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

1. Helium Electrons Per Shell
2. Helium Electrons Protons Neutrons
3. Helium Electrons To Fill Outer Shell

1 Answer

For the element of HELIUM, you already know that the atomic numbertells you the number of electrons. That means there are 2 electrons in a helium atom. Looking at the picture, you can see there are two electrons in shell one. That means the first shell is full.

Now, we consider the Helium atom andwill see that due to the attendant 3-body problem for which we cannot determine a close-for, rst-principles analytic solution, we will have to nd recourse in approximate methods. The Helium atom has 2 electrons with coordinates r1 and r2. Now, we consider the Helium atom andwill see that due to the attendant 3-bodyproblemforwhichwecannot determineaclosed-form, rst-principles analytic solution, we will have to nd recourse in approximate methods. The Helium atom has 2 electrons with coordinates r1 and r2 as well as a single nucleus with coordinate R. The nucleus carries a Z= +2echarge.

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

Helium Electrons Per Shell

#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.

Helium Electrons Protons Neutrons

#Z_'eff' = Z – S = 2 – 0.30 = 1.70#

Helium Electrons To Fill Outer Shell

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