How to calculate the effective nuclear charge of the 1s electrons in helium ?

The effective nuclear charge experienced by a 1s electron in helium is +1.70.

The effective nuclear charge ##Z_"eff"## is the net positive charge experienced by an electron in a multi-electron atom.

A given electron does not experience a full nuclear charge because the other electrons are sometimes between it and the nucleus and shield it from the nucleus.

The formula for effective nuclear charge is

##Z_"eff" = Z – S##

where

##Z## is the number of protons in the nucleus, and ##S## is the shielding constant, the average number of electrons between the nucleus and the electron in question.

The American physicist John Slater derived a number of rules to determine the shielding constant.

He found that for electrons in a 1s orbital, the second electron shields the first by 0.30 units.

##Z_"eff" = Z – S = 2 – 0.30 = 1.70##