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

Answer 1

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


Effective Nuclear Charge- the (net) positive charge experienced by an electron in a many electron atom. This charge is not the full nuclear charge. It accounts for the shielding of the nucleus by other electrons in the atom.


The nucleus is surrounded by electrons. These electrons are shielded from the nucleus by electron repulsions. The effective nuclear charge is less than the actual nuclear charge because the repulsions of the electrons needs to be taken into account.
This is done in the equation
Zeff = Z (protons) - S (screening constant, the inner core amount of electrons)


b) Which experiences a greater effective nuclear charge in a Be atom, the 1s electrons or the 2s electrons?

The 1s electrons would have a greater nuclear charge. The number of electrons between the 1s electrons and the nucleus is less than the number of electrons between the 2s electrons and the nucleus. This means the screening constant is larger. When you subtract the larger amount of electrons from the amount of protons, 4, the difference will be less, meaning the value of the effective nuclear charge will be less.

Answer 2

The concept of effective nuclear charge takes into account the shielding effect of inner electrons on the outer electrons. By considering the net positive charge experienced by an electron due to both the nucleus and inner electrons, the effective nuclear charge simplifies the analysis of electron-electron repulsions in a many-electron atom. This simplification helps in predicting the electron distribution and properties of atoms more accurately.