The effective nuclear charge (ZeffZ_{eff}Zeff) is calculated by subtracting the shielding constant (SSS) from the actual nuclear charge (ZZZ), which is the atomic number (number of protons). The formula is:
Zeff=Z−SZ_{eff}=Z-SZeff=Z−S
Here, ZZZ is the number of protons in the nucleus, and SSS is the shielding constant that accounts for the screening effect of inner electrons that reduce the full nuclear charge felt by an outer electron. To calculate SSS, Slater's rules are commonly used, which assign different shielding contributions depending on the electron's and other electrons' shells:
- Electrons in orbitals to the right of the considered electron contribute 0 to shielding.
- For s or p electrons with principal quantum number nnn:
- Electrons in the same shell contribute 0.35 (except 1s electrons contribute 0.30).
- Electrons in the n−1n-1n−1 shell contribute 0.85.
- Electrons in shells n−2n-2n−2 or lower contribute 1.00.
- For d or f electrons, the shielding values differ slightly but generally follow a similar pattern with electrons in lower shells contributing more to shielding.
For example, for an outermost electron of lithium (Z=3Z=3Z=3), which has two 1s core electrons, the shielding SSS is approximately 2, so
Zeff=3−2=1Z_{eff}=3-2=1Zeff=3−2=1
meaning the valence electron experiences a net nuclear charge of +1. In summary, the steps to calculate effective nuclear charge are:
- Determine the atomic number ZZZ.
- Calculate the shielding constant SSS using Slater's rules based on electron configuration.
- Subtract SSS from ZZZ to get ZeffZ_{eff}Zeff.
This method helps estimate the net positive charge an electron feels in an atom after accounting for electron-electron repulsions and shielding.
