z_eff Calculation to Each Element

For Mg (atomic number 12), the core electrons are 10 (from the first two shells) and the valence electrons are 2. For Si (atomic number 14), the core electrons are 10 and the valence electrons are 4. For Br (atomic number 35), the core electrons are 28 (from the first three shells and the 18 electrons of the fourth shell that are not valence electrons) and the valence electrons are 7.

Key concepts

Atomic Number

The atomic number, often denoted as 'Z', is a fundamental concept in chemistry and physics. It represents the total number of protons in the nucleus of an atom, and because it's unique for each element, it effectively defines the chemical identity of the element on the periodic table. In a neutral atom, the atomic number also equals the number of electrons orbiting the nucleus since the positive charge of protons is balanced by the negative charge of electrons.

Understanding atomic number is essential not just for identifying an element, but also for predicting its chemical behavior and its placement in the periodic table. For example, magnesium (Mg) has an atomic number of 12, silicon (Si) has 14, and bromine (Br) has 35. This atomic hierarchy directly influences their properties and reactivity.

Core and Valence Electrons

Electrons in an atom occupy regions known as electron shells, and these can be further divided into core and valence electrons. Core electrons are found in the inner shells of an atom. They are close to the nucleus and often shielded by other electrons, making them less involved in chemical reactions.

On the other hand, valence electrons are the outermost electrons of an atom and they play a crucial role in chemical bonding. Because they are farther away from the positive pull of the nucleus, they are more readily available for interactions with other atoms. For instance, Mg has two valence electrons in its outer shell, while Si has four. These valence electrons immensely affect the way an element will participate in bonding.

Z_eff Calculation

The effective nuclear charge (\(Z_{\text{eff}}\)) concept provides insight into the net positive charge experienced by an electron in the valence shell of an atom. It factors in both the actual nuclear charge and the screen effect of core electrons. Mathematically, it's the difference between the number of protons in the nucleus (the atomic number 'Z') and the number of core electrons that shield the valence electrons.

When calculating the effective nuclear charge, we assume that core electrons provide complete shielding, while valence electrons provide none. Therefore, for Mg with an atomic number of 12 and 10 core electrons, the effective nuclear charge felt by a valence electron would be 12 - 10 = 2.

Chemical Bonding Principles

The principles of chemical bonding are fundamentally grounded in the interactions between valence electrons of atoms. Atoms bond to achieve electron configurations that are more stable, which often resembles that of the nearest noble gas. Bonds can be ionic, where electrons are transferred between atoms; covalent, where electrons are shared; or metallic, where electrons are delocalized in a 'sea' of electrons.

The effective nuclear charge exerts a significant influence on bonding. Atoms with a higher effective nuclear charge attract electrons more strongly, which can affect bond lengths and strengths. Understanding how effective nuclear charge varies across the periodic table, with elements like Br having a higher effective nuclear charge than Mg or Si, helps us predict and explain various bonding behaviors in molecules.

Periodic Table Elements

The periodic table is more than just a chart of elements; it reflects underlying patterns in atomic structure and properties. Elements are arranged in order of increasing atomic number, and this arrangement brings to light trends in properties such as electronegativity, ionization energy, and atomic radius.

For example, as you move from left to right across a period, effective nuclear charge typically increases. This happens because electrons are being added to the same energy level, while protons are being added to the nucleus, resulting in a stronger attraction of electrons towards the nucleus. The periodic table thus not only organizes elements in a meaningful way but also allows us to make predictions regarding an element's behavior in chemical bonding.