Calculating Z_eff

One set of estimates for the effective nuclear charge (Zeff )  we described Zeff as being less than the actual nuclear charge (Z) because of the repulsive interaction between core and valence electrons. We can quantitatively represent this difference between Z and Zeff as follows:

Rearranging this formula to solve for Zeff we obtain:

We can then substitute the shielding constant obtained using Equation 2 to calculate an estimate of Zeff for the corresponding atomic electron.

Given: Boron (B)

Asked for: Zeff for a valence p- electron

Strategy:

1. Determine the electron configuration of boron and identify the electron of interest.
2. Use the appropriate Slater Rule to calculate the shielding constant for the electron.
3. Use the Periodic Table to determine the actual nuclear charge for boron.
4. Determine the effective nuclear constant.

Solution:

A B: 1s² 2s² 2p¹ . The valence p- electron in boron resides in the 2p subshell.

B (1s²)(2s² 2p¹)

B S[2p] = 1.00(0) + 0.85(2) + 0.35(2) = 2.40

C Z = 5

D     Zeff=2.60