What is Effective Nuclear Charge?
Effective nuclear charge refers to the positive charge felt or experienced by the outermost electrons in an atom that contains multiple electrons. These outermost electrons are also called ‘valence’ or ‘orbital’ electrons. The charge is called “effective” because inner electrons with negative charge provide some sort of shield that prevents the full charge from reaching the outermost or orbital electrons.

The electrons of a particular atom are arranged in such a way that they concentrically line up with the nucleus in the middle. The inner electrons will act to repel a particular positive nuclear charge, resulting to less nuclear charge felt by the electrons which are farthest from the nuclear center. In this simple definition, it can be said that to calculate effective nuclear charge you just need to subtract the number of inner electrons from the atom’s total atomic number. Using the formula Z-eff = Z – N, Z-eff represents the effective nuclear charge, Z represents the total atomic number or the total number of protons present in the particular atom, and N represents the number of electrons found on the atom’s inner shell, otherwise known as non-valence electrons. The N involved in this formula represents only the “average” number of non-valence electrons and not the actual number. So with shielding and repulsive force from the inner electrons on the positive nuclear charge, valence electrons, or the electrons on the outermost shells will have lesser nuclear charge.

Using sodium cation as an example, the total number of protons or the atomic number is 10, while the number of non-valence electrons is 2. With the formula Z-eff for Na+ (sodium) = Z – N or Z-eff (Na+) = 10 – 2, the result would be 8. The number ‘8’ represents the effective nuclear charge on the valence or orbital electrons of sodium cation.