The effective nuclear charge (Z_eff) is found by subtracting the shielding effect from the actual nuclear charge of an atom.
Formula
Zeff=Z−SZ_{eff}=Z-SZeff=Z−S
- ZZZ is the atomic number (number of protons in the nucleus).
- SSS is the shielding constant, which accounts for the repulsion caused by inner shell electrons.
Concept
- Electrons in inner shells shield outer electrons from the full positive charge of the nucleus.
- This shielding reduces the net positive charge that an electron actually experiences.
- Effective nuclear charge represents this "net" charge felt by an electron.
How to calculate Shielding (S)
- Slater's rules provide a systematic way to estimate shielding.
- Electrons in the same shell shield less (around 0.35 per electron).
- Electrons one shell closer to the nucleus shield more (around 0.85 per electron).
- Electrons two or more shells inside shield fully (1.00 per electron).
- Electrons in higher shells or orbitals to the right do not contribute to shielding the electron in question.
Example
For a valence electron in lithium (atomic number 3, with 2 inner electrons):
Zeff=3−2=1Z_{eff}=3-2=1Zeff=3−2=1
So the effective nuclear charge felt by the valence electron is approximately
- This method gives an approximate but useful way of understanding atomic structure and periodic trends in chemistry.
