Frequently Asked Question

Slater's rules are a set of guidelines used to approximate the effective nuclear charge (Zeff) experienced by an electron in a polyelectronic atom. For a d orbital, the effective nuclear charge is calculated by subtracting the shielding constant (S) from the atomic number (Z): Zeff = Z - S.
Here's how to apply Slater's rules to a d orbital:
1. Group electrons: Group the electrons into different categories based on their principal quantum number (n) and their subshells (s, p, d, f). For a d orbital, we will have electrons in the (n-1)s and (n-1)p subshells, as well as the nd subshell.
2. Assign shielding constants: Each electron in the atom is assigned a shielding constant based on its position relative to the electron in the d orbital.

Electrons in the same group as the d orbital (nd): Shielding constant (S) = 0.35 for each electron in the nd subshell (excluding the electron itself).

Electrons in the (n-1)s and (n-1)p subshells: Shielding constant (S) = 1.00 for each electron in these subshells.

Electrons in lower energy levels (n-2 and below): Shielding constant (S) = 1.00 for each electron in these subshells.
3. Calculate the effective nuclear charge: Sum up the shielding constants (S) for all the electrons in the atom and subtract this sum from the atomic number (Z) to get the effective nuclear charge (Zeff).
For example, consider the d orbital in a titanium atom (Ti). Titanium has an atomic number of 22. The electron configuration of Ti is [Ar]3d² 4s². Applying Slater's rules:

Shielding from 3d electrons (2 electrons): 2 x 0.35 = 0.70
Shielding from 3s and 3p electrons (8 electrons): 8 x 1.00 = 8.00
Shielding from 2s and 2p electrons (8 electrons): 8 x 1.00 = 8.00
Shielding from 1s electrons (2 electrons): 2 x 1.00 = 2.00
Total shielding (S) = 0.70 + 8.00 + 8.00 + 2.00 = 18.70
Effective nuclear charge (Zeff) = Z - S = 22 - 18.70 = 3.30
This means that the d electron in titanium experiences an effective nuclear charge of approximately 3.30.