Question

How is the concept of effective nuclear charge used to simplify the numerous electron-electron repulsions in a many-electron atom?

A. Repulsion between electrons increases the amount of energy of a given electron, where attraction to the nucleus decreases the energy. The effective nuclear charge (Zett) gives us a rough estimate of these interactions without the need for extensive experimentation.
B. The effective nuclear charge (Zeft) essentially ignores any contribution of electrons to the organization of the atom. Because the protons are the most important subatomic particle and are directly involved in all of an atom's chemistry, this simplification helps us to understand why the atom reacts the way it does, all due to the activity of the protons in the nucleus.
C. The effective nuclear charge (Zett) tells us that we can assume all the electrons are one big ball of negative potential. Doing this makes the electrons similar to the nucleus of an atom, and we can consider each to have one charge, rather than dealing with multiple charges, multiple attractions, and multiple repulsons in an atom when trying to understand how the electrons are interacting.
D. It actually doesn't simplify it, it purposely complicates it. Most people look at the electron as a negatively charged ball in space flying around the nucleus, but we need to also consider the wavelike properties of the electron. The effective nuclear charge (Zeff) tells us how an electron interacts with the nucleus will simultaneously acting as a wave.

Answer 1

The effective nuclear charge (Zeff) simplifies the complex interactions in many-electron atoms by adjusting the nuclear charge by the degree of electron shielding, allowing for a clearer understanding of atomic properties such as atomic radii.

Step-by-step explanation:

The concept of effective nuclear charge (Zeff) is used to simplify the complex interactions between electrons in a many-electron atom. The effective nuclear charge is the charge that leads to the Coulomb force exerted by the nucleus on an electron, calculated as the nuclear charge (Z) minus any shielding by other electrons. As we move across a period on the periodic table, Z increases by one for each element, but the shielding effect of the inner electrons increases only slightly. Hence, Zeff increases, which in turn draws the outer electrons closer to the nucleus, making the atoms smaller despite having more electrons.

This concept helps explain why the covalent radii of elements decrease across a period, as the increasingly positive Zeff exerts a stronger pull on the electrons. The inner electrons act as a shield, diminishing the full nuclear charge experienced by the outer electrons. This shielding effect, which involves the probability of another electron being between the electron of interest and the nucleus, along with electron-electron repulsions, allows for a simplification of electron-nucleus interactions without extensive calculations or experimentation.